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1
Beke, Dezső L., Z. Erdélyi i G. L. Katona. "Nonlinear Stress Effects in Diffusion". Defect and Diffusion Forum 264 (kwiecień 2007): 117–22. http://dx.doi.org/10.4028/www.scientific.net/ddf.264.117.
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According to classical Nernst-Einstein equation the diffusive flux is proportional to the driving force. However, this linear law is not valid if the driving force is very large. Attempts in the literature for the derivation of an “improved relation” till now were mostly restricted to the cases when the diffusion coefficient was independent of the composition. On the other hand, even if there are no externaldriving forces (other than related to the chemical driving force) present, deviations from the Fick I law are expected (transition from parabolic to linear growth-behaviour) on nanoscale for composition dependent diffusion coefficients. General description for the case when the driving forces and the diffusion asymmetry are large, is treated. The special case of large pressure gradients is discussed in detail and their effects on the deviation form the parabolic growth law on nanoscale will be analyzed. Effect of a pressure gradient on the crossover thickness between parabolic and linear regimes and on the interface transfer coefficient, K, is also treated.
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Wang, Dan, Yajun Yin, Jiye Wu, Xugui Wang i Zheng Zhong. "Interaction Potential between Parabolic Rotator and an Outside Particle". Journal of Nanomaterials 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/464925.
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At micro/nanoscale, the interaction potential between parabolic rotator and a particle located outside the rotator is studied on the basis of the negative exponential pair potential1/Rnbetween particles. Similar to two-dimensional curved surfaces, we confirm that the potential of the three-dimensional parabolic rotator and outside particle can also be expressed as a unified form of curvatures; that is, it can be written as the function of curvatures. Furthermore, we verify that the driving forces acting on the particle may be induced by the highly curved micro/nano-parabolic rotator. Curvatures and the gradient of curvatures are the essential elements forming the driving forces. Through the idealized numerical experiments, the accuracy of the curvature-based potential is preliminarily proved.
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Dobson, John F., Jun Wang i Hung M. Le. "Some Experimental Prospects involving Parabolic Quantum Wells". Australian Journal of Physics 53, nr 1 (2000): 119. http://dx.doi.org/10.1071/ph99048.
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We discuss two possible lines of experimental investigation based on parabolic quantum wells. In the first proposal, we note that the Generalised Kohn Theorem/Harmonic Potential Theorem forbids electron–electron damping of the Kohn mode in an electron layer gas under strictly parabolic confinement. This applies even for very strong driving. It is therefore interesting to attempt reduction of other sources of broadening in GaAlAs parabolic wells, so as to achieve a prominent narrow resonance in the far infrared. We concentrate here on phononic bandgap structures, which may be of interest for reduction of phonon effects in other systems as well. The second class of proposed experiment involves twinned parabolic wells in an attempt to observe van der Waals forces directly in GaAlAs systems. In a first approximation, the parabolic or Hooke's-law nature of the confinement allows one to use the well as a kind of spring balance to measure the weak van der Waals force. The influence of an applied magnetic field on these forces appears to be significant, and this system might provide the first measurement of such an effect.
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Kuzmina, Natalia, i Jae Hak Lee. "Driving Forces of Interleaving in the Baroclinic Front at the Equator". Journal of Physical Oceanography 35, nr 12 (1.12.2005): 2501–19. http://dx.doi.org/10.1175/jpo2828.1.
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Abstract The different types of instability in the equatorial β-plane approximation are analyzed by means of a 2D linear stability problem. The double-diffusive (DD) and diffusive/baroclinic (2D baroclinic and McIntyre) instabilities are shown not to develop if contours of the mean salinity/density have a parabolic, symmetrical-relative-to-the-equator shape. Using modeling results, an illustrative scheme of Equatorial Undercurrent (EUC) regions where different types of instability can develop is presented and subsequently applied to understand the driving forces of the intrusions observed in a closed spaced CTD section, located between the equator and 1°N. Long coherence intrusions are situated within two isopycnal layers, aligned to 25 (layer 1) and 26.3 (layer 2) σT, where the vertical shear is low. It was shown from the model that the layer-1 intrusions being observed in the midlayer of the EUC where the mean horizontal gradient of salinity is approximately constant are likely generated by a combined effect of DD instability and instability due to linear horizontal shear. The layer-2 intrusions being observed in the lower part of EUC where the mean salinity contours have a parabolic shape likely arise because of linear horizontal shear only, while double diffusion can be considered as an effect that increases the growth rate of unstable modes. Special attention is focused on two different parts of the EUC in the mixing of the thermocline. It is noted that the EUC only makes the mass transfer by long coherence intrusions in certain layers where the vertical shear is small. Conversely, the EUC contributes to the growth rate of unstable modes due to the horizontal linear shear.
