Journal articles on the topic 'Laminar geometry constant'
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1
Thomas, Scott K., Richard C. Lykins, and Kirk L. Yerkes. "Fully-Developed Laminar Flow in Sinusoidal Grooves." Journal of Fluids Engineering 123, no. 3 (April 16, 2001): 656–61. http://dx.doi.org/10.1115/1.1385832.
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The flow of a constant property fluid through a sinusoidal groove has been analyzed. A numerical solution of the conservation of mass and momentum equations for fully developed flow is presented. The mean velocity, volumetric flow rate, and Poiseuille number are presented as functions of the groove geometry, meniscus contact angle, and shear stress at the liquid-vapor interface. In addition, a semi-analytical solution for the normalized mean velocity in terms of the normalized shear stress at the meniscus is shown to agree with the numerical data quite well.
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Xu, Yang, Jin-Jun Wang, Li-Hao Feng, Guo-Sheng He, and Zhong-Yi Wang. "Laminar vortex rings impinging onto porous walls with a constant porosity." Journal of Fluid Mechanics 837 (January 5, 2018): 729–64. http://dx.doi.org/10.1017/jfm.2017.878.
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For the first time, an experiment has been conducted to investigate synthetic jet laminar vortex rings impinging onto porous walls with different geometries by time-resolved particle image velocimetry. The geometry of the porous wall is changed by varying the hole diameter on the wall (from 1.0 mm to 3.0 mm) when surface porosity is kept constant ($\unicode[STIX]{x1D719}=75\,\%$). The finite-time Lyapunov exponent and phase-averaged vorticity field derived from particle image velocimetry data are presented to reveal the evolution of the vortical structures. A mechanism associated with vorticity cancellation is proposed to explain the formation of downstream transmitted vortex rings; and both the vortex ring trajectory and the time-mean flow feature are compared between different cases. It is found that the hole diameter significantly influences the evolution of the flow structures on both the upstream and downstream sides of the porous wall. In particular, for a porous wall with a small hole diameter ($d_{h}^{\ast }=0.067$, 0.10 and 0.133), the transmitted finger-type jets will reorganize into a well-formed transmitted vortex ring in the downstream flow. However, for the case of a large hole diameter of $d_{h}^{\ast }=0.20$, the transmitted vortex ring is not well formed because of insufficient vorticity cancellation. Additionally, the residual vorticity gradually evolves into discrete jet-like structures downstream, which further weaken the intensity of the transmitted vortex ring. Consequently, the transmitted flow structures for the $d_{h}^{\ast }=0.20$ case would lose coherence more easily (or probably even transition to turbulence), resulting in a faster decay of the axial velocity and stronger entrainment of the transmitted jet. For all porous wall cases, the velocity profile of the transmitted jet exhibits self-similar behaviour in the far field ($z/D_{0}\geqslant 6.03$), which agrees well with the velocity distribution of free synthetic jets. With the help of the control-volume approach, the time-mean drag of the porous wall is evaluated experimentally for the first time. It is shown that the porous wall drag increases with the decrease in the hole diameter. Moreover, for a porous wall with a small hole diameter ($d_{h}^{\ast }=0.067$, 0.10 and 0.133), it appears that the porous wall drag mainly derives from the viscous effect. However, as $d_{h}^{\ast }$ increases to 0.20, the form drag associated with the porous wall geometry becomes significant.
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Lecampion, Brice, and Haseeb Zia. "Slickwater hydraulic fracture propagation: near-tip and radial geometry solutions." Journal of Fluid Mechanics 880 (October 10, 2019): 514–50. http://dx.doi.org/10.1017/jfm.2019.716.
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We quantify the importance of turbulent flow on the propagation of hydraulic fractures (HF) accounting for the addition of friction reducing agents to the fracturing fluid (slickwater fluid). The addition in small quantities of a high molecular weight polymer to water is sufficient to drastically reduce friction of turbulent flow. The maximum drag reduction (MDR) asymptote is always reached during industrial-like injections. The energy required for pumping is thus drastically reduced, allowing for high volume high rate hydraulic fracturing operations at a reasonable cost. We investigate the propagation of a hydraulic fracture propagating in an elastic impermeable homogeneous solid under a constant (and possibly very high) injection rate accounting for laminar and turbulent flow conditions with or without the addition of friction reducers. We solve the near-tip HF problem and estimate the extent of the laminar boundary layer near the fracture tip as a function of a tip Reynolds number for slickwater. We obtain different propagation scalings and transition time scales. This allows us to easily quantify the growth of a radial HF from the early-time turbulent regime(s) to the late-time laminar regimes. Depending on the material and injection parameters, some propagation regimes may actually be bypassed. We derive both accurate and approximate solutions for the growth of radial HF in the different limiting flow regimes (turbulent smooth, rough, MDR) for the zero fracture toughness limit (corresponding to the early stage of propagation of a radial HF). We also investigate numerically the transition(s) between the early-time MDR regime to the late-time laminar regimes (viscosity and toughness) for slickwater fluid. Our results indicate that the effect of turbulent flow on high rate slickwater HF propagation is limited and matters only at early times (at most during the first minutes for industrial hydraulic fracturing operations).
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Littlefield, D., and P. Desai. "Buoyant Laminar Convection in a Vertical Cylindrical Annulus." Journal of Heat Transfer 108, no. 4 (November 1, 1986): 814–21. http://dx.doi.org/10.1115/1.3247017.
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Solution to natural convective motion in a vertical cylindrical annulus of large aspect ratio is examined, with the inner wall subject to a constant heat flux. Similar transformations of the appropriately simplified Navier–Stokes model of the annular flow are sought. The issue of boundary condition limitations for the considered flow is resolved in terms of acceptable error bounds for valid solutions. Results are generated for a variety of outer wall boundary conditions over various ranges of the Rayleigh number, highlighting the effects on the patterns of streamlines and “heatlines.” Correlations presented for the Nusselt number are shown to be dependent on both the boundary conditions and the geometry.
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Kurnia, Jundika, Agus Sasmito, and Arun Mujumdar. "Laminar convective heat transfer for in-plane spiral coils of noncircular cross sections ducts: A computational fluid dynamics study." Thermal Science 16, no. 1 (2012): 109–18. http://dx.doi.org/10.2298/tsci100627014k.
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The objective of this study was to carry out a parametric study of laminar flow and heat transfer characteristics of coils made of tubes of several different cross-sections e.g. square, rectangular, half-circle, rectangular and trapezoidal. For the purpose of ease of comparison, numerical experiments were carried out base on a square-tube Reynolds number of 1000 and a fixed fluid flow rate while length of the tube used to make coils of different diameter and pitch was held constant. A figure of merit was defined to compare the heat transfer performance of different geometry coils; essentially it is defined as total heat transferred from the wall to the surroundings per unit pumping power required. Simulations were carried out for the case of constant wall temperature as well as constant heat flux. In order to allow reasonable comparison between the two different boundary conditions - constant wall temperature and constant wall heat flux - are tested; the uniform heat flux boundary condition was computed by averaging the heat transferred per unit area of the tube for the corresponding constant wall temperature case. Results are presented and discussed in the light of the geometric effects which have a significant effect on heat transfer performance of coils.
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Rastogi, Pallavi, and Shripad P. Mahulikar. "Geometry-Based Entropy Generation Minimization in Laminar Internal Convective Micro-Flow." Journal of Non-Equilibrium Thermodynamics 44, no. 1 (January 28, 2019): 81–90. http://dx.doi.org/10.1515/jnet-2018-0036.
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Abstract In this theoretical study, fully developed forced convective laminar water flow is considered in circular micro-tubes, for the constant wall heat flux boundary condition. The change in entropy generation rate (\Delta {\dot{S}_{\mathrm{gen}}}) for N micro-tubes (each of diameter {D_{\mathrm{N}}}) relative to a reference tube (of 1 mm diameter) was investigated towards the micro-scale, for different tube length (l). A given total heat flow rate is to be removed using a fixed total mass flow rate through N tubes. Hence, the wall heat flux for one of the N tubes decreases towards the micro-scale, which is “thermal under-loading”. For given l, \Delta {\dot{S}_{\mathrm{gen}}} due to fluid conduction decreases and \Delta {\dot{S}_{\mathrm{gen}}} due to fluid friction increases towards the micro-scale. There exists an optimum {D_{\mathrm{N}}} (={D_{\mathrm{N},\mathrm{opt}}}) at which the change in sum-total {\dot{S}_{\mathrm{gen}}} (\Delta {\dot{S}_{\mathrm{gen},\mathrm{tot}}}) is minimum; where {D_{\mathrm{N},\mathrm{opt}}} decreases with decreasing l. For given l, cooling capacity of the heat sink increases towards the micro-scale. A general criterion for minimization of \Delta {\dot{S}_{\mathrm{gen},\mathrm{tot}}} is obtained in terms of Reynolds number, Brinkman number, and dimensionless l.
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Minea, Alina Adriana, Razvan Silviu Luciu, and Oronzio Manca. "Influence of Microtube Heating Geometry on Behavior of an Alumina Nanofluid at Low Reynolds Numbers." Applied Mechanics and Materials 371 (August 2013): 596–600. http://dx.doi.org/10.4028/www.scientific.net/amm.371.596.
