Journal articles: 'Equations in fluid flow study'

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Ueyama, K. "A study of two-fluid model equations." Journal of Fluid Mechanics 690 (November 25, 2011): 474–98. http://dx.doi.org/10.1017/jfm.2011.452.

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AbstractA theoretical study of the interaction term in the two-fluid model equations is presented. The relevant Navier–Stokes equation is volume-integrated in a control volume fixed in a field of dispersed two-phase flow; then it is time-integrated. An expression for the interaction term is obtained in the limit of infinitesimal control volume, which rigorously fits to the two-fluid model equation based on time averaging. The interaction term is then analysed for dispersed two-phase flow with homogeneous particle size. The mathematical expression of the resulting interaction term clearly shows its property, which has been overlooked for more than 40 years. It can be decomposed into the conventional interaction term and an additional ‘virtual force’ term. The virtual force term is evaluated approximately for two types of dispersed multiphase flow in order to demonstrate its effectiveness. The first is solid–liquid dispersed two-phase flow with spherical solid particles undergoing creeping flow, and the second is gas–liquid dispersed two-phase flow with large bubbles in a highly turbulent flow field. For solid spherical particles in a homogeneous creeping flow, the term vanishes, as was found numerically by Ten Cate and Sundaresan (Intl J. Multiphase Flow, vol. 32, 2006, pp. 106–131), although the term could be significant for a flow field with velocity gradient. For large bubbles in bubble columns in a recirculating turbulent flow regime, the term is significant. The two-fluid model equations are corrected by the introduction of these virtual force terms, which in some circumstances are important in simulating the macroscopic properties of dispersed two-phase flow with spatial variations.

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Nguyen, P. V., and O. P. Chandna. "Hodographic study of non-Newtonian MHD aligned steady plane fluid flows." International Journal of Mathematics and Mathematical Sciences 13, no. 1 (1990): 93–113. http://dx.doi.org/10.1155/s0161171290000138.

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A study is made of non-Newtonian HHD aligned steady plane fluid flows to find exact solutions for various flow configurations. The equations of motion have been transformed to the hodograph plane. A Legendre-transform function is used to recast the equations in the hodograph plane in terms of this transform function. Solutions for various flow configurations are obtained. Applications are investigated for the fluids of finite and infinite electrical conductivity bringing out the similarities and contrasts in the solutions of these types of fluids.

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Madani Tonekaboni, Seyed Ali, Ramin Abkar, and Reza Khoeilar. "On the Study of Viscoelastic Walters' B Fluid in Boundary Layer Flows." Mathematical Problems in Engineering 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/861508.

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Viscoelastic Walters' B fluid flows for three problems, stagnation-point flow, Blasius flow, and Sakiadis flow, have been investigated. In each problem, Cauchy equations are changed to a nondimensional differential equations using stream functions and with assumption of boundary layer flow. The fourth-order predictor-corrector finite-difference method for solving these nonlinear differential equations has been employed. The results that have been obtained using this method are compared with the results of the last studies, and it is clarified that this method is more accurate. It is also shown that the results of last study about Sakiadis flow of Walter's B fluid are not true. In addition, the effects of order of discretization in the boundaries are investigated. Moreover, it has been discussed about the valid region of Weissenberg numbers for the second-order approximation of viscoelastic fluids in each case of study.

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Hsu, C. H., S. Y. Hu, K. Y. Kung, C. C. Kuo, and C. C. Chang. "A Study on the Flow Patterns of a Second Grade Viscoe-Lastic Fluid Past a Cavity in a Horizontal Channel." Journal of Mechanics 29, no. 2 (December 20, 2012): 207–15. http://dx.doi.org/10.1017/jmech.2012.143.

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AbstractThis paper studies the behavior of second grade viscoelastic fluid past a cavity in a horizontal channel. The effects of Reynolds number, fluid elasticity and the aspect ratio of the cavity on the flow field are simulated numerically. The equations are converted into the vorticity and stream function equations. The solution is obtained by the finite difference method.The behavior of viscoelastic fluids is quite different from the Newtonian fluid, due to the effects of fluid elasticity. Only one flow pattern appears when the Newtonian fluid past the cavity. However, three kinds of flow patterns appear while the viscoelastic fluids past the cavity by increasing Reynolds number from 20 to 300. The flow field is affected by the fluid elasticity as well as the aspect ratio of the cavity. The transitional flow pattern appears at lower Reynolds number as the higher elasticity fluid past the cavity with larger aspect ratio.

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Ganji, Davood D., Mofid Gorji-Bandpy, and Mehdi Mostofi. "Study of Electroosmotic Flow in a Nanotube with Power Law Fluid." Applied Mechanics and Materials 110-116 (October 2011): 3633–38. http://dx.doi.org/10.4028/www.scientific.net/amm.110-116.3633.

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In this paper, electroosmotic phenomena in power law fluids are investigated. This assumption is applicable in many cases such as blood. Flow channels assumed to be in nanoscale. Navier-Stokes, Poisson-Boltzmann and electrochemical equilibrium equations govern these phenomena. It is notable that, these governing equations should be modified according to fluid complexity. Electroosmotic phenomena occur in the presence of electric double layer (EDL). Potential in the edge of the inner layer (stern layer) is called zeta potential. In this paper, according to follow the applicability of the subject, zeta potential is assumed to be so small, that makes the Poisson-Boltzmann equation linear and be able to solve analytically. Method employed for analytical solution is based on developed Bessel differential equation. This paper aims to investigate the fluid properties, zeta potential and Debye-Huckel parameter effect on the viscosity, electroosmotic mobility and velocity field in the nanotube. These expected achievements help us to study the properties of blood and some other non-Newtonian fluids more precisely.

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6

Adluri, Indrasena. "Hodographic study of plane micropolar fluid flows." International Journal of Mathematics and Mathematical Sciences 18, no. 2 (1995): 357–64. http://dx.doi.org/10.1155/s0161171295000445.

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Equations of steady flow of a plane micropolar fluid are transformed to the hodograph plane by means of the Legendre transform function of the streamfunction. Results are summarized in the form of a theorem, some flow problems are investigated as applications of this theorem and exact solutions and geometry of the flow are obtained in each case.

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Khan, Masood, and Azeem Shahzad. "Falkner–Skan Boundary Layer Flow of a Sisko Fluid." Zeitschrift für Naturforschung A 67, no. 8-9 (September 1, 2012): 469–78. http://dx.doi.org/10.5560/zna.2012-0049.