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Beke, Dezső L., Z. Erdélyi i B. Parditka. "Effect of Diffusion Induced Driving Forces on Interdiffusion - Stress Development/Relaxation and Kinetics of Diffusion Processes". Defect and Diffusion Forum 309-310 (marzec 2011): 113–20. http://dx.doi.org/10.4028/www.scientific.net/ddf.309-310.113.
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General description of the interplay between the Kirkendall shift (as a special way of relaxation) and diffusion induced driving forces in diffusion intermixing of binary systems is given. It is shown that, if the Kirkendall shift is negligible, a steady state Nernts-Planck regime is established with diffusion coefficient close to the slower diffusivity, independently of the type of the diffusion induced field and also independently whether this is a single field or a combination of different fields (e.g. stress field and extra chemical potential of non-equilibrium vacancies). Deviations from parabolic kinetics are expected only before or after this steady state stage. Using the results of our previous paper, on development and relaxation of diffusion induced stresses, it is illustrated that the setting of time of the Nernst-Planck regime is very short: intermixing on the scale of few tenths of nanometer is enough to reach it. It is also illustrated that this stage is realized even in the case of asymmetric interdiffusion (in one side of the diffusion zone the diffusion is orders of magnitude higher than in the other), when the stress distribution has a more complex form (having a sharp peak at the interface). Surprisingly the steady state is longer than it would be expected from the relaxation time of Newtonian flow: This is so because the composition profile is not static but changes fast in the timescale of the stress relaxation, and thus the stress re-develops continuously.
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Liu, Jie, Yi Zhao, Yongfei Yang, Qingyan Mei, Shan Yang i Chenchen Wang. "Multicomponent Shale Oil Flow in Real Kerogen Structures via Molecular Dynamic Simulation". Energies 13, nr 15 (24.07.2020): 3815. http://dx.doi.org/10.3390/en13153815.
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As an unconventional energy source, the development of shale oil plays a positive role in global energy, while shale oil is widespread in organic nanopores. Kerogen is the main organic matter component in shale and affects the flow behaviour in nanoscale-confined spaces. In this work, a molecular dynamic simulation was conducted to study the transport behaviour of shale oil within kerogen nanoslits. The segment fitting method was used to characterise the velocity and flow rate. The heterogeneous density distributions of shale oil and its different components were assessed, and the effects of different driving forces and temperatures on its flow behaviours were examined. Due to the scattering effect of the kerogen wall on high-speed fluid, the heavy components (asphaltene) increased in bulk phase regions, and the light components, such as methane, were concentrated in boundary layers. As the driving force increased, the velocity profile demonstrated plug flow in the bulk regions and a half-parabolic distribution in the boundary layers. Increasing the driving force facilitated the desorption of asphaltene on kerogen walls, but increasing the temperature had a negative impact on the flow velocity.
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KUHLMANN, H. C., i U. SCHOISSWOHL. "Flow instabilities in thermocapillary-buoyant liquid pools". Journal of Fluid Mechanics 644 (10.02.2010): 509–35. http://dx.doi.org/10.1017/s0022112009992953.
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The linear stability of the incompressible axisymmetric flow in a buoyant-thermocapillary liquid pool is considered which is heated from above by a heat flux with a parabolic radial profile. Buoyancy forces and radial thermocapillary stresses due to the inhomogeneous surface temperature distribution drive a toroidal vortex. In the absence of buoyancy and for low Prandtl numbers the basic flow becomes unstable typically by a stationary centrifugal instability. At moderate Prandtl numbers the rotational symmetry is broken by hydrothermal waves. In the limit of vanishing Prandtl number two other critical modes are found if the pool is very shallow. One mode is a centrifugally destabilized rotating wave with high azimuthal wavenumber. The other mode is steady and it is driven by the deceleration of the radial inward return flow as it approaches the axis. The deceleration results from an entrainment of fluid into the thin layer of rapid radial outward surface flow. The centrifugal instability of the toroidal vortex flow is assisted by buoyancy in the low-Prandtl-number limit, because the cooling from the sidewall augments the thermocapillary driving. For moderately high Prandtl numbers a stable thermal stratification suppresses the hydrothermal-wave instabilities.