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A numerical program is employed to solve two-dimensional continuum-based governing differential equations for liquid flow in axisymmetric circular microchannel geometry. The effects of variable thermal properties in single-phase laminar forced convection with constant wall heat flux boundary conditions are studied. The numerical analysis of fully developed flow behavior investigates the effect of tube length on convection characteristics. The governing equations were discretized using the control volume method and solved numerically via the SIMPLE algorithm. Water - Al2O3nanofluids with different volume fractions ranged from 1% to 3% were used. This investigation covers Reynolds number in the range of 500 to 1500. The results have shown that convective heat transfer coefficient for a nanofluid is enhanced than that of the base liquid. Wall heat transfer flux is increasing with the particle volume concentration and Reynolds number. Moreover, a study on microtube length influence on heat transfer was attempted and few correlations were established. As a conclusion, a 6-11% decrease in heat transfer enhancement was noticed when the tube length is increasing in laminar flow.
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Damian, Iulia Rodica, Nicoleta Octavia Tănase, Ștefan Mugur Simionescu, and Mona Mihăilescu. "Vortex Rings - Experiments and Numerical Simulations." Mathematical Modelling in Civil Engineering 10, no. 4 (December 1, 2014): 1–8. http://dx.doi.org/10.2478/mmce-2014-0017.
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Abstract The present paper was concerned with the experimental study of the time evolution of a single laminar vortex ring generated at the interface between water and isopropyl alcohol. The experiment was performed by the submerged injection of isopropyl alcohol in a water tank of 100×100×150 mm. A constant rate of Q0 = 2 ml/min was maintained using a PHD Ultra 4400 Syringe Pump with a needle having the inner diameter D0 = 0.4 mm. The dynamics of the vortex formation was recorded with a Photron Fastcam SA1 camera at 1000 fps equipped with an Edmund Optics objective VZM1000i. The numerical simulations were performed on a 2D geometry using the ANSYS-FLUENT code with the Volume of Fluid multiphase model and the viscous-laminar solver. The numerical flow patterns were found to be in good agreement with the experimental visualizations
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Jaona Mamy Nindrina, RAMIARAMANANJAFY. "Numerical study of laminar natural convection in a half ellipsoid of revolution subjected to heat flux of constant density." International Journal of Progressive Sciences and Technologies 34, no. 1 (September 4, 2022): 01. http://dx.doi.org/10.52155/ijpsat.v34.1.4528.
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In this article, we numerically study the natural convection in a half-eliipsoid of revolution filled with a Newtonian fluid (air). The ellipsoid wall is isothermal which is maintained at a heat flux of constant density. The equations that govern the flow and heat transfer are described by the so-called Navier-Stokes equation of motion accompanied by the so-called Fourier equation of heat. The finite element method is used to solve the system of equations. We consider the effect of the shape factor of the elliptical wall and the Grashof number on the results obtained in the form of streamlines, and mean Nusselt numbers. The Nusselt numbers for natural convection inside a system formed by a rectangular geometry and for a curved shape are comparer and analyzed each other. We find that this number is quite higher for a curved system than that of a planar shape. It shows the importance of the form factor, particularly, in circular shape which is much more advantageous compared to the straight shape.In terms of inertia, the geometry of rounded shape ensures the best distribution of energy. In fact, the half ellipsoidal greenhouse with a circular base studied during this research offers a better distribution for the flow of the convection currents from the bottom to the top of the system.
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Nayak H. S., Sathvik, Nitesh Kumar, S. M. A. Khader, and Raghuvir Pai. "Effect of dome size on flow dynamics in saccular aneurysms – A numerical study." Journal of Mechanical Engineering and Sciences 14, no. 3 (September 30, 2020): 7181–90. http://dx.doi.org/10.15282/jmes.14.3.2020.19.0564.
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Image-based Computational Fluid Dynamic (CFD) simulations of anatomical models of human arteries are gaining clinical relevance in present days. In this study, CFD is used to study flow behaviour and hemodynamic parameters in aneurysms, with a focus on the effect of geometric variations in the aneurysm models on the flow dynamics. A computational phantom was created using a 3D modelling software to mimic a spherical aneurysm. Hemodynamic parameters were obtained and compared with the available literature to validate. Further, flow dynamics is studied by varying the dome size of the aneurysm from 3.75 mm to 6.25 mm with an increment of 0.625 mm keeping the neck size constant. The aneurysm is assumed to be located at a bend in the arterial system. Computational analysis of the flow field is performed by using Navier – Stokes equation for laminar flow of incompressible, Newtonian fluid. Parameters such as velocity, pressure, wall shear stress (WSS), vortex structure are studied. It was observed that the location of the flow separation and WSS vary significantly with the geometry of the aneurysm. The reduction of WSS inside the aneurysm is higher at the larger dome sizes for constant neck size.
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Chaturvedi, S. K., T. O. Mohieldin, and G. C. Huang. "Mixed Laminar Convection in Trombe Wall Channels." Journal of Solar Energy Engineering 110, no. 1 (February 1, 1988): 31–37. http://dx.doi.org/10.1115/1.3268234.
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The two-dimensional, steady, combined forced and natural convection in a vertical channel is investigated for the laminar regime. To simulate the Trombe wall channel geometry properly, horizontal inlet and exit segments have been added to the vertical channel. The vertical walls of the channel are maintained at constant but different temperatures while the horizontal walls are insulated. A finite difference method using up-wind differencing for the nonlinear convective terms, and central differencing for the second order derivatives, is employed to solve the governing differential equations for the mass, momentum, and energy balances. The solution is obtained for stream function, vorticity, and temperature as the dependent variables by an iterative technique known as successive substitution with overrelaxation. The flow and temperature patterns in the channel are obtained for Reynolds numbers and Grashof numbers ranging from 25 to 100 and 10,000 to 1,000,000, respectively. Both local and overall heat transfer coefficients are computed for the channel aspect ratio varying from 5 to 15. For a given value of Grashof number, as the Reynolds number is increased, the flow patterns in the vertical channel exhibit a change from natural convection like flow patterns in which a large recirculating region is formed in the vertical part of the channel, to a forced flow type pattern. This is also the case with isotherms. The size of the recirculating region in the channel increases with increasing value of Gr/Re2. At low Reynolds number, the stream function, and isotherms are qualitatively similar to those reported for the natural convection in rectangular slots.
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Li and, A., and B. F. Armaly. "Laminar Mixed Convection Adjacent to Three-Dimensional Backward-Facing Step." Journal of Heat Transfer 124, no. 1 (October 5, 2001): 209–13. http://dx.doi.org/10.1115/1.1423909.
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Simulations of three-dimensional laminar buoyancy-assisting mixed convection adjacent to a backward-facing step in a vertical rectangular duct are presented to demonstrate the influence of Grashof number on the distributions of the Nusselt number, and the reverse flow regions that develop adjacent to the duct’s walls. The Reynolds number, and duct’s geometry are kept constant: heat flux at the wall downstream from the step is kept uniform but its magnitude varied to cover a Grashof number range of 0–4000; all the other walls in the duct are kept at adiabatic condition; and the flow, upstream of the step, is treated as fully developed and isothermal. Increasing the Grashof number results in increasing the Nusselt number; the size of the secondary recirculation flow region adjacent to the stepped wall; the size of the reverse flow region adjacent to the sidewall and the flat wall; and the spanwise flow from the sidewall toward the center of the duct. On the other hand, the size of the primary recirculation flow region adjacent to the stepped wall decreases and detaches partially from the heated stepped wall as the Grashof number increases. Details are presented and discussed.
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Muszyński, Tomasz, and Sławomir Marcin Kozieł. "Parametric study of fluid flow and heat transfer over louvered fins of air heat pump evaporator." Archives of Thermodynamics 37, no. 3 (September 1, 2016): 45–62. http://dx.doi.org/10.1515/aoter-2016-0019.
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Abstract Two-dimensional numerical investigations of the fluid flow and heat transfer have been carried out for the laminar flow of the louvered fin-plate heat exchanger, designed to work as an air-source heat pump evaporator. The transferred heat and the pressure drop predicted by simulation have been compared with the corresponding experimental data taken from the literature. Two dimensional analyses of the louvered fins with varying geometry have been conducted. Simulations have been performed for different geometries with varying louver pitch, louver angle and different louver blade number. Constant inlet air temperature and varying velocity ranging from 2 to 8 m/s was assumed in the numerical experiments. The air-side performance is evaluated by calculating the temperature and the pressure drop ratio. Efficiency curves are obtained that can be used to select optimum louver geometry for the selected inlet parameters. A total of 363 different cases of various fin geometry for 7 different air velocities were investigated. The maximum heat transfer improvement interpreted in terms of the maximum efficiency has been obtained for the louver angle of 16 ° and the louver pitch of 1.35 mm. The presented results indicate that varying louver geometry might be a convenient way of enhancing performance of heat exchangers.
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Nasibullayev, I. Sh, and E. Sh Nasibullaeva. "Fluid flow through the hydraulic resistance with a dynamically variable geometry." Proceedings of the Mavlyutov Institute of Mechanics 12, no. 1 (2017): 59–66. http://dx.doi.org/10.21662/uim2017.1.009.
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In this paper the fluid flow in a flat channel with a hydraulic resistance is studied for two cases of a dynamic change in the channel geometry: transverse compression of the opening of the hydraulic resistance (the flow is caused by a pressure drop applied to the layer) and longitudinal movement of the hydraulic resistance along the channel (the flow is caused by this movement). It is obtained that in a geometry with transverse compression the flow is laminar without the formation of vortices. In a geometry with longitudinal movement of the hydraulic resistance the flow rate of the liquid remains constant with the formation of stable vortices that move along the channel at the rate of motion of the hydraulic resistance. On the base of the modeling results an analytical model that takes into account the flow rate of the fluid from the width of the through hole of the resistance is constructed. This model contains four interpolation parameters and it can be used as an element of a computational stand for determining the generalized flow of liquid in the system under consideration.