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In this paper, we investigate the steady boundary layer flow of a non-Newtonian fluid, represented by a Sisko fluid, over a wedge in a moving fluid. The equations of motion are derived for boundary layer flow of an incompressible Sisko fluid using appropriate similarity variables. The governing equations are reduced to a single third-order highly nonlinear ordinary differential equation in the dimensionless stream function, which is then solved analytically using the homotopy analysis method. Some important parameters have been discussed by this study, which include the power law index n, the material parameter A, the wedge shape factor b, and the skin friction coefficient Cf. A comprehensive study is made between the results of the Sisko and the power-law fluids.

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Jayalakshmamma, D. V., P. A. Dinesh, and D. V. Chandrashekhar. "Numerical Study of Micropolar Fluid Flow Past an Impervious Sphere." Defect and Diffusion Forum 388 (October 2018): 344–49. http://dx.doi.org/10.4028/www.scientific.net/ddf.388.344.

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The numerical study of axi-symmetric, steady flow of an incompressible micropolar fluid past an impervious sphere is presented by assuming uniform flow far away from the sphere. The continuity, linear and angular momentum equations are considered for incompressible micropolar fluid in accordance with Eringen. The governing equations of the physical problem are transformed to ordinary differential equation with variable co-efficient by using similarity transformation method. The obtained differential equation is then solved numerically by assuming the shooting technique. The effect of coupling and coupling stress parameter on the properties of the fluid flow is studied and demonstrated by graphs.

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hamid, Aamir, Abdul Hafeez, and Masood Khan. "Characteristics of combined heat and mass transfer on mixed convection flow of Sisko fluid model: A numerical study." Modern Physics Letters B 34, no. 24 (June 6, 2020): 2050255. http://dx.doi.org/10.1142/s0217984920502553.

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In this paper, the combined heat and mass transfer of mixed convection, non-similar Sisko fluid flow in the presence of a magnetic field is studied. The combined effects of thermal radiation and heat generation/absorption are examined for Sisko fluid flow via local non-similar method. For the radiative heat transfer, Rosseland approximation model is used. The governing partial differential equations of the present problem are transformed into a system of nonlinear ordinary differential equations by employing the Sparrow–Quack–Boerner local non-similarity method (LNM). The obtained equations are then numerically investigated by utilizing the bvp4c function in MATLAB. The impact of different supervising parameters on the velocity, temperature, skin friction and rate of heat transfer is performed graphically. It is observed that the velocity is more for a higher rate of the buoyancy force parameter while it is less for opposing buoyancy fluid. The thermal boundary layer thickness for the shear thickening fluids is smaller than the shear thinning fluids.

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10

Akhter, Shaheen, and Muhammad Ashraf. "Numerical study of flow and heat transfer in a porous medium between two stretchable disks using quasi-linearization method." Thermal Science, no. 00 (2019): 163. http://dx.doi.org/10.2298/tsci180801163a.

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In this study, the flow as well as heat transfer of a classical Newtonian fluid of constant density and viscosity in a porous medium between two radially stretching disks is explored. The role of the porosity of the medium, the stretching of the disks, the viscous dissipation and radiation on the flow and temperature fields is taken into account. The flow and heat equations are transformed into nonlinear ordinary differential equations by invoking the classical similarity transformations. These nonlinear differential equations were linearized using Quasi linearization method. Further the linearized equations were discretized by employing the finite differences which were then solved numerically using the successive over relaxation parameter method. Some features of the flow and temperature are discussed in detail in the form of tables and graphs. The present study may be beneficial in lubricants and computational storage devices as well as fluid flows and heat transmission in rotor-stator systems.

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Tawfeeq, Yahya Jirjees. "Mathematical modeling and numerical simulation of porous media single-phase fluid flow problem: a scientific review." International research journal of engineering, IT & scientific research 6, no. 4 (July 9, 2020): 15–28. http://dx.doi.org/10.21744/irjeis.v6n4.955.

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The complexity of porous media makes the classical methods used to study hydrocarbon reservoirs inaccurate and insufficient to predict the performance and behavior of the reservoir. Recently, fluid flow simulation and modeling used to decrease the risks in the decision of the evaluation of the reservoir and achieve the best possible economic feasibility. This study deals with a brief review of the fundamental equations required to simulate fluid flow through porous media. In this study, we review the derivative of partial differential equations governing the fluid flow through pores media. The physical interpretation of partial differential equations (especially the pressures diffusive nature) and discretization with finite differences are studied. We restricted theoretic research to slightly compressible fluids, single-phase flow through porous media, and these are sufficient to show various typical aspects of subsurface flow numerical simulation. Moreover, only spatial and time discretization with finite differences will be considered. In this study, a mathematical model is formulated to express single-phase fluid flow in a one-dimensional porous medium. The formulated mathematical model is a partial differential equation of pressure change concerning distance and time. Then this mathematical model converted into a numerical model using the finite differences method.

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Radhika, T. S. L., and T. Raja Rani. "On a Study of Flow Past Non-Newtonian Fluid Bubbles." WSEAS TRANSACTIONS ON FLUID MECHANICS 16 (April 15, 2021): 79–91. http://dx.doi.org/10.37394/232013.2021.16.8.

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In the current work, we aim at finding an analytical solution to the problem of fluid flow past a pair of separated non-Newtonian fluid bubbles. These bubbles are assumed to be spherical and non-permeable with the non-Newtonian fluid, viz. the couple stress fluid filling their interior. Further, the bubbles are presumed to be static in the flow domain, where a Newtonian fluid streams past these bubbles with a constant velocity (U) along the negative x-direction. We developed a mathematical model in the bipolar coordinate system for the fluid flow outside the bubbles and the spherical coordinate system inside the bubbles to derive a separable solution for their respective governing equations. Furthermore, to evaluate the model's applicabilities on the industrial front, the data on some widely used industrial fluids are given as inputs to the model, such as density, the viscosity of air or water for the fluid flow model developed for the region outside the fluid bubbles and the data on Cyclopentane or DIDP (non-Newtonian) for that within the bubbles. Some interesting findings are: the pressure in the outer region of the bubbles is higher when filled with low viscous industrial fluid, Cyclopentane, than a high viscous fluid, DIDP. Furthermore, an increase in the viscosity of Cyclopentane did not alter the pressure distribution in the region outside the bubbles. However, there is a considerable effect on this pressure in the case of DIDP bubbles.

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13

Li, Wang, Bo Yu, Yi Wang, Xin-Ran Wang, Qing-Yuan Wang, and Wen-Quan Tao. "Study on General Governing Equations of Computational Heat Transfer and Fluid Flow." Communications in Computational Physics 12, no. 5 (November 2012): 1482–94. http://dx.doi.org/10.4208/cicp.220111.281111a.

