Magnetogravitational Instability of a Walters B’ Viscoelastic Rotating Anisotropic Heat‐Conducting Fluid in Brinkman Porous Medium

Instability of a Walters B′ viscoelastic rotating anisotropic heat‐conducting plasma with modified Chew–Goldberger–Low equations is discussed under a gravitational force and uniform magnetic field in a Brinkman porous medium. The general dispersion relation is obtained using normal mode analysis, and it is reduced for propagation parallel and perpendicular to the direction of the magnetic field. These conditions are discussed for the axis of rotation along and perpendicular to the magnetic field. The stability of the system in the two directions is discussed both analytically and numerically. The numerical analysis is performed to show the effects of various parameters, namely, rotation, pressure anisotropy, medium permeability, porosity of porous medium, kinematic viscosity, kinematic viscoelasticity, and heat flux on the stability of the considered system. The Jeans condition of gravitational instability is obtained for both cases of propagation. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res 43(2): 93‐112, 2014; Published online 31 July 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21064     

Analysis of Flow and Heat Transfer in a Parallelogram Non‐Uniformly Heated Enclosure Filled with Porous Medium

The flow and heat transfer in a parallelogram enclosure filled with a porous medium is analyzed numerically. The heated bottom wall has a sinusoidal temperature distribution and side walls cooled isothermally while the upper wall is well insulated. Dimensionless Darcy law and energy equations are solved using the finite difference method along with the corresponding boundary condition. Computations were carried out for four inclination angles of side walls (γ = 45°, 60°, 75°, 90°) with different Rayleigh numbers (100≤Ra≤1000) and their effects on the flow field and heat transfer are discussed. It is found that the inclination angle has a significant effect on flow pattern and heat transfer and an increase in the angle leads to a decrease in the strength of the right vortex. The study also revealed that as the Rayleigh number increases at γ = 45°, another (third) vortex develops along the left wall and its strength enhances with Rayleigh number. At the end, a correlation is extracted from the numerical data which represents the relation between the Nusselt number, inclination angle, and the Rayleigh number. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 497–506, 2010; Published online in Wiley Online Library ( wileyOnlinelibrary.com ). DOI 10.1002/htj.20312     

Numerical Analysis of the Effects of Selected Geometrical Parameters and Fluid Properties on MHD Natural Convection Flow in an Inclined Elliptic Porous Enclosure with Localized Heating

Magnetohydrodynamic (MHD) natural convection flow and associated heat convection in an oriented elliptic enclosure has been investigated with numerical simulations. A magnetic field was applied to the cylindrical wall of the configuration, the top and bottom walls of the enclosure were circumferentially cooled and heated, respectively, while the extreme ends along the cross‐section of the elliptic duct were considered adiabatic. The full governing equations in terms of continuity, momentum, and energy transport were transformed into nondimensional form and solved numerically using finite difference method adopting Gauss–Seidel iteration technique. The selected geometrical parameters and flow properties considered for the study were eccentricity (0, 0.2, 0.4, 0.6, and 0.8), angle of inclination (0°, 30°, 60°, and 90°), Hartmann number (0, 25, and 50), Grashof number (10⁴, 10⁵, and 10⁶), and Darcy number (10^?3, 10^?4, and 10^?5). The Prandtl number was held constant at 0.7. Numerical results were presented by velocity distributions as well as heat transfer characteristics in terms of local and average Nusselt numbers (i.e., rate of heat transfer). The optimum heat transfer rate was attained at e value of 0.8. Also, the heat transfer rate increased significantly between the angles of inclination 58° and 90°. In addition, Hartmann number increased with decreased heat transfer rate and flow circulation. A strong flow circulation (in terms of velocity distribution) was observed with increased Grashof and Darcy numbers. The combination of the geometric and fluid properties therefore can be used to regulate the circulation and heat transfer characteristics of the flow in the enclosure.     