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Bakhshi, Hesam, Erfan Khodabandeh, Omidali Akbari, Davood Toghraie, Mohammad Joshaghani, and Alireza Rahbari. "Investigation of laminar fluid flow and heat transfer of nanofluid in trapezoidal microchannel with different aspect ratios." International Journal of Numerical Methods for Heat & Fluid Flow 29, no. 5 (May 7, 2019): 1680–98. http://dx.doi.org/10.1108/hff-05-2018-0231.
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Purpose In the present study, laminar steady flow of nanofluid through a trapezoidal channel is studied by using of finite volume method. The main aim of this paper is to study the effect of changes in geometric parameters, including internal and external dimensions on the behavior of heat transfer and fluid flow. For each parameter, an optimum ratio will be presented. Design/methodology/approach The results showed that in a channel cell, changing any geometric parameter may affect the temperature and flow field, even though the volume of the channel is kept constant. For a relatively small hydraulic diameter, microchannels with different angles have a similar dimensionless heat flux, while channels with bigger dimensions show various values of dimensionless heat flux. By increasing the angles of trapezoidal microchannels, dimensionless heat flux per unit of volume increases. As a result, the maximum and minimum heat transfer rate occurs in a trapezoidal microchannel with 75° and 30 internal’s, respectively. In the study of dimensionless heat flux rate with hydraulic diameter variations, an optimum hydraulic diameter (Dh) was observed in which the heat transfer rate per unit volume attains maximum value. Findings This optimum state is predicted to happen at a side angle of 75° and hydraulic diameter of 290 µm. In addition, in trapezoidal microchannel with higher aspect ratio, dimensionless heat flux rate is lower. Changing side angles of the channels and pressure drop have the same effect on pressure drop. For a constant pressure drop, if changing the side angles causes an increase in the rectangular area of the channel cross-section and the effect of the sides are not felt by the fluid, then the dimensionless heat flux will increase. By increasing the internal aspect ratio (t_2/t_3), the amount of t_3 decreases, and consequently, the conduction resistance of the hot surface decreases. Originality/value The effects of geometry of the microchannel, including internal and external dimensions on the behavior of heat transfer and fluid flow for pressure ranges between 2 and 8 kPa.
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Su, Duan, He, Ma, and Xu. "Thermally Developing Flow and Heat Transfer in Elliptical Minichannels with Constant Wall Temperature." Micromachines 10, no. 10 (October 21, 2019): 713. http://dx.doi.org/10.3390/mi10100713.
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Laminar convective heat transfer of elliptical minichannels is investigated for hydrodynamically fully developed but thermal developing flow with no-slip condition. A three-dimensional numerical model is developed in different elliptical geometries with the aspect ratio varying from 0.2 to 1. The effect of Reynolds number (25 ≤ Re ≤ 2000) on the local Nusselt number is examined in detail. The results indicate that the local Nusselt number is a decreasing function of Reynolds number and it is sensitive to Reynolds number especially for Re less than 250. The effect of aspect ratio on local Nusselt number is small when compared with the effect of Reynolds number on local Nusselt number. The local Nusselt number is independent of cross-section geometry at the inlet. The maximum effect of aspect ratio on local Nusselt number arises at the transition section rather than the fully developed region. However, the non-dimensional thermal entrance length is a monotonic decreasing concave function of aspect ratio but a weak function of Reynolds number. Correlations for the local Nusselt number and the thermal developing length for elliptical channels are developed with good accuracy, which may provide guidance for design and optimization of elliptical minichannel heat sinks.
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Chakroun, W. M., and S. F. Al-Fahed. "The Effect of Twisted-Tape Width on Heat Transfer and Pressure Drop for Fully Developed Laminar Flow." Journal of Engineering for Gas Turbines and Power 118, no. 3 (July 1, 1996): 584–89. http://dx.doi.org/10.1115/1.2816688.
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A series of experiments was conducted to study the effect of twisted-tape width on the heat transfer and pressure drop with laminar flow in tubes. Data for three twisted-tape wavelengths, each with five different widths, have been collected with constant wall temperature boundary condition. Correlations for the friction factor and Nusselt number are also available. The correlations predict the experimental data to within 10 to 15 percent for the heat transfer and friction factor, respectively. The presence of the twisted tape has caused the friction factor to increase by a factor of 3 to 7 depending on Reynolds number and the twisted-tape geometry. Heat transfer results have shown an increase of 1.5 to 3 times that of plain tubes depending on the flow conditions and the twisted-tape geometry. The width shows no effect on friction factor and heat transfer in the low range of Reynolds number but has a more pronounced effect on heat transfer at the higher range of Reynolds number. It is recommended to use loose-fit tapes for low Reynolds number flows instead of tight-fit in the design of heat exchangers because they are easier to install and remove for cleaning purposes.
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JING, DALEI, JIAN SONG, and YI SUI. "HYDRAULIC AND THERMAL PERFORMANCES OF LAMINAR FLOW IN FRACTAL TREELIKE BRANCHING MICROCHANNEL NETWORK WITH WALL VELOCITY SLIP." Fractals 28, no. 02 (March 2020): 2050022. http://dx.doi.org/10.1142/s0218348x2050022x.
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This work theoretically studies the effects of wall velocity slip on the hydraulic resistance and convective heat transfer of laminar flow in a microchannel network with symmetric fractal treelike branching layout. It is found that the slip can reduce the hydraulic resistance and enhance the Nusselt number of laminar flow in the network; furthermore, the slip can also affect the optimal structure of the fractal treelike microchannel network with minimum hydraulic resistance and maximum convective heat transfer. Under the size constraint of constant total channel surface area, the optimal diameter ratio of microchannels at two successive branching levels of the symmetric fractal treelike microchannel network with a minimized hydraulic resistance is only dependent on branching number [Formula: see text] in the manner of [Formula: see text] for no slip condition, but decreases with the increasing slip length, the increasing branching number and the increasing length ratio of microchannels at two successive branching levels for slip condition. The convective heat transfer of the treelike microchannel network is independent on the diameter ratio for no slip condition, but displays an increasing after decreasing trend with the increasing diameter ratio for slip condition. The symmetric treelike microchannel network with the worst convective heat transfer performance is the network with diameter ratio equaling one for slip condition.
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Małysiak, Agata, Tomasz Walica, Tomasz Fronczyk, and Marcin Lemanowicz. "Influence of Hydrodynamic Conditions on Precipitation Kinetics of Barium Sulfate in a Multifunctional Reactor." Processes 10, no. 1 (January 11, 2022): 146. http://dx.doi.org/10.3390/pr10010146.
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In this paper, the influence of hydrodynamic conditions in Kenics static mixer, which acts as a multifunctional reactor, on precipitation kinetics of barium sulfate is investigated. The investigated range of the Reynolds number varied between 500 and 5000, which covered both laminar and turbulent flow regimes. In all experiments, the relative supersaturation was maintained at the constant level (σ = 205). The obtained precipitate was collected and used for crystal size distribution (CSD) determination. On that basis, the kinetic parameters of the process were calculated using the mixed suspension mixed product removal (MSMPR) mathematical model of the process. It was found that for the whole investigated range of Reynolds number, the mixing conditions were satisfactory. CSD analysis showed that in the laminar regime, a clear tendency in crystal behavior could not be noticed. However, during the analysis of the turbulent regime, the presence of a critical Reynolds number was noticed. Above this value, there is a change in the flow pattern, which results in a change of kinetic parameters (B, G), as well as manifests in a form of a decrease in the value of mean diameters of crystals. The flow pattern change is caused by the geometry of the reactor’s inserts.
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Pramanik, Debashis, and Sujoy K. Saha. "Thermohydraulics of Laminar Flow Through Rectangular and Square Ducts With Transverse Ribs and Twisted Tapes." Journal of Heat Transfer 128, no. 10 (April 29, 2006): 1070–80. http://dx.doi.org/10.1115/1.2345432.
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The heat transfer and the pressure drop characteristics of laminar flow of viscous oil through rectangular and square ducts with internal transverse rib turbulators on two opposite surfaces of the ducts and fitted with twisted tapes have been studied experimentally. The tapes have been full length, short length, and regularly spaced types. The transverse ribs in combination with full-length twisted tapes have been found to perform better than either ribs or twisted tapes acting alone. The heat transfer and the pressure drop measurements have been taken in separate test sections. Heat transfer tests were carried out in electrically heated stainless steel ducts incorporating uniform wall heat flux boundary conditions. Pressure drop tests were carried out in acrylic ducts. The flow was periodically fully developed in the regularly spaced twisted-tape elements case and decaying swirl flow in the short-length twisted tapes case. The flow characteristics are governed by twist ratio, space ratio, and length of twisted tape, Reynolds number, Prandtl number, rod-to-tube diameter ratio, duct aspect ratio, rib height, and rib spacing. Correlations developed for friction factor and Nusselt number have predicted the experimental data satisfactorily. The performance of the geometry under investigation has been evaluated. It has been found that on the basis of both constant pumping power and constant heat duty, the regularly spaced twisted-tape elements in specific cases perform marginally better than their full-length counterparts. However, the short-length twisted-tape performance is worse than the full-length twisted tapes. Therefore, full-length twisted tapes and regularly spaced twisted-tape elements in combination with transverse ribs are recommended for laminar flows. However, the short-length twisted tapes are not recommended.