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AbstractThe governing equations for heat transfer and fluid flow are often formulated in a general form for the simplification of discretization and programming, which has achieved great success in thermal science and engineering. Based on the analysis of the popular general form of governing equations, we found that energy conservation cannot be guaranteed when specific heat capacity is not constant, which may lead to unreliable results. A new concept of generalized density is put forward, based on which a new general form of governing equations is proposed to guarantee energy conservation. A number of calculation examples have been employed to verify validation and feasibility.

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Voigt, A. "Fluid deformable surfaces." Journal of Fluid Mechanics 878 (September 4, 2019): 1–4. http://dx.doi.org/10.1017/jfm.2019.549.

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Lipid membranes are examples of fluid deformable surfaces, which can be viewed as two-dimensional viscous fluids with bending elasticity. With this solid–fluid duality any shape change contributes to tangential flow and vice versa any tangential flow on a curved surface induces shape deformations. This tight coupling between shape and flow makes curvature a natural element of the governing equations. The modelling and numerical tools outlined in Torres-Sánchez et al. (J. Fluid Mech., vol. 872, 2019, pp. 218–271) open a new field of study by enabling the exploration of the role of curvature in this context.

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Akbar, Noreen Sher. "Biomathematical study of Sutterby fluid model for blood flow in stenosed arteries." International Journal of Biomathematics 08, no. 06 (October 15, 2015): 1550075. http://dx.doi.org/10.1142/s1793524515500758.

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In this paper, we have discussed the biomathematical analysis of Sutterby fluid model for blood flow in stenosed tapered arteries. The equations for the Sutterby fluid model are modeled in cylindrical geometry. The equations have been developed for the case of mild stenosis. Perturbation solutions are attained in terms of small Sutterby fluid parameter β for the velocity, impedance resistance and wall shear stress. Three types of arteries i.e. converging, diverging and non-tapered have been considered for the analysis and discussion. Graphical results have been presented for different parameters of interest. Streamlines have been plotted at the end of the paper.

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Liao, Chang Rong, J. H. Hao, D. X. Zhao, and K. L. Wang. "Study on Design Method of Magneto-Rheological Fluid Shock Absorber Employing Shear Rate Profiles and Experimental Tests." Applied Mechanics and Materials 121-126 (October 2011): 1095–99. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.1095.

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The flow differential equation for Magneto-rheological (MR) fluids in annular channels of MR fluid shock absorber is set up and several rational simplifications are made. Analytical shear stress profiles of MR fluids through annular channels are obtained via solution of the flow differential equation. An analytical study on MR fluid shock absorber is present employing shear stress profiles. Both boundary conditions and compatible conditions are established. Both flow velocity profiles and total volumetric flow rate are developed by integration by parts and numerical integration. The prediction method for damping force of MR fluid shock absorber is developed via simultaneous equations. The analytical study on MR fluid shock absorber is validated by means of reformative Herschel–Bulkley constitutive model, in which flow velocity profiles and flow regions boundary radii are drawed. A MR fluid shock absorber, which is designed and fabricated in Chongqing University, is tested by electro-hydraulic servo vibrator in National Center for Test and Supervision of Coach Quality. The experimental results reveal that the methodology is able to predict damping force of MR fluid shock absorber via shear rate profiles and experimental damping forces are in good agreement with analytical those.

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Ellahi, Rahmat, Farooq Hussain, Syed Asad Abbas, Mohammad Mohsen Sarafraz, Marjan Goodarzi, and Mostafa Safdari Shadloo. "Study of Two-Phase Newtonian Nanofluid Flow Hybrid with Hafnium Particles under the Effects of Slip." Inventions 5, no. 1 (January 20, 2020): 6. http://dx.doi.org/10.3390/inventions5010006.

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This paper investigates the role of slip in a two-phase flow of Newtonian fluid. The nano-size Hafnium particles are used in the base fluid. The fluid under consideration is studied for two cases namely (i) fluid phase (ii) phase of particles. Both cases are examined for three types of geometries. The governing equations are simplified in nondimensional form for each phase along with boundary conditions. The resulting equations have been analytically solved to get exact solutions for both fluid and particle phases. Different features of significant physical factors are discussed graphically. The flow patterns have been examined through streamlines.

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Maraj, E. N., Noreen Sher Akbar, and S. Nadeem. "Mathematical study for peristaltic flow of Williamson fluid in a curved channel." International Journal of Biomathematics 08, no. 01 (January 2015): 1550005. http://dx.doi.org/10.1142/s1793524515500059.

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In this paper, we have investigated the peristaltic flow of Williamson fluid in a curved channel. The governing equations of Williamson fluid model for curved channel are derived including the effects of curvature. The highly nonlinear partial differential equations are simplified by using the wave frame transformation, long wavelength and low Reynolds number assumptions. The reduced nonlinear partial differential equation is solved analytically with the help of homotopy perturbation method. The physical features of pertinent parameters have been discussed by plotting the graphs of pressure rise, velocity profile and stream functions.

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Mohyud-din, Syed Tauseef, Muhammad Asad Iqbal, and Muhammad Shakeel. "A study for steady nanofluid flow between parallel plates." Engineering Computations 34, no. 8 (November 6, 2017): 2514–27. http://dx.doi.org/10.1108/ec-04-2017-0142.

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Purpose In this paper, the authors study the behavior of heat and mass transfer between parallel plates of a steady nanofluid flow in the presence of a uniform magnetic field. In the model of nanofluids, the essential effect of thermophoresis and Brownian motion has been encompassed. Design/methodology/approach The variation of parameters method has been exploited to solve the differential equations of nanofluid model. The legitimacy of the variation of parameters method has been corroborated by a comparison of foregoing works by many authors on viscous fluid. Findings An analysis of the model is performed for different parameters, namely, viscosity parameter, Brownian parameter, thermophoretic parameter and magnetic parameter. Originality/value The variation of parameters method proves to be very effective in solving nonlinear system of ordinary differential equations which frequently arise in fluid mechanics.

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Dey, Debasish, and Barbie Chutia. "MODELLING OF MULTI-PHASE FLUID FLOW WITH VOLUME FRACTION PAST A PERMEABLE STRETCHING VERTICAL CYLINDER AND ITS NUMERICAL STUDY." Latin American Applied Research - An international journal 51, no. 3 (June 25, 2021): 165–71. http://dx.doi.org/10.52292/j.laar.2021.604.

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A steady two-dimensional mixed convective multi-phase fluid (base fluid containing dust particles) flow past a vertical stretching cylinder in presence of volume fraction has been investigated. The surface of cylinder is embedded by porous medium in presence of non-uniform source/sink. Governing partial differential equations of the problem for both fluid and dust phases are converted into ordinary differential equations using similarity transformations. MATLAB built-in bvp4c solver technique is used to solve the resulting non-linear differential equations. The results are presented in graphical forms for various values of flow parameters.