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Guo, Chang Hong, Xiang Dong Liu i Shao Mei Fang. "Exact Traveling Wave Solutions to a Model for Solid-Solid Phase Transitions Driven by Configurational Forces". Advanced Materials Research 418-420 (grudzień 2011): 1694–97. http://dx.doi.org/10.4028/www.scientific.net/amr.418-420.1694.
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This paper studies the exact traveling wave solutions to a model for solid-solid phase transitions driven by configurational forces. The model consists of the partial differential equations of linear elasticity coupled to a quasilinear nonuniformly parabolic equation of second order, which describes the diffusionless phase transitions of solid materials. By using the hyperbolic tangent function expansion method and homogeneous balance method, some exact traveling wave solutions, including solitary wave solutions are obtained for the phase transitions model in one space dimension.
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Alber, Hans-Dieter, i Peicheng Zhu. "Solutions to a Model with Nonuniformly Parabolic Terms for Phase Evolution Driven by Configurational Forces". SIAM Journal on Applied Mathematics 66, nr 2 (styczeń 2005): 680–99. http://dx.doi.org/10.1137/050629951.
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Cordy, C. "A Strong, Low-Cost Mount for Parabolic Dish Solar Collectors". Journal of Solar Energy Engineering 117, nr 3 (1.08.1995): 205–9. http://dx.doi.org/10.1115/1.2847786.
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This paper presents the design of a cradle for mounting solar energy concentrator dishes. The cradle is strong and provides unobstructed space to mount a well braced dish. It will survive high winds without being driven to a stow position. The axes of rotation of the dish pass near the plane of the edge of the dish to reduce wind-induced torques in the drive system. Large radius tracks are attached to both the dish and cradle so the gear train on the drive motors can be simple and inexpensive. The cradle is a strong gimbal mount built of 12 structural members in the form of three tetrahedra. It provides a polar axis mount for the concentrator dish. All forces parallel to the polar axis are delivered to the earth at the end of the cradle closest to the equator.
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Mahmood, Rashid, Afraz Hussain Majeed, Qurrat ul Ain, Jan Awrejcewicz, Imran Siddique i Hasan Shahzad. "Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics". Materials 15, nr 2 (11.01.2022): 529. http://dx.doi.org/10.3390/ma15020529.
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In the current work, an investigation has been carried out for the Bingham fluid flow in a channel-driven cavity with a square obstacle installed near the inlet. A square cavity is placed in a channel to accomplish the desired results. The flow has been induced using a fully developed parabolic velocity at the inlet and Neumann condition at the outlet, with zero no-slip conditions given to the other boundaries. Three computational grids, C1, C2, and C3, are created by altering the position of an obstacle of square shape in the channel. Fundamental conservation and rheological law for viscoplastic Bingham fluids are enforced in mathematical modeling. Due to the complexity of the representative equations, an effective computing strategy based on the finite element approach is used. At an extra-fine level, a hybrid computational grid is created; a very refined level is used to obtain results with higher accuracy. The solution has been approximated using P2 − P1 elements based on the shape functions of the second and first-order polynomial polynomials. The parametric variables are ornamented against graphical trends. In addition, velocity, pressure plots, and line graphs have been provided for a better physical understanding of the situation Furthermore, the hydrodynamic benchmark quantities such as pressure drop, drag, and lift coefficients are assessed in a tabular manner around the external surface of the obstacle. The research predicts the effects of Bingham number (Bn) on the drag and lift coefficients on all three grids C1, C2, and C3, showing that the drag has lower values on the obstacle in the C2 grid compared with C1 and C3 for all values of Bn. Plug zone dominates in the channel downstream of the obstacle with augmentation in Bn, limiting the shear zone in the vicinity of the obstacle.
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ZOHAR, YITSHAK, SYLVANUS YUK KWAN LEE, WING YIN LEE, LINAN JIANG i PIN TONG. "Subsonic gas flow in a straight and uniform microchannel". Journal of Fluid Mechanics 472 (30.11.2002): 125–51. http://dx.doi.org/10.1017/s0022112002002203.