Numerical Simulation of Natural Convection in a Parallelogrammic Enclosure Containing Volumetric Heat Source with Non‐uniformly Heated Left Sidewall

The influence of the external Rayleigh number, inclination angle, and internal Rayleigh number on natural convection within an air‐filled parallelogrammic enclosure containing a volumetric source has been investigated numerically. The left sidewall of the enclosure is subjected to a non‐uniformly hot temperature and the right sidewall experiences a uniform cold temperature while the remaining top and bottom walls are kept adiabatic. The physical problems are represented mathematically by various sets of governing equations along with the corresponding boundary conditions. Buoyancy forces are taken into account during the analysis of the present investigation. By using the finite volume method, the dimensionless governing equations are discretized numerically based on a non‐uniform collocated grid system. Results are obtained for a wide range of external Rayleigh numbers varying from 10³ to 10⁶ with internal Rayleigh numbers varying from (0) to (10⁸) while the left sidewall from vertical is varied as 0, 30, –30, 60, and ?60^°, respectively. In the present study, the obtained results are presented in terms of streamlines, isotherms, and average Nusselt number along the hot and cold sidewalls. Two pairs of rotating vortices are observed due to the non‐uniform heating process while the shape of this rotating vortices is sensitive to the inclination angle. Furthermore, the flow field circulation and the average Nusselt number increase remarkably with the increase in the external Rayleigh number. The results of the present work are compared with other published results and give excellent agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 542–560, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21096     

Onset of Darcy‐Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer with Internal Heat Source

The onset of Darcy‐Brinkman convection in a binary viscoelastic fluid‐saturated sparsely packed porous layer with an internal heat source is studied using both linear and nonlinear stability analyses. The Oldroyd‐B model is employed to describe the rheological behavior of binary fluid. An extended form of the Darcy‐Oldroyd law incorporating Brinkman's correction and time derivative is used to describe the flow through a porous layer. The onset criterion for stationary, oscillatory, and finite amplitude convection is derived analytically. There is a competition between the processes of thermal diffusion, solute diffusion, and viscoelasticity that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effect of internal Rayleigh number, relaxation and retardation parameters, solute Rayleigh number, Darcy number, Darcy‐Prandtl number, and Lewis number on the stability of a system is investigated and is shown graphically. The nonlinear theory based on the truncated representation of the Fourier series method is used to find heat and mass transfer. The transient behavior of the Nusselt and Sherwood numbers is obtained using numerical methods. Some known results are recovered for the particular cases of the present study. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(8): 676–703, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21056     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

CHF in a circumferentially non‐uniformly heated tube under low‐pressure and low‐mass‐flux condition (inclined upward flow)

Most investigations on forced convective boiling have been conducted by using uniformly heated round tubes under a vertical upward flow condition, although the actual system has a non‐uniformly heated condition with several tube orientations. The non‐uniformity of the heat flux and tube inclination causes the liquid film distribution, which in turn affects the critical heat flux. In this investigation, the flow and heat‐transfer characteristics were experimentally investigated under non‐uniformly heated conditions along the circumferential direction with a 45° tube inclination. In the experiment, CHF was measured by using two different heated lengths, i.e., 900 and 1800 mm. The experimental results showed a unique tendency of CHF caused by the interrelationship of the non‐uniform heat flux distribution, the tube inclination, and liquid film redistribution. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20333     

Soret Effect on Darcy–Brinkman Convection in a Binary Viscoelastic Fluid‐Saturated Porous Layer

A linear and weakly nonlinear stability analyses is performed to study the onset of Darcy–Brinkman double diffusive convection in a binary viscoelastic fluid‐saturated porous layer in the presence of the Soret effect. The modified Darcy–Brinkman–Oldroyd model including the time derivative term is employed for the momentum equation. The expressions for stationary, oscillatory, and finite amplitude Rayleigh number are obtained as a function of the governing parameters. There is a competition between the processes of the Soret coefficient, viscoelasticity, thermal diffusion, and solute diffusion that causes the convection to set in through an oscillatory mode rather than a stationary mode. The effects of the Soret parameter, Darcy number, relaxation and retardation parameters, and Darcy–Prandtl number on the stationary, oscillatory, and finite amplitude convection is shown graphically. The weakly nonlinear theory is based on truncated representation of the Fourier series method and is used to find the Nusselt and Sherwood numbers. Further, the transient behavior of the Nusselt and Sherwood numbers is investigated by solving the nonlinear system of ordinary differential equations numerically using the Runge–Kutta method. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(4): 297–320, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21076     