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Nasu, Shoichi, and Mutsuto Kawahara. "An Analysis of Compressible Viscous Flows Around a Body Using Finite Element Method." Advanced Materials Research 403-408 (November 2011): 461–65. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.461.

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The objective of this paper is an analysis of a body in a compressible viscous flow using the finite element method. Generally, when the fluid flow is analyzed, an incompressible viscous flow is often applied. However fluids have compressibility in actual phenomena. Therefore, the compressibility should be concerned in Computational Fluid Dynamics [CFD]. In this study, two kind of equation is applied to basic equations. One is compressible Navier-stokes equation, the other is incompressible Navier-stokes equation considering density variation. These analysis results of both equations are compared.

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Abdel-Rahman, Gamal M., and Faiza M. N. El-Fayez. "Nanofluid Viscoelastic Fluid Flow with Thermophoresis." Nanoscience and Nanotechnology Letters 11, no. 12 (December 1, 2019): 1739–49. http://dx.doi.org/10.1166/nnl.2019.3061.

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We in this study investigated Brownian motion and thermophoresis effects embedded in a porous medium flow with heat transfer generation and chemical reaction on a stretching sheet and Jeffrey fluid model for viscoelastic nanofluid under the effects of magnetic field and thermal radiation. The nanofluid was assumed incompressible and the flow was laminar, with base fluid containing the following types of nanoparticles: Copper (Cu), Aluminum (Al2O3) and Titanium Oxide (TiO2). The governing continuity, momentum, and energy equations for the nanofluid were reduced using similarity transformation and converted into a system of non-Linear ordinary differential equations which were solved numerically. Numerical solutions were also obtained for the velocity, temperature and nanoparticle concentration fields, as well as for skin friction coefficient and Nusselt number. Finally, numerical values for the physical quantities, such as local skin-friction coefficient, local Nusselt number, local Sherwood number and wall deposition flux are herein presented in tabular form.

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Abdel-Rahman, Gamal M., and Faiza M. N. El-Fayez. "Nanofluid Viscoelastic Fluid Flow with Thermophoresis." Nanoscience and Nanotechnology Letters 11, no. 12 (December 1, 2019): 1739–49. http://dx.doi.org/10.1166/nnl.2019.30611739.

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We in this study investigated Brownian motion and thermophoresis effects embedded in a porous medium flow with heat transfer generation and chemical reaction on a stretching sheet and Jeffrey fluid model for viscoelastic nanofluid under the effects of magnetic field and thermal radiation. The nanofluid was assumed incompressible and the flow was laminar, with base fluid containing the following types of nanoparticles: Copper (Cu), Aluminum (Al2O3) and Titanium Oxide (TiO2). The governing continuity, momentum, and energy equations for the nanofluid were reduced using similarity transformation and converted into a system of non-Linear ordinary differential equations which were solved numerically. Numerical solutions were also obtained for the velocity, temperature and nanoparticle concentration fields, as well as for skin friction coefficient and Nusselt number. Finally, numerical values for the physical quantities, such as local skin-friction coefficient, local Nusselt number, local Sherwood number and wall deposition flux are herein presented in tabular form.

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Diep, Nguyen Van. "Generalized diffusion theory of micromorphicly deformable particle-fluid continuum and bubble-liquid two-phase flows." Vietnam Journal of Mechanics 15, no. 2 (June 30, 1993): 21–26. http://dx.doi.org/10.15625/0866-7136/10198.

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In the paper [1] the basic concepts and equations were derived for the micromorphicly deformable particle-fluid two-phase flows, the constitutive equations have been constructed. The flow us fluid with deformable spherical particles, when the particle only expands radially, rotates and translates, is considered in this paper. For this case one can obtain the full motion's equations system. These equation together with the constitutive equations are sufficient to determine all of unknowns, and they can be used to study the bubble- liquid two-phase flow. The problems of kinematic wave and acoustic wave propagation in the bubble-liquid two-phase flow is studied.

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Liu, Zheng, Jing Zhu, and Lian Cun Zheng. "Research on Fluid Mechanics with Slip Flow of Viscoelastic Fluid in the Micro Channel." Applied Mechanics and Materials 387 (August 2013): 51–54. http://dx.doi.org/10.4028/www.scientific.net/amm.387.51.

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Stagnation flow, an import research branch of fluid mechanics, describing the fluid motion near the stagnation region, exists on all solid bodies moving in a fluid. And stagnation point boundary layer flow problems described by partial differential equations have attracted many scholars attention nowadays. These problems have become difficult and hot in the study of applied mathematics, mechanics and materials engineering. This paper has transformed the governing boundary layer equations into a system of nonlinear differential equations through the similarity transformation, and the analytical approximations of solutions are derived by homotopy analysis method (HAM). In addition, the effects of physical factors (such as the slip parameter, Magnetic field parameter and Reynolds number) on the flow are examed and discussed graphically. They have a great impact on the speed.

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Butbaia, G., and Z. N. Osmanov. "Fluid dynamics in the Ellis wormhole." International Journal of Modern Physics D 30, no. 10 (June 9, 2021): 2150072. http://dx.doi.org/10.1142/s0218271821500723.

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In the Ellis wormhole metrics, we study the characteristics of fluid dynamics and the properties of linear sound waves. By implying the energy–momentum equation and the continuity equation in the general relativistic manner, we examine the flow dynamics and solve the corresponding equations for a relatively simple case — radial flow. To study the linear sound waves, the equations governing the mentioned physical system are linearized and solved and interesting characteristic properties are found.

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Rashidi, Mohammad, Muhammad Ashraf, Behnam Rostami, Taher Rastegari, and Sumra Bashir. "Mixed convection boundary-layer flow of a micro polar fluid towards a heated shrinking sheet by homotopy analysis method." Thermal Science 20, no. 1 (2016): 21–34. http://dx.doi.org/10.2298/tsci130212096r.

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A comprehensive study of two dimensional stagnation flow of an incompressible micro polar fluid with heat transfer characteristics towards a heated shrinking sheet is analyzed analytically. The main goal of this paper is to find the analytic solutions using a powerful technique namely the Homotopy Analysis Method (HAM) for the velocity and the temperature distributions and to study the steady mixed convection in two-dimensional stagnation flows of a micro polar fluid around a vertical shrinking sheet. The governing equations of motion together with the associated boundary conditions are first reduced to a set of self-similar nonlinear ordinary differential equations using a similarity transformation and are then solved by the HAM. Some important features of the flow and heat transfer for the different values of the governing parameters are analyzed, discussed and presented through tables and graphs. The heat transfer from the sheet to the fluid decreases with an increase in the shrinking rate. Micro polar fluids exhibit a reduction in shear stresses and heat transfer rate as compared to Newtonian fluids, which may be beneficial in flow and thermal control of polymeric processing.