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A nonlinear equation based on the hydrodynamic equations is solved analytically using perturbation expansions to calculate the flow field of a steady isothermal, compressible and laminar gas flow in either a circular or a planar microchannel. The solution takes into account slip-flow effects explicitly by utilizing the classical velocity-slip boundary condition, assuming the gas properties are known. Consistent expansions provide not only the cross-stream but also the streamwise evolution of the various flow parameters of interest, such as pressure, density and Mach number. The slip-flow effect enters the solution explicitly as a zero-order correction comparable to, though smaller than, the compressible effect. The theoretical calculations are verified in an experimental study of pressure-driven gas flow in a long microchannel of sub-micron height. Standard micromachining techniques were utilized to fabricate the microchannel, with integral pressure microsensors based on the piezoresistivity principle of operation. The integrated microsystem allows accurate measurements of mass flow rates and pressure distributions along the microchannel. Nitrogen, helium and argon were used as the working fluids forced through the microchannel. The experimental results support the theoretical calculations in finding that acceleration and non-parabolic velocity profile effects were found to be negligible. A detailed error analysis is also carried out in an attempt to expose the challenges in conducting accurate measurements in microsystems.
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Nakamura, Noboru, i Da Zhu. "Formation of Jets through Mixing and Forcing of Potential Vorticity: Analysis and Parameterization of Beta-Plane Turbulence". Journal of the Atmospheric Sciences 67, nr 9 (1.09.2010): 2717–33. http://dx.doi.org/10.1175/2009jas3159.1.
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Abstract Formation of multiple jets in forced beta-plane turbulence is studied from the perspective of nonuniform nonconservative arrangement of potential vorticity (PV). Numerical simulations are analyzed to show that mixing and forcing reinforce jets by concentrating PV gradients at the axes of prograde jets. Based on the formalism developed in the companion paper, the nonconservative driving of jets is diagnosed and parameterized through the diffusive flux of PV and the source of wave activity. It is found that the two terms nearly balance on a long time scale, and they are both strongly anticorrelated with the PV gradient, which suggests that PV controls the nonconservative processes and that these processes could be parameterized as functions of the PV gradient. The flux is modeled using the effective diffusivity formula recently obtained by Ferrari and Nikurashin. Consistent with the PV barrier concept, the nonlinear diffusivity is a decreasing function of the squared PV gradient and agrees well with the diffusivity diagnosed from the numerical simulation. The source term is assumed to be inversely proportional to the PV gradient. The parameterization gives rise to a nonlinear partial differential equation (PDE) for the mean flow. A finite-difference model of the PDE predicts formation of a piecewise linear PV (staircase) and piecewise parabolic jets from a near-uniform initial condition when anisotropy and mixing of the flow are sufficiently strong. The origin of the discontinuities is antidiffusive instability of PV gradients, and although nonlinearity allows the discrete model to integrate stably, the solution is sensitive to the initial condition and resolution. The emerging jets in the 1D model have similar characteristics to those in the numerical simulation, but the details of the transient behavior are distinct. Similar discrete models of ill-posed PDEs in which discontinuities form also appear in image processing and granular matter dynamics.
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Balla, Mounika, Manoj Kumar Tripathi, Kirti Chandra Sahu, George Karapetsas i Omar K. Matar. "Non-isothermal bubble rise dynamics in a self-rewetting fluid: three-dimensional effects". Journal of Fluid Mechanics 858 (8.11.2018): 689–713. http://dx.doi.org/10.1017/jfm.2018.774.
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The dynamics of a gas bubble in a square channel with a linearly increasing temperature at the walls in the vertical direction is investigated via three-dimensional numerical simulations. The channel contains a so-called ‘self-rewetting’ fluid whose surface tension exhibits a parabolic dependence on temperature with a well-defined minimum. The main objectives of the present study are to investigate the effect of Marangoni stresses on bubble rise in a self-rewetting fluid using a consistent model fully accounting for the tangential surface tension forces, and to highlight the effects of three-dimensionality on the bubble rise dynamics. In the case of isothermal and non-isothermal systems filled with a ‘linear’ fluid, the bubble moves in the upward direction in an almost vertical path. In contrast, strikingly different behaviours are observed when the channel is filled with a self-rewetting fluid. In this case, as the bubble crosses the location of minimum surface tension, the buoyancy-induced upward motion of the bubble is retarded by a thermocapillary-driven flow acting in the opposite direction, which in some situations, when thermocapillarity outweighs buoyancy, results in the migration of the bubble in the downward direction. In the later stages of this downward motion, as the bubble reaches the position of arrest, its vertical motion decelerates and the bubble encounters regions of horizontal temperature gradients, which ultimately lead to the bubble migration towards one of the channel walls. These phenomena are observed at sufficiently small Bond numbers (high surface tension). For stronger self-rewetting behaviour, the bubble undergoes spiralling motion. The mechanisms underlying these three-dimensional effects are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow. The effects of other dimensionless numbers, such as Reynolds and Froude numbers, are also investigated.