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Ibrahim, Basar, and Hussein Zekri. "Numerical Assessment of Symmetric Wedge Water-entry Impact Using OpenFOAM." European Journal of Pure and Applied Mathematics 15, no. 4 (October 31, 2022): 1998–2010. http://dx.doi.org/10.29020/nybg.ejpam.v15i4.4615.
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The hydrodynamic problem of a two-dimensional symmetric wedge vertically entering the water, initially flat, with a deadrise angle of 30° is considered. This numerical study assesses turbulence, gravity, viscosity, and surface tension during the early stage of penetration. The OpenFOAM software package has been used to simulate the water entry of the wedge at a constant speed of 3 m/s. The governing equations have been numerically built in the solver called overInterDyMFoam. The method has also been used to model the turbulence effect. The effects of turbulent and laminar flow assumptions and for the laminar flow, viscosity, gravity, and surface tension influence on pressure distributions along the wedge's walls have been investigated. It is illustrated that turbulence, viscosity, and surface tension have negligible effects on the pressure distribution in the primary water entry process. However, the pressure distribution is found to be significantly influenced by gravity.
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Ji Ying, Choong, Yu Kok Hwa, and Mohd Zulkifly Abdullah. "Numerical Study of Heat Transfer Characteristics of Laminar Nanofluids Flow in Oblique Finned Microchannel Heat Sink: Effects of Different Base Fluids and Volume Fraction of Nanoparticles." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 76, no. 3 (October 29, 2020): 25–37. http://dx.doi.org/10.37934/arfmts.76.3.2537.
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This paper demonstrates a numerical study of heat transfer characteristics of laminar flow in oblique finned microchannel heat sink using nanofluid with nanoparticles added to various base fluids including water, ethylene glycol and turbine oil as coolant fluid. The width of the primary channel was 0.5 mm and the secondary channel was less than 0.15 mm in the oblique finned microchannel heat sink with an aspect ratio of 3. ANSYS Fluent was employed to model the flow in the geometry of microchannel. Single phase model and constant heat flux boundary condition were used in this numerical study. The modeling was validated by comparing the published data for conventional and enhanced microchannel heat sink. The base fluid acted as a comparison baseline to the nanofluid with volume fraction of 1.0% and 4.0%. Besides, the study was carried out in laminar flow regime, whereby the Reynold number ranged between 320 to 700. It was found that turbine oil based nanofluid had the highest Nusselt number among all fluids, followed by ethylene glycol and water to be the least. However, the heat transfer coefficient among all fluids were contrary to the Nusselt number where water achieved the highest heat transfer coefficient. The addition of nanoparticles increased the heat transfer coefficient of all fluids but it did not enhance their Nusselt number except water.
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Ga, Bui Van, Nguyen Van Dong, and Bui Van Hung. "Turbulent burning velocity in combustion chamber of SI engine fueled with compressed biogas." Vietnam Journal of Mechanics 37, no. 3 (August 25, 2015): 205–16. http://dx.doi.org/10.15625/0866-7136/37/3/5939.
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Turbulent burning velocity is the most important parameter in analyzing pre-mixed combustion simulation of spark ignition engines. It depends on the laminar burning velocity and turbulence intensity in the combustion chamber. The first term can be predicted if one knows fuel composition, physico chemical properties of the fluid. The second term strongly depends on the geometry of the combustion chamber and fluid movement during the combustion process. One cannot suggest a general expression for different cases of engine. Thus, for accuracy modeling, one should determine turbulent burning velocity in the combustion chamber of each case of engine individually. In this study, the turbulent burning velocity is defined by a linear function of laminar burning velocity in which the proportional constant is defined as the turbulent burning velocity coefficient. This coefficient was obtained by analyzing the numerical simulation results and experimental data and this is applied to a concrete case of a Honda Wave motorcycle engine combustion chamber that fueled with compressed biogas. The results showed that the turbulent burning velocity coefficient in this case is around 1.3 when the average engine revolutions is in the range of 3000 rpm to 6000 rpm with biogas containing 80% Methane. We can then predict the effects of different parameters on the performance of the engine fueled with compressed biogas by simulation.
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Azzawi, Itimad D. J., Samir Gh Yahya, Layth Abed Hasnawi Al-Rubaye, and Senaa Kh Ali. "Heat Transfer Enhancement of Different Channel Geometries Using Nanofluids and Porous Media." International Journal of Heat and Technology 39, no. 4 (August 31, 2021): 1197–206. http://dx.doi.org/10.18280/ijht.390417.
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In this study, natural convection of heat transfer in various channel geometries with a constant surface area under laminar flow condition has been investigated numerically. Various hot surface temperatures (Th = 35-95°C) have been applied on the surfaces of the channels to investigate four different geometries of annular channels (Circular (C), Square (S), Elliptic (E) and Airfoil (F)) on the heat transfer rate. Once the optimum geometry was exhibited, the effect of three nanofluids (Al2O3/water, CuO/water and SiO2/water) is investigated in the analysis and compared to pure water to enhance the convective heat transfer of the base fluid. Moreover, with these nanofluids, analysis has been performed for three different volume concentrations of nanoparticles of Ø = 2%, 4% and 6% along with 0% (pure water). Porous foams (ε = 0.9 to 0.99) were used in addition to nanofluids to see if heat transfer could be improved. Results indicate that the heat transfer rate was greatly increased when the airfoil geometry was used, with a maximum and minimum increase in heat transfer coefficient of 60% and 46%, respectively. Also, higher nanoparticle of Al2O3 dispersion to the base fluid enhances the heat transfer rate by 15% compared to other nanofluids.
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Khan, Zeeshan, Haroon Ur Rasheed, Murad Ullah, Ilyas Khan, Tawfeeq Abdullah Alkanhal, and Iskander Tlili. "Shooting method analysis in wire coating withdrawing from a bath of Oldroyd 8-constant fluid with temperature dependent viscosity." Open Physics 16, no. 1 (December 31, 2018): 956–66. http://dx.doi.org/10.1515/phys-2018-0117.
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Abstract The most important plastic resins used in wire coating are high/low density polyethylene (LDPE/HDPE), plasticized polyvinyl chloride (PVC), nylon and polysulfone. To provide insulation and mechanical strength, coating is necessary for wires. Simulation of polymer flow during wire coating dragged froma bath of Oldroyd 8-constant fluid incompresible and laminar fluid inside pressure type die is carried out numerically. In wire coating the flow depends on the velocity of the wire, geometry of the die and viscosity of the fluid.The non-dimensional resulting flow and heat transfer differential equations are solved numerically by Ruge-Kutta 4th-order method with shooting technique. Reynolds model and Vogel’s models are encountered for temperature dependent viscosity. The numerical solutions are obtained for velocity field and temperature distribution. The solutions are computed for different physical parameters.It is observed that the non-Newtonian propertis of fluid were favourable, enhancing the velocity in combination with temperature dependent variable. The Brinkman number contributes to increase the temperature for both Reynolds and Vogel’smodels. With the increasing of pressure gradient parameter of both Reynolds and Vogel’s models, the velocity and temperature profile increases significantly in the presence of non-Newtonian parameter. Furthermore, the present result is also compared with published results as a particular case.
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Okuducu, Mahmut Burak, and Mustafa M. Aral. "Toward the Next Generation of Passive Micromixers: A Novel 3-D Design Approach." Micromachines 12, no. 4 (March 30, 2021): 372. http://dx.doi.org/10.3390/mi12040372.
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Passive micromixers are miniaturized instruments that are used to mix fluids in microfluidic systems. In microchannels, combination of laminar flows and small diffusion constants of mixing liquids produce a difficult mixing environment. In particular, in very low Reynolds number flows, e.g., Re < 10, diffusive mixing cannot be promoted unless a large interfacial area is formed between the fluids to be mixed. Therefore, the mixing distance increases substantially due to a slow diffusion process that governs fluid mixing. In this article, a novel 3-D passive micromixer design is developed to improve fluid mixing over a short distance. Computational Fluid Dynamics (CFD) simulations are used to investigate the performance of the micromixer numerically. The circular-shaped fluid overlapping (CSFO) micromixer design proposed is examined in several fluid flow, diffusivity, and injection conditions. The outcomes show that the CSFO geometry develops a large interfacial area between the fluid bodies. Thus, fluid mixing is accelerated in vertical and/or horizontal directions depending on the injection type applied. For the smallest molecular diffusion constant tested, the CSFO micromixer design provides more than 90% mixing efficiency in a distance between 260 and 470 µm. The maximum pressure drop in the micromixer is found to be less than 1.4 kPa in the highest flow conditioned examined.
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Takeda, Kazuki, Yohann Duguet, and Takahiro Tsukahara. "Intermittency and Critical Scaling in Annular Couette Flow." Entropy 22, no. 9 (September 4, 2020): 988. http://dx.doi.org/10.3390/e22090988.
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The onset of turbulence in subcritical shear flows is one of the most puzzling manifestations of critical phenomena in fluid dynamics. The present study focuses on the Couette flow inside an infinitely long annular geometry where the inner rod moves with constant velocity and entrains fluid, by means of direct numerical simulation. Although for a radius ratio close to unity the system is similar to plane Couette flow, a qualitatively novel regime is identified for small radius ratio, featuring no oblique bands. An analysis of finite-size effects is carried out based on an artificial increase of the perimeter. Statistics of the turbulent fraction and of the laminar gap distributions are shown both with and without such confinement effects. For the wider domains, they display a cross-over from exponential to algebraic scaling. The data suggest that the onset of the original regime is consistent with the dynamics of one-dimensional directed percolation at onset, yet with additional frustration due to azimuthal confinement effects.