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Ahmad, Shabbir, Kashif Ali, Sohail Ahmad, and Jianchao Cai. "Numerical Study of Lorentz Force Interaction with Micro Structure in Channel Flow." Energies 14, no. 14 (July 15, 2021): 4286. http://dx.doi.org/10.3390/en14144286.

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The heat transfer Magnetohydrodynamics flows have been potentially used to enhance the thermal characteristics of several systems such as heat exchangers, electromagnetic casting, adjusting blood flow, X-rays, magnetic drug treatment, cooling of nuclear reactors, and magnetic devices for cell separation. Our concern in this article is to numerically investigate the flow of an incompressible Magnetohydrodynamics micropolar fluid with heat transportation through a channel having porous walls. By employing the suitable dimensionless coordinates, the flow model equations are converted into a nonlinear system of dimensionless ordinary differential equations, which are then numerically treated for different preeminent parameters with the help of quasi-linearization. The system of complex nonlinear differential equations can efficiently be solved using this technique. Impact of the problem parameters for microrotation, temperature, and velocity are interpreted and discussed through tables and graphs. The present numerical results are compared with those presented in previous literature and examined to be in good contact with them. It has been noted that the imposed magnetic field acts as a frictional force which not only increases the shear stresses and heat transfer rates at the channel walls, but also tends to rotate the micro particles in the fluid more rapidly. Furthermore, viscous dissipation may raise fluid temperature to such a level that the possibility of thermal reversal exists, at the geometric boundaries of the domain. It is therefore recommended that external magnetic fields and viscous dissipation effects may be considered with caution in applications where thermal control is required.

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Vajravelu, K., K. V. Prasad, and S. R. Santhi. "Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension." Advances in Applied Mathematics and Mechanics 7, no. 3 (May 28, 2015): 369–86. http://dx.doi.org/10.4208/aamm.2013.m379.

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AbstractAn analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena.

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Isayev, M. M., M. B. Mammadova, N. M. Khasayeva, F. Sh Aghayeva, and N. Kh Badalova. "Study oil density in flow, system of automated measurement and inaccuracies." Azerbaijan Oil Industry, no. 12 (December 15, 2020): 39–44. http://dx.doi.org/10.37474/0365-8554/2020-12-39-44.

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The paper reviews the issues of specification of fluid fuel amount with high measuring accuracy transported through oil pipelines. The operation algorithm of vibration-frequency densitometer for automatic measurement of fluid fuel density with high measuring accuracy in technological process in the exploitation conditions is based on the hybrid test method. For this purpose test equations on measuring links using simple additive and multiplicative tests, as well as their combinations have been developed, test equations composed, and as a result of their solution the main test equation obtained. The mathematic-statistic estimation of the results of densitometer measurements correcting test algorithms for the definition of measurement errors and composing inaccuracies, the method of automated calibration are presented as well.

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Haider, Sajjad, Nouman Ijaz, A. Zeeshan, and Yun-Zhang Li. "Magneto-hydrodynamics of a solid-liquid two-phase fluid in rotating channel due to peristaltic wavy movement." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 5 (August 31, 2019): 2501–16. http://dx.doi.org/10.1108/hff-02-2019-0131.

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Purpose Numerous researchers have probed the peristaltic flows because of their immense usage in industrial engineering, biomedical engineering and biological sciences. However, the investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap in the existing literature, this paper will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of a magnetic field. The purpose of this study is to investigate the two-phase velocity distribution and rotation parameter when magneto-hydrodynamics is applied. Design/methodology/approach The constituent equations are solved under the condition of low Reynolds number and long wavelength. The exact method is used to attain the subsequent equations and a comprehensive graphical study for fluid phase, particulate phase velocity and flow rates are furnished. The impacts of pertinent parameters, magnetic field and rotation are discussed in detail. Findings It is witnessed that the velocity profile of particulate phase gets higher values for the same parameters as compared to the fluid phase velocity. Moreover, the axial velocity increases with different values of particle volume fraction, but in case of magnetic field and rotation parameter, it shows the opposite behavior. Practical implications The outcomes of study have viable industrial implementations in systems comprising solid-liquid based flows of fluids involving peristaltic movement. Originality/value The investigation of peristaltic flow in two-phase fluid of a rotating frame in the presence of a magnetic field has not been yet discussed. Therefore, to fulfill this gap, the present study will explicate the peristaltic flow of two-phase fluid across a rotating channel with the effect of wall properties in the presence of magnetic field.

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Ak, M. Mehmet, and Sundaram Gunasekaran. "Simulation of Lubricated Squeezing Flow of a Herschel-Bulkley Fluid Under Constant Force." Applied Rheology 10, no. 6 (December 1, 2000): 274–79. http://dx.doi.org/10.1515/arh-2000-0017.

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AbstractLubricated squeezing flow (LSF) of a Herschel-Bulkley fluid between parallel disks under constant force was theoretically analyzed. An analytical expression for the fluid thickness as a function of time was obtained in terms of a hypergeometric function. The fluid thickness profiles in LSF were simulated for a range of each of the model parameters (n, K, τo). The solution obtained in this study reduces to the corresponding analytical equations previously derived for LSF of Newtonian and power-law fluids. The simulations for Herschel-Bulkley fluid were compared with the response of Newtonian and power-law fluids. The dependence of the limiting fluid thickness (i.e. H(t)/H0 at 180 s) on model parameters is presented.

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Dey, Debasish. "Gravity Modulation Effects of Hydromagnetic Elastico-Viscous Fluid Flow past a Porous Plate in Slip Flow Regime." ISRN Applied Mathematics 2014 (May 21, 2014): 1–7. http://dx.doi.org/10.1155/2014/492906.

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The two-dimensional hydromagnetic free convective flow of elastico-viscous fluid (Walters liquid Model B′) with simultaneous heat and mass transfer past an infinite vertical porous plate under the influence of gravity modulation effects has been analysed. Generalized Navier’s boundary condition has been used to study the characteristics of slip flow regime. Fluctuating characteristics of temperature and concentration are considered in the neighbourhood of the surface having periodic suction. The governing equations of fluid motion are solved analytically by using perturbation technique. Various fluid flow characteristics (velocity profile, viscous drag, etc.) are analyzed graphically for various values of flow parameters involved in the solution. A special emphasis is given on the gravity modulation effects on both Newtonian and non-Newtonian fluids.