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Salama, Amgad. "Investigation of the imbibition/drainage of two immiscible fluids in capillaries with arbitrary axisymmetric cross-sections: a generalized model". Journal of Fluid Mechanics 947 (17.08.2022). http://dx.doi.org/10.1017/jfm.2022.642.
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Abstract In this work, we investigate the problem of imbibition/drainage of a fluid in capillaries of arbitrary axisymmetric cross-sections filled initially with another immiscible one. The model predicts the location of the meniscus and its speed along the tube length with time. The two immiscible fluids may assume any density and viscosity contrasts. In addition, the axisymmetric profile of the tube maintains a relatively small angle of tangency to warrant that the axial velocity distribution assumes, approximately, a parabolic profile. The driving forces that may be encountered in this system include the capillary force, pressure force, gravitational force and an opposing viscous force. The orientation of the capillary force can be in the direction of the flow (e.g. during imbibition) or opposite to the flow (e.g. during drainage). Likewise, the gravitational force can be in the direction of the flow or opposite to it. In this work we account for all these possibilities. A differential equation is developed that defines the location of the meniscus with time. A fourth-order-accurate Runge–Kutta scheme has been developed to provide solutions for the different scenarios associated with this system. It is shown that the developed model reduces to those appropriate for straight tubes, which builds confidence in the modelling approach. The effects of changing the tangent along the profile of the tube, which influences the calculation of the radius of curvature of the meniscus, is also considered. Unlike the cases of straight capillary tubes, in tubes with arbitrary symmetric profiles, the friction force depends on the variations of the tube profile. Examples of converging/diverging capillary tubes that follow straight and power law profiles are investigated. In addition, the case of sinusoidal profiles has also been considered.
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Lee, Cheong-Ah, i Dong-Guk Paeng. "Numerical simulation of spatiotemporal red blood cell aggregation under sinusoidal pulsatile flow". Scientific Reports 11, nr 1 (11.05.2021). http://dx.doi.org/10.1038/s41598-021-89286-1.
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AbstractPrevious studies on red blood cell (RBC) aggregation have elucidated the inverse relationship between shear rate and RBC aggregation under Poiseuille flow. However, the local parabolic rouleaux pattern in the arterial flow observed in ultrasonic imaging cannot be explained by shear rate alone. A quantitative approach is required to analyze the spatiotemporal variation in arterial pulsatile flow and the resulting RBC aggregation. In this work, a 2D RBC model was used to simulate RBC motion driven by interactional and hydrodynamic forces based on the depletion theory of the RBC mechanism. We focused on the interaction between the spatial distribution of shear rate and the dynamic motion of RBC aggregation under sinusoidal pulsatile flow. We introduced two components of shear rate, namely, the radial and axial shear rates, to understand the effect of sinusoidal pulsatile flow on RBC aggregation. The simulation results demonstrated that specific ranges of the axial shear rate and its ratio with radial shear rate strongly affected local RBC aggregation and parabolic rouleaux formation. These findings are important, as they indicate that the spatiotemporal variation in shear rate has a crucial role in the aggregate formation and local parabolic rouleaux under pulsatile flow.
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Díaz Palencia, José Luis, i Enrique Reyes. "Analysis of a fire extinguishing model with a p-Laplacian operator and with non-linear advection and reaction". Physica Scripta, 21.06.2023. http://dx.doi.org/10.1088/1402-4896/ace08c.
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Abstract We provide a new model to describe the fire extinguisher dynamics in an aircraft engine nacelle. We connect the mathematical properties introduced by a non-linear operator with the physical mechanisms of a fire extinguishing process. Some discussions about diffusion and non-linear parabolic operators are carried out to justify the governing equation. In addition, the model introduces phenomena like forced convection and fast reaction to account for the discharge of pressurized fire suppressant agent that is released from the fire bottles. The driving equation is firstly discussed analytically to obtain existence and uniqueness results concerning weak solutions. Afterward, we explore profiles of solutions and a characterization of the propagating extinguisher front is introduced. In order to provide a validity note on the analytical conceptions used, a flight test has been executed. Based on this, we obtain particular values for the parameters involved in the model. The proposed assessments permit to obtain different time levels, for which the suppressant agent extinguishes a fire. Such times depend strongly on the involved physical processes connected with diffusion, forced convection and reaction.
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Pirozzoli, Sergio, i Davide Modesti. "Direct numerical simulation of one-sided forced thermal convection in plane channels". Journal of Fluid Mechanics 957 (23.02.2023). http://dx.doi.org/10.1017/jfm.2023.104.