Mixed Convection Over a Vertical Plate in a Doubly Stratified Fluid‐Saturated Non‐Darcy Porous Medium with Cross‐Diffusion Effects

The present article investigates the influence of Dufour and Soret effects on mixed convection heat and mass transfer over a vertical plate in a doubly stratified fluid‐saturated porous medium. The plate is maintained at a uniform and constant wall heat and mass fluxes. The Darcy–Forchheimer model is employed to describe the flow in porous medium. The nonlinear governing equations and their associated boundary conditions are initially transformed into dimensionless forms. The resulting system of nonlinear partial differential equations is then solved numerically by the Keller‐box method. The variation of the dimensionless velocity, temperature, concentration, heat, and mass transfer rates for different values of governing parameters involved in the problem are analyzed and presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21114     

Soret and Dufour Effects on Non‐Darcy Free Convection in a Power‐Law Fluid in the Presence of a Magnetic Field and Stratification

In this article, effects of Soret and Dufour on free convection heat and mass transfer along a vertical plate embedded in a doubly stratified power‐law fluid‐ saturated non‐Darcy porous medium in the presence of a magnetic field is considered. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations, with the location along the plate as a parameter and then solved numerically. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 592–606, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21098     

Solutal Dispersion and Viscous Dissipation Effects on Non‐Darcy Free Convection Over a Cone in Power‐Law Fluids

The effects of viscous dissipation and solutal dispersion on free convection about an isothermal vertical cone with a fixed apex half angle, pointing downwards in a power‐law fluid‐saturated non‐Darcy porous medium are analyzed. The governing partial differential equations are transformed into partial differential equations using non‐similarity transformation. The resulting equations are solved numerically using an accurate local non‐similarity method. The accuracy of the numerical results is validated by a quantitative comparison of the heat and mass transfer rates with previously published results for a special case and the results are found to be in good agreement. The effects of viscous dissipation, solutal dispersion, and/or buoyancy ratio on the velocity, temperature, and concentration field as well as on the heat and mass transfer rates are illustrated, by insisting on the comparison between pseudo‐plastic, dilatant, and Newtonian fluids. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 476–488, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21095     

Free Convective Flow of Pseudo‐Plastic and Newtonian Fluid Past a Convectively Heated Vertical Plate in a Darcian Porous Medium with Heat Generation/Absorption

We study the effect of thermal convective boundary condition and yield stress on free convection heat transfer for a pseudo‐plastic and Newtonian fluid past a permeable vertical flat plate which is embedded in a Darcian porous medium in the presence of heat generation/absorption numerically. Instead of using similarity transformations available in the literature, we have developed them by one point transformation and hence transform the governing boundary layer equations into corresponding similarity equations. The resulting similarity equations were solved using Runge–Kutta–Fehlberg fourth fifth (RKF45) order numerical method. The effect of the governing parameters, namely the power index of pseudo‐plastic fluids n, the rheological parameter Ω, heat generation/absorption parameter Q, suction/injection parameter , and the convective heat parameter B on the dimensionless velocity, the temperature and the heat transfer rates were investigated. A close agreement is found between our results and published results. Our present study finds application in printing and polymer industries and fluid phenomena associated with concentrated suspensions.     

Numerical Investigation of Nanofluid Mixed‐Convection Flow in the Entrance Region of a Vertical Channel Partially Filled with Porous Medium

In this article, transient two‐dimensional mixed convection of nanofluids in the entrance region of a vertical channel has been studied carefully. The geometry under consideration consisted of a parallel‐plate channel partly filled with a porous medium with a constant wall temperature. In the free flow region, the two‐dimensional flow field has been governed by the Navier–Stokes equations. The general formulation of the momentum equations accounting for the inertial and the viscous effects in the presence of a porous medium has been used. Viscous dissipation effects have also been incorporated in the thermal energy equation. Effects of Brownian diffusion and thermophoresis have also been included for nanoparticles in the nanofluid. The governing equations have been given in terms of the stream function‐vorticity formulation and have been non‐dimensionalized and then solved numerically subject to appropriate boundary conditions. The characteristics of the flow and temperature fields have been presented in the terms of mixed‐convection parameter (GR), Brinkman number (Br), Darcy number (Da), Lewis number (Le), and other important parameters. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 607–627, 2014; Published online 21 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21099     