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Dey, Prasenjit, and Ajoy Kumar Das. "Heat Transfer Enhancement Around a Cylinder – A CFD Study of Effect of Corner Radius and Prandtl Number." International Journal of Chemical Reactor Engineering 14, no. 2 (April 1, 2016): 587–97. http://dx.doi.org/10.1515/ijcre-2015-0109.
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Abstract An unsteady two-dimensional laminar forced convection heat transfer around a square cylinder with rounded corner edge is numerically investigated for Prandtl Number, Pr=0.01–1,000 and non-dimensional corner radius, r=0.50–0.71 at low Reynolds number, Re=100. The effect of gradual transformation of square cylinder into circular cylinder on heat transfer phenomenon is studied. The lateral sides of the computational domain are kept constant to maintain the blockage as 5 %. A structured non-uniform mesh is used for the computational domain and the Finite Volume Method (FVM) based commercial software Ansys FLUENT is used for numerical simulation. The heat transfer characteristics over the rounded corner square cylinder are analyzed with the isotherm patterns, local Nusselt number (Nulocal), average Nusselt number (Nuavg) at various Pr and various corner radii. It is found that the heat transfer rate of a circular cylinder can be enhanced 14 % by introducing a new cylinder geometry of corner radius, r=0. 51.
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Vedel, Søren, Emil Hovad, and Henrik Bruus. "Time-dependent Taylor–Aris dispersion of an initial point concentration." Journal of Fluid Mechanics 752 (July 2, 2014): 107–22. http://dx.doi.org/10.1017/jfm.2014.324.
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AbstractBased on the method of moments, we derive a general theoretical expression for the time-dependent dispersion of an initial point concentration in steady and unsteady laminar flows through long straight channels of any constant cross-section. We retrieve and generalize previous case-specific theoretical results, and furthermore predict new phenomena. In particular, for the transient phase before the well-described steady Taylor–Aris limit is reached, we find anomalous diffusion with a dependence of the temporal scaling exponent on the initial release point, generalizing this finding in specific cases. During this transient we furthermore identify maxima in the values of the dispersion coefficient which exceed the Taylor–Aris value by amounts that depend on channel geometry, initial point release position, velocity profile and Péclet number. We show that these effects are caused by a difference in relaxation time of the first and second moments of the solute distribution and may be explained by advection-dominated dispersion powered by transverse diffusion in flows with local velocity gradients.
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Abdulkarim, Ali Hussein, Muhammad Asmail Eleiwi, Tahseen Ahmad Tahseen, and Eyub Canli. "Numerical Forced Convection Heat Transfer of Nanofluids over Back Facing Step and Through Heated Circular Grooves." Mathematical Modelling of Engineering Problems 8, no. 4 (August 31, 2021): 597–610. http://dx.doi.org/10.18280/mmep.080413.
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Backward facing step arrangement is a classical case for fluid dynamics and heat transfer research. It is well characterized and therefore, used for benchmarking. However, ongoing studies reveal that the geometry also provide advantages in industry, especially in combustion and burners. This work utilizes computational fluid dynamics to investigate a specific laminar back facing step flow heat transfer case. Aluminium oxide nano particles are considered as an additive to water base fluid, forming nanofluid with different volumetric concentrations. Laminar flow passes a back facing step and encounters three circular grooves at bottom surface. All surfaces are adiabatic except the grooves. Constant surface temperature applies to the grooves. According to the simulation results, a separation bubble after back facing step and a reattachment point occur. Grooves alter expected wake due to physical and thermal interference. Investigation parameters are nano-particle concentration and Reynolds number. Reynolds number changes between 10 and 250. Nano particle volume fraction percentage changes between 2 and 6 percent. Sectional heating downstream of the step poses interesting heat flux in the presence of Aluminium oxide nano-particle concentrations. There is a pseudo-linear relationship between parameters and heat transfer. Combined effects of enhanced thermal conductivity and secondary flow structures are seen. As expected, thermal convection increases as flow velocity and nano-particle concentrations increase. Heat flux and accordingly Nusselt number are highly affected from Reynolds number since flow structure changes dramatically. Also, direct proportion is seen between nano-particle concentration and enhanced convection.
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Baïri, Abderrahmane, Juan Mario García de María, Nacim Alilat, Najib Laraqi, and Jean-Gabriel Bauzin. "Nu-Ra correlations for natural convection at high Ra numbers in air-filled tilted hemispherical cavities with dome oriented upwards. Disk submitted to constant heat flux." International Journal of Numerical Methods for Heat & Fluid Flow 25, no. 3 (April 7, 2015): 504–12. http://dx.doi.org/10.1108/hff-12-2013-0335.
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Purpose – The purpose of this paper is to propose correlations between Nusselt and Rayleigh numbers for the case of inclined and closed air-filled hemispherical cavities. The disk of such cavities is subjected to a constant heat flux. The study covers a wide range of Rayleigh numbers from 5×107 to 2.55×1012. Design/methodology/approach – Correlations are obtained from numerical approach validated by experimental measurements on some configurations, valid for several angles of inclination of the cavity between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°. Findings – The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones. Practical implications – The proposed correlations provide solutions for applications in several fields of engineering such as solar energy, aerospace, building, safety and security. Originality/value – The new relations proposed are the first published for high Rayleigh numbers for this type of geometry. They supplement the knowledge of natural convection in hemispherical inclined cavities and constitute a useful tool for application in various engineering areas as solar energy (thermal collector, still, pyranometer, albedometer, pyrgeometer), aerospace (embarked electronics), building, safety and security (controlling and recording sensors).
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Cunningham, A. B., E. Visser, Z. Lewandowski, and M. Abrahamson. "Evaluation of a coupled mass transport-biofilm process model using dissolved oxygen microsensors." Water Science and Technology 32, no. 8 (October 1, 1995): 107–14. http://dx.doi.org/10.2166/wst.1995.0274.
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A 2-dimensional model has been developed which couples hydrodynamics, solute transport and reaction in a steady state biofilm system of irregular geometry under laminar flow. Biofilm thickness is initially specified over the domain and remains constant during the simulations. The Navier-Stokes equations are coupled with advection-diffusion-reaction equations describing oxygen transport and solved using finite differences. This model facilitates computational investigation of fluid velocity and solute concentration distributions in proximity to the fluid-biofilm interface. Model evaluation has been carried out using dissolved oxygen profiles measured by microsensors in a rectangular open channel with a 300 μm (approximate) artificial biofilm composed of alginate gel with an 8×1010 cells/ml concentration of Ps. aeruginosa cells. Significant variability in dissolved oxygen profile shape was observed at three locations on the artificial biofilm. Model simulations of these experiments facilitated a direct comparison between observed and computed values of dissolved oxygen concentration in the vicinity of the fluid-biofilm interface. Simulated profiles agreed closely with measured profiles at all three locations.
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Ayas, Mehmet, Jan Skocilas, and Tomas Jirout. "Analysis of Power Input of an In-Line Rotor-Stator Mixer for Viscoplastic Fluids." Processes 8, no. 8 (August 1, 2020): 916. http://dx.doi.org/10.3390/pr8080916.
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In this work, the power draw and shear profile of a novel in-line rotor-stator mixer were studied experimentally and the laminar flow regime was simulated. The power draw of the rotor-stator mixer was investigated experimentally using viscoplastic shear-thinning fluid and the results of the obtained power consumptions were verified through simulations. The power draw constant and Otto-Metzner coefficient were determined from the result of experimental data and through simulations. A new method is suggested for the determination of the Otto-Metzner coefficient for the Herschel–Bulkley model and the term efficiency is introduced. It was shown that the proposed method can be applied successfully for the prediction of the Otto-Metzner coefficient for the mixing of viscoplastic shear-thinning fluids. The effect of geometry and rotor speed on power consumption and shear rate profile in the investigated mixer is discussed from the results of the simulations. It was found that numerical methods are a convenient tool and can predict the power draw of the in-line rotor-stator mixer successfully.
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Jani, S., M. H. Saidi, and A. A. Mozaffari. "Second Law Based Optimization of Falling Film Single Tube Absorption Generator." Journal of Heat Transfer 126, no. 5 (October 1, 2004): 708–12. http://dx.doi.org/10.1115/1.1795791.
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The objective of this paper is to provide optimization of falling film LiBr solution on a horizontal single tube based on minimization of entropy generation. Flow regime is considered to be laminar. The effect of boiling has been ignored and wall temperature is constant. Velocity, temperature and concentration distributions are numerically determined and dimensionless correlations are obtained to predict the average heat transfer coefficient and average evaporation factor on the horizontal tube. Thermodynamic imperfection due to passing lithium bromide solution is attributed to nonisothermal heat transfer; fluid flow friction and mass transfer irreversibility. Scale analysis shows that the momentum and mass transfer irreversibilities can be ignored at the expense of heat transfer irreversibility. In the process of optimization, for a specified evaporation heat flux, the entropy generation accompanying the developed dimensionless heat and mass transfer correlations has been minimized and the optimal geometry and the optimum thermal hydraulic parameters are revealed. The investigation cited here indicates the promise of entropy generation minimization as an efficient design and optimization tool.