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We carry out direct numerical simulations (DNS) of turbulent flow and heat transfer in pressure-driven plane channels, by considering cases with heating on both walls, as well as asymmetric heating limited to one of the channel walls. Friction Reynolds numbers up to ${Re}_{\tau } \approx 2000$ are considered, and Prandtl numbers from ${Pr}=0.025$ to ${Pr} = 4$ , the temperature field being regarded as a passive scalar. Whereas cases with symmetric heating show close similarity between the temperature and the streamwise velocity fields, with turbulent structures confined to either half of the channel, in the presence of one-sided heating the temperature field exhibits larger regions with coherent fluctuations extending beyond the channel centreline. Validity of the logarithmic law for the mean temperature is confirmed, as well as universality of the associated von Kármán constant, which we estimate to be $k_{\theta } = 0.459$ . Deviations from the logarithmic behaviour are much clearer in cases with one-sided heating, which feature a wide outer region with parabolic mean temperature profile. The DNS data are exploited to construct a predictive formula for the heat transfer coefficient as a function of both Reynolds and Prandtl number. We find that the reduction of the thermal efficiency in the one-sided case is approximately $20\,\%$ at unit Prandtl number; however, it can become much more significant at low Prandtl number.
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Castaneda, Alexander J., Nathaniel O'Connor, Jamal Yagoobi, Jeffrey Didion, Mario Martins i Mohammad M. Hasan. "Dielectrophoretically-Assisted EHD-Driven Liquid Film Flow Boiling in the Presence and Absence of Gravity". Journal of Heat Transfer, 9.09.2022. http://dx.doi.org/10.1115/1.4055566.
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Abstract The ongoing development of modern electronic systems leads to smaller, more powerful devices that are expected to operate in complex environments. Therefore, advanced thermal management technologies are required to meet the growing demand, especially in space where two-phase thermal systems are limited by the absence of gravity. Electrohydrodynamic (EHD) and dielectrophoretic (DEP) forces can be used to sustain stable liquid film flow boiling in the absence of gravity, which is otherwise impractical due to the lack of a required buoyancy force to initiate bubble departure. EHD is a phenomenon that is represented by the interaction between electric fields and fluid flow. The DEP force is characterized by its ability to act on liquid/vapor interfaces due to a high gradient of electrical permittivity. This study investigates the heat transfer characteristics of EHD conduction pumping driven liquid film flow boiling coupled with DEP vapor extraction during a microgravity parabolic flight and on the ground. The results of this study show that EHD and DEP raise the critical heat flux, lower heater surface temperature, and successfully sustain boiling in both micro-gravity and on the ground with low power consumption. Additionally, the heat transfer data captured in terrestrial, microgravity, and 1.8 g conditions compare well, indicating that combining these mechanisms provides thermal enhancement independent of gravity. This study provides fundamental understanding of electrically driven liquid film flow boiling in the presence of phase change, paving the way toward developing next generation heat transport devices for space and terrestrial applications.
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Azese, Martin Ndi, Valjacques Nyemb Nsoga, Barbare J. Avouna Mvondo, Oluwole Daniel Makinde, Gilbert Batjom Batjom i Hollandine Sami Kouaji. "Transient Dynamics Of Pressure-Driven Encroachment in narrow Conduits with Rate-Dependent body Force". Physics of Fluids, 9.12.2022. http://dx.doi.org/10.1063/5.0129864.
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We analytically explore the flow of a Newtonian liquid forced to encroach a narrow tube of uniform cross-section, by an unsteady pressure gradient, assisted by an encroachment-rate dependent external force. This novel problem is thought to have interesting implications. For instance in medicine where narrow tubes like syringes and needles are typically used to administer medication and in the printing industry. Using an unsteady eigenfunction expansion, the velocity distribution is accurately defined to yield unsteady profiles, contrasting with the classical Poiseuille parabola. We subsequently used our unsteady spectral decomposition to properly capture the kinematics and dynamics hidden in the models. The comparison of the rectangular and circular channels shows as model ducts yield interesting similarities that can inform the choices of channels.By a detailed comparison between rectangular and circular channels, we show that such model ducts yield interesting similarities that can inform the choices of channels. Moreover, we obtain short and long-time dynamic behaviors, captured using a robust perturbation scheme that elegantly highlights the early and long-time characteristics. In the end, we present plots for encroachment depth and rate and the early and long-term asymptotic approximations and appropriately their graphical trends.