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     

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     

Mixed Convection Effect on Melting from a Vertical Plate Embedded in Porous Medium with Soret and Dufour Effects

The present work analyzed the impact of mixed convection on melting from a vertical flat plate embedded in porous medium in the presence of Dufour and Soret effects. The partial differential equations governing the problem under consideration have been transformed by a similarity transformation into a system of ordinary differential equation which is solved numerically by Runge–Kutta–Gill methods. Dimensionless velocity, temperature, and concentration profiles are presented graphically for various values of the Dufour number (Df), Soret number (Sr), melting parameter (M), and buoyancy parameter (Gr/Re). During the investigation, it was found that the melting phenomenon decreases the local Nusselt number and local Sherwood number at the solid–liquid interface. Also, it is interesting to note that the velocity as well as temperature increases while the concentration decreases with an increase in the Dufour number Df (or simultaneous decrease in the Soret number Sr). © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 667–676, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21113     

g‐Jitter–Induced Electrothermoconvection in a Dielectric Fluid Saturated Porous Layer

This paper presents linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated sparsely packed porous layer subject to the combined effect of time‐periodic gravity modulation (GM) and an AC electric field. In the domain of linear theory, the critical stability parameters are computed by the regular perturbation method in the form of a perturbation series in powers of frequency of modulation. The local nonlinear theory based on the truncated Fourier series method gives information on convection amplitudes and heat transfer. The principle of the exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system, several qualitative results on stability are discussed. The sensitive dependence of the solution of a Lorenz system of electrothermal convection subject to the choice of initial conditions points to the possibility of chaos. Low‐frequency g‐jitter is found to have a significant stabilizing influence, which is in turn diminished by an imposed AC electric field. The role of sparseness of the porous layer, viscosity ratio, and normalized porosity on the stability criterion and on heat transport is determined.     

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     

Soret and Dufour effects on MHD flow of viscoelastic fluid past an infinite vertical stretching sheet

Heat and mass transmission taking place in a magnetohydrodynamics fluid of substantial viscosity via a permeable object has been currently a subject of study inviting research. This transmission takes place along an infinite expanding vertical surface showing Soret and Dufour effects. Differential forms of nonlinear nature such as energy, momentum, and equations defining concentration are ascertained by means of similarity transformation with the existing buoyancy force, and by making use of the homotopy analysis method, the equations have been analytically resolved. The impacts arising out of applied factors on temperature, velocity, and concentration forms have been appropriately designed and established.     

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     

Non－Darcian and Anisotropic Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

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Soret and Dufour effects on free convection boundary layer over a vertical cylinder in a saturated porous medium

This paper deals with an analysis of the Soret and Dufour effects on the boundary layer flow due to free convection heat and mass transfer over a vertical cylinder in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A suitable coordination transformation is used to derive the similar governing boundary-layer equations, and the cubic spline collocation method is then employed to solve the similar governing boundary-layer equations. The variation of the Nusselt number and the Sherwood number with the Dufour parameter and the Soret parameter for various Lewis numbers and buoyancy ratios have been presented in this work. Results show that an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number. The local Nusselt number tends to decrease as the Dufour parameter is increased. Moreover, an increase in the Lewis number enhances the effect of the Dufour parameter on the local Nusselt number.     

Soret and Dufour effects on natural convection heat and mass transfer from a vertical cone in a porous medium

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a downward-pointing vertical cone in a porous medium saturated with Newtonian fluids with constant wall temperature and concentration. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local Nusselt number tends to decrease as the Dufour parameter is increased. The effect of the Dufour parameter on the local Nusselt number becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret number leads to a decrease in the local Sherwood number and an increase in the local Nusselt number.     

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     

Heat and Mass Transfer by Mixed Convection from a Vertical Slender Cylinder with Chemical Reaction and Soret and Dufour Effects

This work is focused on the study of heat and mass transfer by mixed convection over a vertical slender cylinder in the presence of chemical reaction and thermal‐diffusion and diffusion‐thermo effects. The resulting equations have the property whereby they reduce to various special cases previously considered in the literature. An adequate implicit, tri‐diagonal finite‐difference scheme is employed for the numerical solution of the obtained equations. Various comparisons with previously published work are performed and the results are found to be in excellent agreement. Representative results for the local skin‐friction coefficient, local Nusselt number, and the local Sherwood number illustrating the influence of the surface transverse curvature parameter, Richardson number, concentration to thermal buoyancy ratio, Schmidt number, chemical reaction, and the Dufour and Soret numbers are presented and discussed. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 618–629, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21045     

Soret and Dufour effects on natural convection boundary layer flow over a vertical cone in a porous medium with constant wall heat and mass fluxes

This work studies the Soret and Dufour effects on the boundary layer flow due to natural convection heat and mass transfer over a vertical cone in a fluid-saturated porous medium with constant wall heat and mass fluxes. A similarity analysis is performed, and the obtained similar equations are solved by the cubic spline collocation method. The effects of the Dufour parameter, Soret parameter, Lewis number, and buoyancy ratio on the heat and mass transfer characteristics have been studied. The local surface temperature tends to increase as the Dufour parameter is increased. The effect of the Dufour parameter on the local surface temperature becomes more significant as the Lewis number is increased. Moreover, an increase in the Soret parameter leads to an increase in the local surface concentration and a decrease in the local surface temperature.     