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Wahid, Mazlan Abdul, Ahmad Ali Gholami, and H. A. Mohammed. "Numerical Study of Fluid Flow and Heat Transfer Enhancement of Nanofluids over Tube Bank." Applied Mechanics and Materials 388 (August 2013): 149–55. http://dx.doi.org/10.4028/www.scientific.net/amm.388.149.
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In the present work, laminar cross flow forced convective heat transfer of nanofluid over tube banks with various geometry under constant wall temperature condition is investigated numerically. We used nanofluid instead of pure fluid ,as external cross flow, because of its potential to increase heat transfer of system. The effect of the nanofluid on the compact heat exchanger performance was studied and compared to that of a conventional fluid.The two-dimensional steady state Navier-Stokes equations and the energy equation governing laminar incompressible flow are solved using a Finite volume method for the case of flow across an in-line bundle of tube banks as commercial compact heat exchanger. The nanofluid used was alumina-water 4% and the performance was compared with water. In this paper, the effect of parameters such as various tube shapes ( flat, circle, elliptic), and heat transfer comparison between nanofluid and pure fluid is studied. Temperature profile, heat transfer coefficient and pressure profile were obtained from the simulations and the performance was discussed in terms of heat transfer rate and performance index. Results indicated enhanced performance in the use of a nanofluid, and slight penalty in pressure drop. The increase in Reynolds number caused an increase in the heat transfer rate and a decrease in the overall bulk temperature of the cold fluid. The results show that, for a given heat duty, a mas flow rate required of the nanofluid is lower than that of water causing lower pressure drop. Consequently, smaller equipment and less pumping power are required.
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Coutelieris, Frank A. "Modeling of Transport Phenomena in a Fuel Cell Anode." Defect and Diffusion Forum 273-276 (February 2008): 820–28. http://dx.doi.org/10.4028/www.scientific.net/ddf.273-276.820.
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A mathematical model for the simulation of the transport phenomena occurred in the anode of a typical fuel cell is presented here. The model initially considers a simple onedimensional geometry where the mass transport equation is combined with a Tafel-type description for the current density. By assuming isothermal conditions, the numerical solution of the differential equations was achieved with the use of a non-linear shooting scheme in conjunction with the multidimensional Newton algorithm. The space was discretized through a constant-step mesh while the resulting nonlinear system of ordinary differential equations was solved by using the 4th order Runge-Kutta method. The whole algorithm was implemented by developing a new FORTRAN code. In addition, a planar two-dimensional geometry is also considered, where the mass transport is described by the convection-diffusion equation within the catalyst layer together with the Navier- Stokes equation for laminar flow conditions and the electrochemical effects, while the convective heat transfer within the developed diffusion layer is also taken into account. This approach has been numerically implemented and solved by using the finite volume method being applicable through the CFD-RC© commercial package. For the sake of simplicity, the feedstream of the fuel cell was assumed to be a hydrogen-rich mixture (H2 >90%) for all cases. Both SOFC and PEM type fuel cells were considered in this study, while the results are presented in terms of fuel concentration, produced current density and overpotential.
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Del Aghenese, Ana Paula, Eliander Manke Heinemann, Gabriel de Avila Barreto, Filipe Branco Teixeira, Liércio André Isoldi, Luiz Alberto Oliveira Rocha, and Elizaldo Domingues dos Santos. "Geometrical Evaluation of a Pair of Elliptical Tubes Subjected to a Flow with Forced Convection Heat Transfer." Defect and Diffusion Forum 396 (August 2019): 155–63. http://dx.doi.org/10.4028/www.scientific.net/ddf.396.155.
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In the present work it is performed a study on the geometric evaluation of a pair of elliptical tubes subjected to external flow with forced convection by means of numerical approach. The objectives are the maximization of Nusselt number (NuD) and the minimization of drag coefficient (CD). The degrees of freedom for the pair of tubes arrangement are: the ratio between the transverse pitch and characteristic length of tubes (ST/D), where D = (A)1/2, the ratio of the main and secondary axes of the elliptical tube (a/b) and the angle of incidence of the flow on the pair of tubes (α). The simulations were carried out considering two-dimensional forced convective flows, in the laminar regime and incompressible conditions. For all configurations, Reynolds and Prandtl numbers are constant, ReD = 100 and Pr = 0.71. The Finite Volume Method (FVM) is used to solve conservation equations of mass, momentum and energy. The software Gmsh is used for creation of the geometries and generation of the meshes. Results showed that the degrees of freedom affected the fluid dynamic and thermal performance of the forced convective flow. According to the objectives outlined in this study, the best performance for the maximization of heat transfer was obtained when α = 0o, a/b = 1⁄2 and ST/D = 3.5. In the case of the fluid dynamics study, the optimal result for CD minimization occurred when α = 0o, a/b = 2.0 and ST/D = 4.0. Thus, the optimal geometry will depend on the indicator performance where the problem is evaluated.
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Kim, Kyung Tae, Jo Eun Park, Seon Yeop Jung, and Tae Gon Kang. "Fouling Mitigation via Chaotic Advection in a Flat Membrane Module with a Patterned Surface." Membranes 11, no. 10 (September 23, 2021): 724. http://dx.doi.org/10.3390/membranes11100724.
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Fouling mitigation using chaotic advection caused by herringbone-shaped grooves in a flat membrane module is numerically investigated. The feed flow is laminar with the Reynolds number (Re) ranging from 50 to 500. In addition, we assume a constant permeate flux on the membrane surface. Typical flow characteristics include two counter-rotating flows and downwelling flows, which are highly influenced by the groove depth at each Re. Poincaré sections are plotted to represent the dynamical systems of the flows and to analyze mixing. The flow systems become globally chaotic as the groove depth increases above a threshold value. Fouling mitigation via chaotic advection is demonstrated using the dimensionless average concentration (c¯w*) on the membrane and its growth rate. When the flow system is chaotic, the growth rate of c¯w* drops significantly compared to that predicted from the film theory, demonstrating that chaotic advection is an attractive hydrodynamic technique that mitigates membrane fouling. At each Re, there exists an optimal groove depth minimizing c¯w* and the growth rate of c¯w*. Under the optimum groove geometry, foulants near the membrane are transported back to the bulk flow via the downwelling flows, distributed uniformly in the entire channel via chaotic advection.
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Calvo, Eduardo M., Mario J. Pinheiro, and Paulo A. Sá. "Modeling of Electrohydrodynamic (EHD) Plasma Thrusters: Optimization of Physical and Geometrical Parameters." Applied Sciences 12, no. 3 (February 4, 2022): 1637. http://dx.doi.org/10.3390/app12031637.
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This work aims to optimize a previous self-consistent model of a single stage electrohydrodynamic (EHD) thruster for space applications. The investigated parameters were the thruster performance (propulsion force T, the thrust to power ratio T/P, the electric potential distribution, the spatial distribution for the electrons and ions, and the laminar flow velocity) under several conditions, such as the design features related to the cathode’s cylindrical geometry (height and radius) and some electric parameters such as the ballast resistor, and the applied potential voltage. In addition, we examined the influence of the secondary electron emission coefficient on the plasma propellant parameters. The anode to cathode potential voltage ranges between 0.9 and 40 kV, and the ballast resistance varies between 500 and 2500 M. Argon and xenon are the working gases. We assumed the gas temperature and pressure constant, 300 K and 1.3 kPa (10 Torr), respectively. The optimal matching for Xe brings off a thrust of 3.80 μN and an efficiency T/P = 434 mN/kW, while for Ar, T = 2.75 μN, and thruster to the power of 295 mN/kW. To our knowledge, the missing data in technical literature does not allow the verification and validation (V&V) of our numerical model.
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Joardar, A., and A. M. Jacobi. "A Numerical Study of Flow and Heat Transfer Enhancement Using an Array of Delta-Winglet Vortex Generators in a Fin-and-Tube Heat Exchanger." Journal of Heat Transfer 129, no. 9 (December 6, 2006): 1156–67. http://dx.doi.org/10.1115/1.2740308.
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This work is aimed at assessing the potential of winglet-type vortex generator (VG) “arrays” for multirow inline-tube heat exchangers with an emphasis on providing fundamental understanding of the relation between local flow behavior and heat transfer enhancement mechanisms. Three different winglet configurations in common-flow-up arrangement are analyzed in the seven-row compact fin-and-tube heat exchanger: (a) single–VG pair; (b) a 3VG-inline array (alternating tube row); and (c) a 3VG-staggered array. The numerical study involves three-dimensional time-dependent modeling of unsteady laminar flow (330⩽Re⩽850) and conjugate heat transfer in the computational domain, which is set up to model the entire fin length in the air flow direction. It was found that the impingement of winglet redirected flow on the downstream tube is an important heat transfer augmentation mechanism for the common-flow-up arrangement of vortex generators in the inline-tube geometry. At Re=850 with a constant tube-wall temperature, the 3VG-inline-array configuration achieves enhancements up to 32% in total heat flux and 74% in j factor over the baseline case, with an associated pressure-drop increase of about 41%. The numerical results for the integral heat transfer quantities agree well with the available experimental measurements.
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Ayoobi, Mohsen, and Ingmar Schoegl. "Numerical analysis of flame instabilities in narrow channels: Laminar premixed methane/air combustion." International Journal of Spray and Combustion Dynamics 9, no. 3 (June 5, 2017): 155–71. http://dx.doi.org/10.1177/1756827717706009.