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Chung, Myung Kyoon, Hyung Jin Sung, and Kye Bock Lee. "Computational Study of Turbulent Gas-Particle Flow in a Venturi." Journal of Fluids Engineering 108, no. 2 (June 1, 1986): 248–53. http://dx.doi.org/10.1115/1.3242571.

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A “two-fluid” model has been applied to predict turbulent dilute gas-particle flow through a Venturi tube. Bulk motion of particles is considered as a secondary fluid flow which exchanges mass and momentum with the primary conveying air stream. Closure of the time-averaged equations is achieved by modelling turbulent second-order correlations with an extended mixing-length theory. Proposed closure model is found to aptly simulate the dependency of the static pressure drop on the particle size, flow rate and the loading ratio.

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Nanjundaswamy, Vinay Kumar Poorigaly, Ulavathi Shettar Mahabaleshwar, Patil Mallikarjun, Mohaddeseh Mousavi Nezhad, and Giulio Lorenzini. "Casson Liquid Flow due to Porous Stretching Sheet with Suction/Injection." Defect and Diffusion Forum 388 (October 2018): 420–32. http://dx.doi.org/10.4028/www.scientific.net/ddf.388.420.

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The theoretical study of laminar boundary layer flows of a non-Newtonian fluid past a stretching sheet in an embedded porous medium in the presence of suction/injection is of significant importance in the crystal growing, geothermal, metallurgical, polymer extrusion and several other technological processes. Casson fluid model is one such fluid model used to characterize the behaviour of non-Newtonian fluids. The present article discusses the Casson fluid flow past a permeable stretching sheet in the presence of mass transpiration. The physical problem is modelled into a system of nonlinear partial differential equations which are analytically solved by transforming them into nonlinear ordinary differential equations with constant coefficient by means of similarity transformations. The analysis reveals the effect of Casson parameter on the velocity boundary. In fact, the increasing Casson parameter results in the suppression of velocity boundary. It is found that the skin friction coefficient decreases with the decreasing values of Casson parameter. The effects of Darcy drag force and the mass transpiration are also analyzed by means of various plots.

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Han, Bumsoo, and R. J. Goldstein. "A Numerical Study of Energy Separation in a Jet Flow." Journal of Heat Transfer 129, no. 4 (December 4, 2006): 577–81. http://dx.doi.org/10.1115/1.2709973.

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Redistribution of the total energy of a fluid in motion, which is called “energy separation,” has been observed in various flow situations. Understanding the underlying mechanism of this interesting phenomenon has been limited due to lack of the temporal information on flow and temperature fields. In the present study, numerical simulation of a viscous circular jet was performed to provide detailed temporal information on pressure, vorticity, and total temperature fields. Nondimensionalized governing equations, including mass, momentum, and total energy conservation equations, were simultaneously solved by an equal-order linear finite element and fractional four-step method. The results show that the formation and transport of vortices induce a pressure fluctuation in the flow field. The fluid, which flows through the disturbed pressure field, exchanges pressure work with the surroundings, and gains or loses total energy. This work exchange leads to higher and lower total temperature regions than the surroundings. In addition to the presence and movement of the vortices, the results indicate that the vortex-pairing process significantly intensifies the pressure fluctuation and corresponding total temperature difference. This implies that the vortex-pairing process is a very important process in intensifying energy separation and might explain the enhancement of energy separation in a jet using acoustic excitation.

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MUTHU, P., B. V. RATHISH KUMAR, and PEEYUSH CHANDRA. "A STUDY OF MICROPOLAR FLUID IN AN ANNULAR TUBE WITH APPLICATION TO BLOOD FLOW." Journal of Mechanics in Medicine and Biology 08, no. 04 (December 2008): 561–76. http://dx.doi.org/10.1142/s0219519408002541.

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The oscillatory flow of micropolar fluid in an annular region with constriction, provided by variation of the outer tube radius, is investigated. It is assumed that the local constriction varies slowly over the cross-section of the annular region. The nonlinear governing equations of the flow are solved using a perturbation method to determine the flow characteristics. The effect of micropolar fluid parameters on mean flow and pressure variables is presented.

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Haider, Sajjad, Adnan Saeed Butt, Imran Syed Muhammad, Asif Ali, Yun-Zhang Li, Syed Muhammad Ali Naqvi, and Muhammad Adnan Qaiser. "Impact of nano-particles shapes on Al2O3-water nano-fluid flow due to a stretching cylinder." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 5 (August 19, 2019): 2809–32. http://dx.doi.org/10.1108/hff-02-2019-0113.

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Purpose The purpose of this study is to theoretically probe the shape impacts of nano-particle on boundary layer flow of nano-fluid toward a stretching cylinder with heat-transmission effects. The base fluid used for this study is pure water, and aluminum oxide nano-particles are suspended in it. Four different shapes of nano-particle, namely, cylindrical, brick, platelets and blades, are considered to carry out the study. Design/methodology/approach The problem is modelled mathematically and the nonlinear system of equations is attained by using appropriate transmutations. The solution of transmuted equations is achieved by utilizing a shooting technique with Fourth-Fifth order Runge–Kutta Fehlberg scheme. Numerically attained results are elucidated through graphs and tables which are further compared under limiting cases with existing literature to check the validity of the results. Findings It is observed that fluid velocity and temperature of cylindrical shaped water nano-fluids are more than the nano-fluid having brick-shaped nano-particles. Moreover, it is seen that the nano-fluids suspended with platelets-shaped nano-particles have higher velocity and temperature than the nano-fluids containing blade-shaped nano-particles. The curvature parameter and nano-particles volume fraction have increasing effects on flow velocity and temperature of nano-fluids containing all types of nano-particle shapes. Originality/value Numerous authors have examined the impacts of nano-particle shapes on characteristics of heat transfer and fluid flow. However, to the best of the authors’ knowledge, the shape impacts of nano-particles on boundary layer flow of nano-fluid toward a stretching cylinder with heat-transmission effects have not been discussed. So, to fulfill this gap, the present paper explicates the impacts of various nano-particle shapes on Al2O3–water-based nano-fluid flow past a stretching cylinder with heat-transfer effects.

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Devakar, M., Ankush Raje, and Shubham Hande. "Unsteady Flow of Couple Stress Fluid Sandwiched Between Newtonian Fluids Through a Channel." Zeitschrift für Naturforschung A 73, no. 7 (July 26, 2018): 629–37. http://dx.doi.org/10.1515/zna-2017-0434.