Effect of double stratification on mixed convection heat and mass transfer from a vertical surface in a fluid‐saturated porous medium

This paper presents the mixed convection heat and mass transfer near a vertical surface in a stratified porous medium using an integral method. The conservation equations that govern the problem are reduced to a system of coupled non‐linear ordinary differential equations, which is then reduced into a single algebraic equation using exponential profiles for the temperature and concentration. The results for heat and mass transfer rates in terms of Nusselt and Sherwood number are presented for a wide range of governing parameters like the buoyancy ratio (N), Lewis number (Le), flow driving parameter (Ra/Pe), in addition to both thermal and solutal parameters (S and R). The results indicate that the stratification effects have considerable influence on both the heat and mass transfer rates. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20300     

Mono‐diffusive Hadley‐Prats flow in a horizontal porous layer subject to variable gravity and internal heat generation

Analysis of internal heated and gravity effect on the onset of Hadley‐Prats flow in a horizontal porous layer with inclined temperature gradients is investigated using the linear and nonlinear instability analysis. The transformed eigenvalue problem is evaluated numerically to find the eigenvalue, which is treated as a vertical thermal Rayleigh number (R_z). It is evaluated by applying shooting and Runge‐Kutta method. Also, the critical R_z is investigated for different parameters governing the flow. A theoretical study is made to understand the influence of gravity field on the mechanism of mono‐diffusive instability of Hadley‐Prats convection in a fluid saturated horizontal porous layer. Nonlinear stability is evaluated by using energy functional. The comparison between linear and nonlinear instability results are presented and it is noted that linear theory of instability may not be useful to capture the complete picture of stability and instabilities may arise before one attains the linear stability threshold. This subcritical instability region is identified between the linear and energy thresholds in the parameter space of the problem considered.     

Double‐Diffusive Convective Transport in a Nanofluid‐Saturated Porous Layer with Cross Diffusion and Variation of Viscosity and Conductivity

The onset of double‐diffusive nanofluid convection in a fluid‐saturated horizontal porous layer is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. The Darcy model has been used for the porous medium, while the nanofluid incorporates the effects of Brownian motion along with thermophoresis. The nanofluid is assumed to be diluted and this enables the porous medium to be treated as a weakly heterogeneous medium with variation in the vertical direction of conductivity and viscosity. In addition, the thermal energy equation includes regular diffusion and cross diffusion terms. The linear stability analysis is based on the normal mode technique, while for nonlinear analysis, minimal representation of the truncated Fourier series representation involving only two terms has been used. It is found that for the stationary mode the Soret parameter, Dufour parameter, viscosity ratio, and conductivity ratio have a stabilizing effect, while the solutal Rayleigh number destabilizes the system. For the oscillatory mode, the Soret parameter, Dufour parameter, and viscosity ratio have a stabilizing effect while the solutal Rayleigh number and conductivity ratio destabilize the system. For steady finite amplitude motions, the heat and mass transport decreases with an increase in the values of the Dufour parameter and solutal Rayleigh number. The Soret parameter enhances the solute concentration Nusselt number while it retards the thermal Nusselt number and concentration Nusselt number. The viscosity ratio and conductivity ratio enhances the heat and mass transports. We also study the effect of time on transient Nusselt numbers which is found to be oscillatory when time is small. However, when time becomes very large, all three transient Nusselt values approach a steady value. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 628–652, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21102     

Effect of anisotropic permeability on double‐diffusive bidisperse porous medium

The model of thermosolutal convection in a fluid‐saturated bidisperse porous medium of Darcy type is studied in this paper. The permeability is allowed to be horizontally isotropic for both the macro‐ and microphases. The linear instability and nonlinear stability are analyzed by taking the Soret effect into account. Furthermore, the effect of anisotropy parameter, Soret coefficient, and other physical parameters on the stability of the system are investigated. It is shown that the linear instability boundaries and the energy stability boundaries do not coincide when the layer is heated and salted from below, where a region of potential subcritical instability occurs. The results reveal that the horizontal to vertical permeability ratio plays a crucial role in the stability of the system. It is also observed that for large values of the salt Rayleigh number, the onset of thermal convection is more likely to be via oscillatory convection rather than stationary convection. Furthermore, the onset of stationary convection is significantly influenced by the presence of the Soret coefficient.     

Soret and Dufour effects on free convection boundary layers of non-Newtonian power law fluids with yield stress in porous media over a vertical plate with variable wall heat and mass fluxes

This work studies the Soret and Dufour effects on the free convection boundary layers over a vertical plate with variable wall heat and mass fluxes in a porous medium saturated with a non-Newtonian power law fluid with yield stress. The governing equations are transformed into a dimensionless form by the similarity transformation and then solved by a cubic spline collocation method. Results are presented for the local surface temperature and concentration for various parameters of the power law fluid with yield stress in porous media. An increase in the power law exponent decreases the local surface temperature and concentration, thus increasing the local Nusselt and Sherwood numbers. An increase in the Soret parameter tends to increase the local surface concentration, thus decreasing the local Sherwood number. Moreover, increasing the Dufour number increases the surface temperature and thus decreases the local Nusselt number.     

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     

Soret and Dufour effects on heat and mass transfer by natural convection from a vertical truncated cone in a fluid-saturated porous medium with variable wall temperature and concentration

This work studies the Soret and Dufour effects on the natural convection heat and mass transfer near a vertical truncated cone with variable wall temperature and concentration in a fluid-saturated porous medium. A coordinate transform is used to obtain the nonsimilar governing equations, and the transformed boundary layer equations are solved by the cubic spline collocation method. Results for local Nusselt number and the local Sherwood number are presented as functions of Soret parameters, Dufour parameters, surface temperature and concentration exponents, buoyancy ratios, and Lewis numbers. Results show that increasing the Dufour parameter tends to decrease the local Nusselt number, while it tends to increase the local Sherwood number. An increase in the Soret number leads to an increase in the Nusselt number and a decrease in the Sherwood number from a vertical truncated cone in a fluid-saturated porous medium. The local Nusselt number and the local Sherwood number of the truncated cones with higher surface temperature and concentration exponents are higher than those with lower exponents.