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Premixed flames propagating within small channels show complex combustion phenomena that differ from flame propagation at conventional scales. Available experimental and numerical studies have documented stationary, non-stationary, or asymmetric modes that depend on properties of the incoming reactant flow as well as channel geometry and wall temperatures. This work seeks to illuminate mechanisms leading to symmetry breaking and limit cycle behavior that are fundamental to these combustion modes. Specifically, four cases of lean premixed methane/air combustion—two equivalence ratios (0.53 and 0.7) and two channel widths (2 mm and 5 mm)—are investigated in a 2D configuration with constant channel length and bulk inlet velocity, where numerical simulations are performed using detailed chemistry. External wall heating is simulated by imposing a linear temperature gradient as a boundary condition on both walls. In the 2 mm channel, both equivalence ratios produce flames that stabilize with symmetric flame fronts after propagating upstream. In the 5 mm channel, flame fronts start symmetrically, although symmetry is broken almost immediately after ignition. Further, 5 mm channels produce non-stationary combustion modes with dramatically different limit cycles: in the leaner case ( φ = 0.53), the asymmetric flame front flops periodically, whereas in the richer case ( φ = 0.7), flames with repetitive extinctions and ignitions (FREI) are observed. To further understand the flame dynamics, reaction fronts and flame fronts are captured and differentiated. Results show that the loss of flame front symmetry originates in a region close to the flame cusp, where flow and chemical characteristics exhibit large gradients and curvatures. Limit cycle behavior is illuminated by investigating flame edges that are formed along the wall, and accompany local or global ignition and extinction processes. In the flopping mode ( φ = 0.53), local ignition and extinction in regions adjacent to the wall result in oblique fronts that advance and recede along the wall and redirect the flow ahead of the flame. In the FREI mode, asymmetric flames propagate much farther upstream, where they experience global extinction due to heat losses, and re-ignite far downstream with opposite flame front orientation. In both cases, an interaction of flow and chemical effects drives the asymmetric limit cycles. The lack of instabilities and asymmetries for the 2mm cases is attributed to insufficient wall separation, which is of the same order of magnitude as the flame thickness.
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KANG, HYUNG SUK, DUANE DENNIS, and CHARLES MENEVEAU. "FLOW OVER FRACTALS: DRAG FORCES AND NEAR WAKES." Fractals 19, no. 04 (December 2011): 387–99. http://dx.doi.org/10.1142/s0218348x1100549x.
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An experimental study of interactions between a high Reynolds number fluid flow and multi-scale, fractal, objects is performed. Studying such interactions is required to improve our current understanding of wind or ocean current effects on vegetation elements, which often display fractal-like branching geometries. The main objectives of the study are to investigate the effects of the range of scales (generation numbers) of the fractal object and of the incoming flow condition on the drag force and drag coefficient, and to observe flow features in the near wake region resulting from the interaction. In this study, Sierpinski carpets and triangles with the scale ratios of 1/3 and 1/2, respectively, are employed. The fractal dimensions of the Sierpinski carpet and triangle are D = 1.893 and 1.585, respectively. Each pre-fractal object is mounted on a load cell at the centerline in a wind tunnel. Two types of inflow conditions are considered: laminar flow and high-turbulence level, active-grid-generated, flow. As a first approximation, we find the drag coefficients are approximately constant of order unity, and do not depend upon generation number of the pre-fractal when defined using the actual frontal area that varies as function of generation number. Still, the drag coefficient of the Sierpinski carpet increases weakly with number of generations indicating that the drag force decreases less than the cross-sectional area. For the Sierpinski triangle a similar trend is observed at large scales. However, the drag coefficient displays a peak at the third generation and then shows a decreasing trend as smaller scales are included for higher generation cases. The drag coefficient for the turbulent flow is larger than that for the laminar flow for all the fractal generations observed. Flow features (mean velocity, mean vorticity, and turbulence root-mean-square distributions) are measured by using stereoscopic Particle Image Velocimetry to observe various scales of the motion in the near wake of the pre-fractal objects. Strong shear layers are formed behind the fractal objects depending on the hole locations of different generations, which results in the formation of various length scales of the dominant turbulence structures. The smaller scale wakes are found to merge behind the Sierpinski carpet, whereas they are merely damped behind the Sierpinski triangle.
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B, Varun Kumar, Darshan S, Shivaraj BW, M. Krishna, Satheesh Babu G, and Manjunatha C. "Modeling and Simulation of TiO2/Se Sensor for Detection of CO Gas Using Comsol Multiphysics." ECS Transactions 107, no. 1 (April 24, 2022): 5867–77. http://dx.doi.org/10.1149/10701.5867ecst.
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Metal oxide sensors are being used from past three decades. They still suffer from some disadvantages, such as high operating temperature, high power consumption, sensor stability, and cross sensitivity. Since the cost of development of these sensors is high, it is important to develop a mathematical model to economically predict the behavior of these sensors. In this context, research work focused on evaluating the performance of these sensors using numerical analysis software. In this work, modeling and simulating the gas sensing properties of Titanium dioxide/Selenium (MOS) sensor material to detect carbon monoxide (CO) gas using Comsol Multiphysics software has been proposed. The gas sensing simulation was performed using ‘Reaction engineering,’ ‘Transport of diluted species,’ ‘Surface reactions,’ and ‘Laminar flow’ interfaces of Comsol Multiphysics software on Titanium dioxide/Selenium material. Two kinds of simulations, space independent and space dependent simulation, was performed on this material in a constant volume gas chamber. The geometry was created in space dependent node, Comsol. The carbon monoxide gas was injected through gaussian pulse feed inlet at different concentrations (1 ppm, 5 ppm, 10 ppm, and 15 ppm) into the gas chamber and MOS sensor layer was allowed to reach steady state. The adsorption simulation on sensor layer exposed to carbon monoxide (CO) gas shows the change in surface concentration of the adsorbed CO molecules on the sensor layer.
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Hayase, T., J. A. C. Humphrey, and R. Greif. "Numerical Calculation of Convective Heat Transfer Between Rotating Coaxial Cylinders With Periodically Embedded Cavities." Journal of Heat Transfer 114, no. 3 (August 1, 1992): 589–97. http://dx.doi.org/10.1115/1.2911322.
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A numerical study has been performed for the flow and heat transfer in the space between a pair of coaxial cylinders with the outer one fixed and the inner one rotating. Of special interest is the case where either one of the cylinders has an axially grooved surface resulting in twelve circumferentially periodic cavities embedded in it. The ends of the cylinder are bounded by flat impermeable walls that are either fixed to the outer cylinder or rotate with the inner one. Such a geometry is common in electric motors where an improved understanding of thermophysical phenomena is essential for analysis and design. Discretized transport equations are solved for two-dimensional and three-dimensional, steady, constant property laminar flow using a second-order accurate finite volume scheme within the context of a SIMPLER-based iterative methodology. The two-dimensional calculations reveal a shear-induced recirculating flow in the cavities. For supercritical values of the Reynolds number, the three-dimensional calculations show how the flow in a cavity interacts with Taylor vortices in the annular space to enhance heat transfer. Relative to coaxial cylinders with smooth surfaces, for the conditions of this study the transport of momentum and heat is raised by a factor of 1.2 in the case of cavities embedded in the inner cylinder and by a factor of 1.1 in the case of cavities embedded in the outer cylinder.
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K., Kalidasan, R. Velkennedy, Jan Taler, Dawid Taler, Pawel Oclon, and Rajesh Kanna P. "Numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 1 (January 2, 2018): 103–17. http://dx.doi.org/10.1108/hff-03-2017-0125.
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Purpose This study aims to perform a numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature under laminar flow conditions. The geometry of the enclosure contains two isothermal blocks placed equidistant along the streamwise direction. The top wall is assumed to be cold (low temperature). The bottom wall temperature is either kept as constant or sinusoidally varied with time. The vertical walls are considered as adiabatic. The flow is diagonally upwards and assisted by the buoyancy force. The inlet is positioned at the bottom of the left wall, and the outlet is placed at the top of the right wall. The parameters considered in this paper are Rayleigh number (104-106), Prantdl number (0.71), amplitude of temperature oscillation (0-0.5) and the period (0.2). The effects of these parameters on heat transfer and fluid flow inside the open cavity are studied. The periodic results of fluid flow are illustrated with streamlines and the heat transfer is represented by isotherms and time-averaged Nusselt number. By virtue of increasing buoyancy, the heat transfer accelerates with an increase in the Rayleigh number. Also, the heat transfer is intensive with an increase in the bottom wall temperature. Design/methodology/approach The momentum and energy equations are solved simultaneously. The energy equation (3) is initially solved using the alternating direction implicit (ADI) method. The results of the energy equation are updated into the vorticity equation. The unsteady vorticity transport equation is also solved using the ADI method. Dimensionless time step equal to 0.01 is used for high Ra (105 and 106) and 0.001 is used for low Ra (104). Convergence criteria of 10−5 is used during the vorticity, stream function and temperature calculations, as the sum of error should be very small. Findings Numerical study of air convection in a rectangular enclosure with two isothermal blocks and oscillating bottom wall temperature is performed under laminar flow condition. The effect of the isothermal blocks on the heat transfer is analyzed for different Rayleigh numbers and the following conclusions are arrived. The hydrodynamic blockage effect is subdued by the isothermal heating of square blocks. Based on the streamline diagrams, it is found that the formation of vortices is greatly influenced by the Rayleigh number when all the walls are exposed to a constant wall temperature. The influence of amplitude on the heat transfer is remarkable on the wall exposed to oscillating temperature and is subtle on the opposite static cold wall. The heat transfer increases with an increase in the Rayleigh number and temperature. Research limitations/implications Flow is assumed to be two-dimensional and laminar subject to oscillatory boundary condition. The present investigation aims to study natural convection inside the cavity filled with air whose bottom wall is subject to time-variant temperature. The buoyancy is further intensified through two isothermal square blocks placed equidistant along the streamwise direction at mid-height. Originality/value The authors have developed a CFD solver to simulate the situation. Effect of Rayleigh number subject to oscillatory thermal boundary condition is simulated. Streamline contour and isotherm contour are presented. Local and average Nusselt numbers are presented.