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AbstractThe aim of this article is to study the unsteady flow of immiscible couple stress fluid sandwiched between Newtonian fluids through a horizontal channel. The fluids and plates are initially at rest. At an instant of time, a constant pressure gradient is applied along the horizontal direction to generate the flow. The time-dependent partial differential equations are solved numerically using the finite difference method. The continuity of velocities and shear stresses at the fluid-fluid interfaces has been considered. The obtained results are displayed through graphs and are discussed for various fluid parameters pertaining the flow. The volume flow rate is also obtained numerically for diverse fluid parameters and is presented through a table. It is noticed that fluid velocities increased with time and reached a steady state after a certain time level. Also, the presence of couple stresses reduced the fluid velocities. Volume flow rate increased with Reynolds number and is reduced by increase of ratio of viscosities.

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Akylas, T. R. "David J. Benney: Nonlinear Wave and Instability Processes in Fluid Flows." Annual Review of Fluid Mechanics 52, no. 1 (January 5, 2020): 21–36. http://dx.doi.org/10.1146/annurev-fluid-010518-040240.

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David J. Benney (1930–2015) was an applied mathematician and fluid dynamicist whose highly original work has shaped our understanding of nonlinear wave and instability processes in fluid flows. This article discusses the new paradigm he pioneered in the study of nonlinear phenomena, which transcends fluid mechanics, and it highlights the common threads of his research contributions, namely, resonant nonlinear wave interactions; the derivation of nonlinear evolution equations, including the celebrated nonlinear Schrödinger equation for modulated wave trains; and the significance of three-dimensional disturbances in shear flow instability and transition.

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Khan, N. A., and F. Naz. "Three dimensional flow and mass transfer analysis of a second grade fluid in a porous channel with a lower stretching wall." International Journal of Applied Mechanics and Engineering 21, no. 2 (May 1, 2016): 359–76. http://dx.doi.org/10.1515/ijame-2016-0022.

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AbstractThis investigation analyses a three dimensional flow and mass transfer of a second grade fluid over a porous stretching wall in the presence of suction or injection. The equations governing the flow are attained in terms of partial differential equations. A similarity transformation has been utilized for the transformation of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are given by the homotopy analysis method (HAM). A comparative study with the previous results of a viscous fluid has been made. The convergence of the series solution has also been considered explicitly. The influence of admissible parameters on the flows is delineated through graphs and appropriate results are presented. In addition, it is found that instantaneous suction and injection reduce viscous drag on the stretching sheet. It is also shown that suction or injection of a fluid through the surface is an example of mass transfer and it can change the flow field.

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Guerbaai, Salah, Mouna Touiker, Kamel Meftah, and Abdeslam Omara. "Numerical Study of Fluid Flow Through a Confined Porous Square Cylinder." Acta Universitatis Sapientiae, Electrical and Mechanical Engineering 11, no. 1 (December 1, 2019): 87–98. http://dx.doi.org/10.2478/auseme-2019-0008.

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Abstract A numerical study is performed to analyze steady state forced convection fluid flow through a confined porous square cylinder. The Darcy-Brinkman-Forchheimer model is adopted for the porous region. The finite volume method and the iterative SIMPLE algorithm are used to solve the governing equations. The results obtained are presented for the streamlines, variation of Nusselt number and drag coefficient for the range of conditions as 5 ≤ Re ≤ 40 and 10−2 ≤ Da ≤ 10−6.

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Bezerra, Wesley De Souza, Antonio Castelo, and Alexandre M. Afonso. "Numerical Study of Electro-Osmotic Fluid Flow and Vortex Formation." Micromachines 10, no. 12 (November 20, 2019): 796. http://dx.doi.org/10.3390/mi10120796.

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The phenomenon of electro-osmosis was studied by performing numerical simulations on the flow between parallel walls and at the nozzle microchannels. In this work, we propose a numerical approximation to perform simulations of vortex formation which occur after the passage of the fluid through an abrupt contraction at the microchannel. The motion of the charges in the solution is described by the Poisson–Nernst–Planck equations and used the generalized finite differences to solve the numerical problem. First, solutions for electro-osmotic flow were obtained for the Phan–Thien/Thanner model in a parallel walls channel. Later simulations for electro-osmotic flow were performed in a nozzle. The formation of vortices near the contraction within the nozzle was verified by taking into account a flow perturbation model.

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Mohd Kasim, Abdul Rahman, Nur Syamilah Arifin, Syazwani Mohd Zokri, Mohd Zuki Salleh, Nurul Farahain Mohammad, Dennis Ling Chuan Ching, Sharidan Shafie, and Noor Amalina Nisa Ariffin. "Convective Transport of Fluid–Solid Interaction: A Study between Non-Newtonian Casson Model with Dust Particles." Crystals 10, no. 9 (September 15, 2020): 814. http://dx.doi.org/10.3390/cryst10090814.

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The Casson model is a fascinating model, which is genuinely recommended for use with fluids of a non-Newtonian type. The conventional model is not capable to represent the Casson model with the suspension of foreign bodies (dust particles). Due to this, the two-phase model for the mixture of Casson model fluid and dust particles is formulated. This study examines the emerging role of dust particles in changing the behavior of Casson model. In particular, two-phase flow of dusty Casson model with modified magnetic field and buoyancy effect under Newtonian heating boundary condition along a vertically stretching sheet is considered. The equations that govern under Casson model, together with dust particles, are reduced to a system of nonlinear ordinary differential equations by employing the suitable similarity variables. These transformed equations are then solved numerically by implementing the Runge–Kutta–Fehlberg (RKF45) method. The numerical results of skin friction coefficient plus Nusselt number are displayed graphically. The results revealed the fluid’s velocity tends to deteriorate due to the existence of dust particles, whilst its temperature is increased. The two-phase flow is one of the mathematical modeling techniques for multiphase flow, where the relationship between the fluid and solid is examined more closely. It is expected that the present findings can contribute to the understanding of the theory of two-phase flow mathematically, which will continue to produce significant research in this field.

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Korib, Kamel, Mohamed ROUDANE, and Yacine Khelili. "Numerical study on characteristics of flow and thermal fields around rotating cylinder." Metallurgical and Materials Engineering 26, no. 1 (April 16, 2020): 71–86. http://dx.doi.org/10.30544/450.

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In this paper, a numerical simulation has been performed to study the fluid flow and heat transfer around a rotating circular cylinder over low Reynolds numbers. Here, the Reynolds number is 200, and the values of rotation rates (α) are varied within the range of 0 < α < 6. Two-dimensional and unsteady mass continuity, momentum, and energy equations have been discretized using the finite volume method. SIMPLE algorithm has been applied for solving the pressure linked equations. The effect of rotation rates (α) on fluid flow and heat transfer were investigated numerically. Also, time-averaged (lift and drag coefficients and Nusselt number) results were obtained and compared with the literature data. A good agreement was obtained for both the local and averaged values.