Flow and Heat Transfer of Maxwell Fluid Over an Exponentially Stretching Sheet: A Non‐similar Solution

In this investigation, the boundary layer flow and heat transfer analysis in a Maxwell fluid over an exponentially continuous moving sheet are studied. The transformed boundary layer equations are solved numerically for a non‐similar solution using a shooting method with the Runge–Kutta algorithm. The purpose of this article is to look into the influence of the Deborah number on the velocity, temperature, and Nusselt number. The obtained results show that an increase in the Deborah number decreases the fluid velocity and boundary layer thickness. On the other hand, it increases the temperature and thermal boundary layer thickness. It is also found that the numerical results are in excellent agreement with the previous existing results for the case of a Newtonian fluid (λ = 0). © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(3): 233–242, 2014; Published online 30 August 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21074     

A Mathematical Study for Laminar Boundary‐Layer Flow,Heat, and Mass Transfer of a Jeffrey Non‐Newtonian Fluid Past a Vertical Porous Plate

In this article, we investigate the nonlinear steady‐state boundary‐layer flow, heat and mass transfer of an incompressible Jeffrey non‐Newtonian fluid past a vertical porous plate. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a versatile, implicit finite‐difference technique. The numerical code is validated with previous studies. The influence of a number of emerging non‐dimensional parameters, namely, Deborah number (De), Prandtl number (Pr), ratio of relaxation to retardation times (λ), Schmidt number (Sc), and dimensionless tangential coordinate (ξ) on velocity, temperature, and concentration evolution in the boundary layer regime are examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate, mass transfer rate, and local skin friction are also investigated. It is found that the velocity is reduced with increasing Deborah number whereas temperature and concentration are enhanced. Increasing λ enhances the velocity but reduces the temperature and concentration. The heat transfer rate and mass transfer rates are found to be depressed with increasing Deborah number, De, and enhanced with increasing λ. Local skin friction is found to be decreased with a rise in Deborah number whereas it is elevated with increasing λ. And an increasing Schmidt number decreases the velocity and concentration but increases temperature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21111     

Elucidating the Effects of Cu‐Nanoparticles in a Porous Medium vis‐à‐vis Heat Transfer Phenomena

In this paper, a numerical simulation technique is developed to investigate the qualitative and quantitative behaviour of Cu‐nanoparticles in a porous medium vis‐a‐vis the heat transfer enhancements—buoyancy driven flow in a two‐dimensional square cavity, with moving walls is presented. The model utilizes the finite volume approach to solve the Brinkman–Darcy equations for Cu‐nanoparticles in a porous media. Discretization is carried out for convective and diffusive fluxes using Quadratic Upwind Interpolation for Convective Kinematics (QUICK) and central difference schemes, respectively. Tri‐Diagonal Matrix Algorithm is invoked to solve the set of algebraic equations. The Darcy number (Da), Prandtl number (Pr), and volume fraction (χ) are varied from 10^?3 to 10^?1, 3 to 7, and 0% to 20%, respectively. Insight into the cause of variations in isotherms, streamlines, Nusselt number (Nu), and mid‐plane velocities is explicated. The present numerical results are compared with the existing literature and found to be in good agreement. Even though nanoparticles slightly hinder the activity of the fluid, they can augment the average Nu by 90% for Pr = 7, Da = 0.1, and χ = 20% as compared to the absence of nanoparticles. Their efficacy is more prominent for flows with higher Da and Pr. Quantitative values for Nu were obtained for various combinations of Pr, Da, and χ.     