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Lei, Jie-Chao, Chien-Cheng Chang, and Chang-Yi Wang. "An analysis of bi-directional Stokes micropump comprising a periodic array of moving belts." Physics of Fluids 34, no. 12 (December 2022): 122005. http://dx.doi.org/10.1063/5.0128944.
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In this study, we present an analysis of a Stokes micropump comprising a periodic array of parallel finite belts moved by rotating shafts. The geometry of the mechanical micropump is uniquely determined by the ratio of the length of the belts to the width between two neighboring belts (i.e., the aspect ratio a). The method of eigenfunction expansions with collocation is applied to solve the Stokes equation for the pumping rate, the stream function, and the velocity field as well as for the pressure gradient, which are all normalized by proper scales. It is found that with increasing a, the normalized pumping rate per unit micropump (or, simply abbreviated as a unit channel) first increases drastically and then decreases exponentially until it becomes a constant for large a, indicating that there exists a critical aspect ratio ( ac = 0.035) at which the maximum pumping rate ( qmax = 0.861) occurs, while the limiting value of q at large a is 0.5. The steady flow is driven by the moving belts against the established pressure gradient, and the pressure gradient at the centerline reaches its maximum value at the channel center and vanishes at distances from the micropump. Moreover, it is shown that the average flow velocity component perpendicular to the moving direction of the belts is relatively small, so that the flow field in the channel is approximately a unidirectional laminar flow, and therefore, the results are not necessarily limited to very low Reynolds numbers.
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LIU, FEI, and DALEI JING. "COMBINED ELECTROOSMOTIC AND PRESSURE DRIVEN FLOW IN TREE-LIKE MICROCHANNEL NETWORK." Fractals 29, no. 05 (June 18, 2021): 2150110. http://dx.doi.org/10.1142/s0218348x21501103.
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The present work presents a simplified mathematical model to calculate the flowrate of the combined electroosmotic flow (EOF) and pressure driven laminar flow (PDLF) in the symmetric tree-like microchannel network under the assumptions of small zeta potential and thin electrical double layer. A numerical analysis of the combined EOF and PDLF in symmetric Y-shaped microchannel is also carried out to validate the mathematical model. The analytical results and numerical results are found to be in good agreement with each other. Using the mathematical model, the present work further investigates the effect of diameter ratio of the tree-like network on the flowrate of the combined EOF and PDLF to recognize a possible conclusion being similar to the Murray’s law. Based on the present work, it is found that the symmetric tree-like network has an optimal diameter ratio to achieve the maximum flowrate for the combined EOF and PDLF when the total microchannel volume is constant; however, this optimal diameter ratio for the combined flow disobeys the generalized Murray’s law in a simple form of power function of the branching number [Formula: see text], and it is not only related on the branching number, but also depends on the branching level and channel length ratio of the tree-like network. Furthermore, the optimal diameter ratio shows a monotonous transition from [Formula: see text] for the pure PDLF to [Formula: see text] for the pure EOF with the increasing ratio of the driven voltage and driven pressure. The present work discusses the effects of these parameters on the optimal diameter ratio for the combined EOF and PDLF.
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Alves, Thiago Antonini, Murilo A. Barbur, and Felipe Baptista Nishida. "Application of Different Conductive Substrate Materials for Heat Transfer Enhancement in Cooling of Electronic Components." Advanced Materials Research 1082 (December 2014): 327–31. http://dx.doi.org/10.4028/www.scientific.net/amr.1082.327.
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In this research, a study of the heat transfer enhancement in electronic components mounted in channels was conducted by using different materials in the conductive substrate. In this context, a numerical analysis was performed to investigate the cooling of 3D protruding heaters mounted on the bottom wall (substrate) of a horizontal rectangular channel using the ANSYS/FluentTM 15.0 software. Three different materials of the conductive substrate were analyzed, polymethyl methacrylate (PMMA), fiberglass reinforced epoxy laminate (FR4), and pure aluminum (Al). Uniform heat generation rate was considered for the protruding heaters and the cooling process happened through a steady laminar airflow, with constant properties. The fluid flow velocity and temperature profiles were uniform at the channel entrance. For the adiabatic substrate, the cooling process occurred exclusively by forced convection. For the conductive substrate, the cooling process was characterized by conjugate forced convection-conduction heat transfer through two mechanisms; one directly between the heaters surfaces and the flow by forced convection, and the other through conduction at the interfaces heater-substrate in addition to forced convection from the substrate to the fluid flow at the substrate surface. The governing equations and boundary conditions were numerically solved through a coupled procedure using the Control Volumes Method in a single domain comprising the solid and fluid regions. Commonly used properties in cooling of electronics components mounted in a PCB and typical geometry dimensions were utilized in the results acquisition. Some examples were presented, indicating the dependence of the substrate thermal conductivity related to the Reynolds number on the heat transfer enhancement. Thus, resulting in a lower work temperature at the electronic components.
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Wheeler, Andrew P. S., and Richard D. Sandberg. "Numerical investigation of the flow over a model transonic turbine blade tip." Journal of Fluid Mechanics 803 (August 17, 2016): 119–43. http://dx.doi.org/10.1017/jfm.2016.478.
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Direct numerical simulations (DNS) are used to investigate the unsteady flow over a model turbine blade tip at engine-scale Reynolds and Mach numbers. The DNS are performed with an in-house multiblock structured compressible Navier–Stokes solver. The particular case of a transonic tip flow is studied since previous work has suggested that compressibility has an important effect on the turbulent nature of the separation bubble at the inlet to the tip–casing gap and subsequent flow reattachment. The flow is simulated over an idealized tip geometry where the tip gap is represented by a constant-area channel with a sharp inlet corner to represent the pressure side edge of the turbine blade. The effects of free-stream disturbances, cross-flow and the pressure side boundary layer on the tip flow aerodynamics and heat transfer are studied. For ‘clean’ inflow cases we find that even at engine-scale Reynolds numbers the tip flow is intermittent in nature, i.e. neither laminar nor fully turbulent. The breakdown to turbulence occurs through the development of spanwise streaks with wavelengths of approximately 15 %–20 % of the gap height. Multidimensional linear stability analysis confirms the two-dimensional base state to be most unstable with respect to spanwise wavelengths of 25 % of the gap height. The linear stability analysis also shows that the addition of cross-flows with 25 % of the streamwise gap exit velocity increases the stability of the tip flow. This is confirmed by the DNS, which also show that the turbulence production is significantly reduced in the separation bubble. For the case when free-stream disturbances are added to the inlet flow, viscous dissipation and the rapid acceleration of the flow at the inlet to the tip–casing gap cause significant distortion of the vorticity field and reductions of turbulence intensity as the flow enters the tip gap. The DNS results also suggest that the assumption of the Reynolds analogy and a constant recovery factor are not accurate, in particular in regions where the skin friction approaches zero while significant temperature gradients remain, such as in the vicinity of flow reattachment.
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Thomsen, Maria Storm, Anders Ø. Madsen, and Thomas Just Sørensen. "Crystal structure and optical properties of a two-sited EuIII compound: an EuIII ion coordinated by two [EuIII(DOTA)]− complexes (DOTA is 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetate)." Acta Crystallographica Section C Structural Chemistry 77, no. 7 (June 10, 2021): 354–64. http://dx.doi.org/10.1107/s2053229621005647.
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The structure and solid-state luminescence properties of an EuIII compound with two different lanthanide sites, [Eu(μ-O)5(OH)(H2O)2][Eu(DOTA)(H2O)]2 (DOTA is 1,4,7,10-tetrazacyclododecane-1,4,7,10-tetraacetate, C16H24N4O8), were determined. The compound crystallizes in a laminar structure in the triclinic space group P\overline{1}, where the two sites are a free europium(III) ion and an [Eu(DOTA)(H2O)]− complex. The crystal structure was determined using complex data treatment due to nonmerohedral twinning. Experimental data sets were recorded with large redundancy and separated according to scattering domains in order to obtain a reliable structure. In the first site, the [Eu(DOTA)(H2O)]− complex was found to adopt a capped twisted square-antiprismatic (cTSAP) conformation, where a capping water molecule increased the coordination number of the europium(III) site to nine (CN = 9). In the second site, the europium(III) ion was found to be coordinated by two water molecules, one hydroxide group and five oxide groups from neighbouring [Eu(DOTA)(H2O)]− complexes. The coordination geometry of this site was found to be a compressed square antiprism (SAP) and the coordination number of the europium(III) ion was found to be eight (CN = 8). A large increase in the rate constant of luminescence was observed for EuIII in [Eu(DOTA)(H2O)]− in solid-state luminescence spectroscopy measurements compared to in solution, which led to investigations of single crystals in deuterated media to exclude additional effects of quenching. We conclude that the most probable cause of the decrease in the observed luminescence lifetimes is the high asymmetry of the coordination environment of [Eu(DOTA)(D2O)]− in the [Eu(μ-O)5(OD)(D2O)2][Eu(DOTA)(D2O)]2 crystals.