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Zhou, Yunxu, and Subhash Nandlal Shah. "Theoretical Analysis of Turbulent Flow of Power-Law Fluids in Coiled Tubing." SPE Journal 12, no. 04 (December 1, 2007): 447–57. http://dx.doi.org/10.2118/84123-pa.

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Summary A comprehensive theoretical analysis of turbulent flow of a power-law fluid in coiled tubing was conducted with the approach of boundary layer approximation. Equations of momentum integrals for the boundary layer flow were derived and solved numerically. Based on the results of the numerical analysis, a new friction-factor correlation was developed which is applicable to a wide range of flow behavior index of power-law fluid model. The new correlation was verified by comparing it with the published Ito correlation for the special case of Newtonian fluid. For non-Newtonian fluids, there is also a close agreement between the new correlation and the experimental data from recent full-scale coiled tubing flow experiments. Introduction Many fluids that are pumped through coiled tubing are typically non-Newtonian fluids, such as polymer gels or drilling muds. Understanding their flow behavior and being able to accurately predict frictional pressure through coiled tubing are essential for better operations design. A recent literature review (Zhou and Shah 2004) indicates that though there are numerous studies on the flow of Newtonian fluids in coiled pipes, there is, however, very little information with regard to the corresponding flow of non-Newtonian fluids. Among the various approaches of investigating fluid flow in coiled pipes, there is one important method called boundary layer approximation analysis. It is especially useful for high-Dean (1927, 1928) number flows where the effect of secondary flow is largely confined in a thin boundary layer adjacent to the pipe wall (Dean number is commonly defined as: (equation). According to this approach, the tubing cross-section can be divided into two regions: the central in viscid core, and the thin viscous boundary layer. This leads to much simplified flow equations for high-Dean number flows in curved geometry. This approach has been used by a number of researchers, for example, by Adler (1934), Barua (1963), Mori and Nakayama (1965), and Ito (1959, 1969) for Newtonian fluids, and by Mashelkar and Devarajan (1976, 1977) for non-Newtonian fluids. In a previous attempt, Zhou and Shah (2007) applied the method of boundary layer approximation to solve the laminar flow problem of a power-law fluid in coiled tubing and obtained an empirical friction-factor correlation based on the theoretical analysis and numerical solutions. In the present study, we take the same analysis approach but consider the turbulent flow of a power-law fluid in coiled tubing. A friction-factor correlation for turbulent flow in coiled tubing is developed, and its validity is evaluated with a published correlation (Ito 1959) and recent full-scale experimental data.

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Ansari, Ali R., Maya K. Mitkova, and Abdul M. Siddiqui. "Couette - Poiseuille Two-Layer Flow of a Third Grade Fluid." Applied Mechanics and Materials 390 (August 2013): 103–10. http://dx.doi.org/10.4028/www.scientific.net/amm.390.103.

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The two-layer Couette-Poiseuille flow of a third grade fluid is examined. The problem is reduced to solving nonlinear differential equations governing the motion of the two immiscible fluids in case of different thickness of layers. The solutions are used to study the effect of the third grade material parameter on the velocity profiles. The investigation focuses especially on the location of the velocity maximum as function of the viscosity and third grade material constant.

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Bellahcene, Lahcene, Djamel Sahel, and Aissa Yousfi. "Numerical Study of Shell and Tube Heat Exchanger Performance Enhancement Using Nanofluids and Baffling Technique." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 80, no. 2 (February 12, 2021): 42–55. http://dx.doi.org/10.37934/arfmts.80.2.4255.

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The aim of this work is to investigate the forced convective heat transfer phenomena and fluid flows of water-based Al2O3 nanofluids in the baffled shell and tubes heat exchanger (STHE). Water as a hot fluid flows in the side of the tubes, and Al2O3 nanofluids as cooling fluid flow in the shell side. Numerical investigations have been carried out based on the continuity, momentum, and energy equations which are solved by using the finite element method with the help of the COMSOL 5.4 CFD software. The obtained results were presented by average Nusselt number, streamlines, isotherms, and various physical parameters which are a volumetric fraction of nanoparticles (1%? Cv ?3%). The results are found that the heat transfer increases with the rise of inlet velocity and volume fraction. In addition, the presence of baffles inside tubular heat exchangers can create a better mixture of fluids which is augmenting heat transfer execution. The choice of these parameters is important to get the maximum improvement of heat transfer with minimum entropy consumption.

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Javed, T., and A. Ghaffari. "Numerical Study of Non-Newtonian Maxwell Fluid in the Region of Oblique Stagnation Point Flow over a Stretching Sheet." Journal of Mechanics 32, no. 2 (December 22, 2015): 175–84. http://dx.doi.org/10.1017/jmech.2015.94.

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AbstractIn this article, a numerical study is carried out for the steady two-dimensional flow of an incompressible Maxwell fluid in the region of oblique stagnation point over a stretching sheet. The governing equations are transformed to dimensionless boundary layer equations. After some manipulation a system of ordinary differential equations is obtained, which is solved by using parallel shooting method. A comparison with the previous studies is made to show the accuracy of our results. The effects of involving parameters are discussed in detail and the streamlines are drawn to predict the flow pattern of the fluid. It is observed that increasing velocities ratio parameter (ratio of straining to stretching velocity) helps to decrease the boundary layer thickness. Furthermore, the velocity of fluid increases by increasing the obliqueness parameter.

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Aliannejadi, Zohreh. "Analytical Investigation of Nusselt Number and Skin Friction of Fluid Flow Over a Stretching Sheet Using Optimal Homotopy Asymptotic Method." Advanced Science, Engineering and Medicine 12, no. 5 (May 1, 2020): 657–61. http://dx.doi.org/10.1166/asem.2020.2570.

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In many cases such as production of metal sheets, the behavior of fluid flow and heat transfer in the neighborhood of a hot plate is very important. The CFD simulation of fluid flow is a widespread study that reveals detail information about the fluid flow in the calculated domain. In this study, the flow and heat transfer of a specific fluid in the above area of a stretching plate is examined analytically to find the variation of skin friction and Nusselt number. For this purpose, the similarity transformations can be employed to achieve the ordinary differential equations from the governing partial differential equations. The optimal homotopy asymptotic method (OHAM) is used to solve the ordinary differential equations which is applicable in solving of nonlinear equations. The effects of magnetic field on the analytical results from solving the equations are evaluated in detail. It is found that the thickness of the flow boundary layer decreases and the thickness of the thermal boundary layer increases by increasing in the magnetic field. Moreover, the Nusselt number is lower and skin friction is higher for the higher values of the magnetic field.

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Journal articles on the topic 'Equations in fluid flow study'

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