Numerical Simulation of Mixed‐Convection Flow in a Lid‐Driven Porous Cavity Using Different Nanofluids

In this study, the effect of mixed convection flow in a lid‐driven porous cavity using different nanoparticles, such as aluminum oxide (Al ₂ O ₃), copper (Cu), silver (Ag), and titanium dioxide (TiO ₂), are investigated. The base fluid is considered as water. The transport equations are solved numerically by finite volume method on a co‐located grid arrangement using quadratic upwind interpolation for convective kinematics (QUICK) scheme. A two‐dimensional square cavity is considered for the present investigation whose horizontal walls are insulated. The cold left wall is moving up and hot right wall is moving down with equal velocities. The variations of temperature distribution, stream function, and Nusselt number (Nu) are analyzed at constant Grashof numbers (Gr), Richardson numbers (Ri), and Darcy numbers (Da) as 1 × 10 ⁴, 100, and 0.1, respectively, for different nanoparticles. The present results are validated by favorable comparison with previously published literature. The predicted results clearly indicate that the presence of nanoparticles inside the porous media enhances the heat transfer significantly. It is observed from the numerical results that the average Nusselt numbers (Nu) were found to increase linearly with an increase in volume fraction (χ). For the given volume fraction, the average Nu is maximum for a silver‐based nanoparticle. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 1–16, 2014; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21075     

Flow and Heat Transfer Characteristics of Two‐Phase Fluid in Inclined Pipes on a Rotation Platform

A rotating platform was used to create dynamic load, and the mixture air–water two‐phase flow and boiling steam–water two‐phase flow were obtained in an inclined test pipe. By changing the parameters, such as inclination of the test pipe, rotational speed, inlet temperature, flow rate, and so on, the experiments for two‐phase flow in the pipe at inclination of 0°, 45°, and 66° were conducted, respectively. The effects of acceleration and inclination on their flow and heat transfer characteristics were investigated. The two‐phase flow patterns in inclined pipes under rotation conditions were caught with a video camera. The images show that the impact mixed flow and churn flow were found in this research. The results show that the acceleration and pipe inclination significantly influence the flow characteristic and heat transfer of the two‐phase pipe flow. As the directions of the dynamic load and the gravity are opposite to the flow direction, the greater the dynamic load and inclination, the higher the pressure drop and the heat emission, and the lower the flow rate, the void fraction, and the fluid temperature. Therefore, the dynamic load and gravity will improve the flow resistance, enhance heat emission and reduce the heat gained by the fluid.     

Effects of Thermal‐Diffusion,Diffusion‐Thermo,and Space Porosity on MHD Mixed Convective Flow of Micropolar Fluid in a Vertical Channel with Viscous Dissipation

This paper examines thermal‐diffusion and diffusion‐thermo effects on the fully developed MHD flow of a micropolar fluid through a porous space in a vertical channel with asymmetric wall temperatures and concentrations. The homotopy analysis method (HAM) is adopted to obtain the approximate analytical solution for the velocity, micro‐rotation, temperature, and concentration field. The convergence and the accuracy of the solutions are discussed. The role of pertinent parameters on the heat and mass transfer characteristics of the flow are presented graphically. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(6): 561–576, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21100     

Finite Element Analysis of Radiative Mixed Convection Magneto‐Micropolar Flow in a Darcian Porous Medium with Variable Viscosity and Convective Surface Condition

A mathematical study is presented for the collective influence of the buoyancy parameter, convective boundary parameter and temperature dependent viscosity on the steady mixed convective laminar boundary flow of a radiative magneto‐micropolar fluid adjacent to a vertical porous stretching sheet embedded in a Darcian porous medium. The fluid viscosity is assumed to vary as an inverse linear function of temperature. Using appropriate transformations, the governing equations of the problem under consideration are transformed into a system of dimensionless nonlinear ordinary differential equations, which are then solved with the well‐tested, efficient finite element method. The results obtained are depicted graphically to illustrate the effect of the various important controlling parameters on velocity, microrotation, and temperature functions. The skin friction coefficient, wall couple stress, and the rate of heat transfer have also been computed and presented in tabular form. Comparison of the present numerical results with earlier published data has been performed and the results are found to be in good agreement, thus validating the accuracy of the present numerical code. The study finds applications in conducting polymer flows in filtration systems, trickle bed magnetohydrodynamics in chemical engineering, electro‐conductive materials processing, and so on.