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.     

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.     

An integral approach for hydromagnetic natural convection heat and mass transfer from vertical surfaces with power-law variation in wall temperature and concentration in porous media

This work uses the integral method to study the heat and mass transfer by natural convection from vertical plates with variable wall temperature and concentration in porous media saturated with an electrically conducting fluid in the presence of a transverse magnetic field. The surface temperature and concentration are assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. The approximate solutions are found to be in reasonable agreement with the similarity solutions. Results are plotted for the local Nusselt number, the local Sherwood number, and the reciprocal of the ratio of the thermal boundary-layer thickness to the concentration boundary-layer thickness. Increasing the power-law exponents tends to increase the local Nusselt number and the local Sherwood number. Increasing the magnetic parameter decreases the local Nusselt number and the local Sherwood number. Moreover, the ratio of the thermal boundary-layer thickness to the concentration boundary-layer thickness increases with the Lewis number, and it also increases with the buoyancy ratio when the Lewis number is not equal to one.     

Numerical simulation of laminar flow development with heat and mass transfer in PEM fuel cell flow channels having oxygen and hydrogen suction at one channel wall

Numerical simulation has been carried out of the fluid flow, heat and mass transfer for the developing laminar flow in polymer electrolyte membrane (PEM) fuel cell cathode and anode flow channels, respectively. Each flow channel is considered to be composed of two parallel walls, one porous (simulating electrode surface) and one non‐porous, or impermeable, wall (simulating bipolar plate surface). Various flow situations have been analyzed, and the local and the averaged friction coefficient, Nusselt number for heat transfer and Sherwood number for mass transfer are determined for various flow conditions corresponding to different stoichiometries, operating current densities and operating pressures of the cell. The effect of suction or injection (blowing) wall boundary condition has also been investigated, corresponding to the oxygen consumption in the cathode and hydrogen consumption in the anode. Correlations for the averaged friction coefficient, Nusselt and Sherwood numbers are developed, which can be useful for PEM fuel cell modeling and design calculations. Copyright © 2010 John Wiley & Sons, Ltd.     

Natural convection with combined heat and mass transfer buoyancy effects in non-homogeneous porous medium

The effect of nonhomogeneity of the medium is investigated in the case of natural convection in a vertical porous layer. The flows are driven by conditions of uniform heat and mass fluxes imposed along the two vertical side walls of the porous layer. It is found that the effect of nonhomogeneity is significant for sharper permeability variations and large Rayleigh numbers, Lewis numbers and absolute buoyancy ratios. Nusselt and Sherwood number estimates in such cases are found to be quite different from that of the homogeneous medium.     

Coupled heat and mass transfer in mixed convection over a wedge with variable wall temperature and concentration in porous media: The entire regime

A boundary layer analysis is used to investigate both heat and mass transfer characteristics of mixed convection about a wedge in saturated porous media under the coupled effects of thermal and mass diffusion. The surface of the wedge is maintained at a variable wall temperature (VWT) and variable wall concentration (VWC). The nonsimilar governing equations are obtained by using a suitable transformation and solved by Keller box method. Numerical results are presented for the local Nusselt number and the local Sherwood number. Increasing the buoyancy ratio N, the exponent of wall temperature/concentration n and the wedge angle parameter λ increases the local Nusselt number and the local Sherwood number. As mixed convection parameter χ varies from 0 to 1, the local Nusselt number and the local Sherwood number decrease initially, reach a minimum in the intermediate value of χ and then increase gradually. It is apparent that the Lewis number has a pronounced effect on the local Sherwood number than it does on the local Nusselt number. Furthermore, increasing the Lewis number decreases (increases) the local heat (mass) transfer rate.     

Double-diffusive natural convection along a vertical wavy truncated cone in non-Newtonian fluid saturated porous media with thermal and mass stratification

This paper studies the double-diffusive natural convection near a vertical wavy truncated cone in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the truncated cone is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary-layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the heat and mass transfer characteristics are studied. Results show that the streamwise distributions of the local Nusselt number and the local Sherwood number are harmonic curves with a wave number twice the wave number of the surface of the vertical wavy truncated cone. An increase in the power-law index leads to a smaller fluctuation of the local Nusselt and Sherwood numbers. Moreover, increasing the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the wavy surface of the vertical truncated cone.     

热质渗透壁面饱和多孔介质通道流动与热质传递的数值模拟

利用数值模拟方法研究了多孔介质中存在温度梯度、浓度梯度并具有热质渗透壁面时的受迫对流对传热传质的影响。采用有限容积法在同位网格上离散控制多孔介质内流体流动与热质传递方程守恒方程(即N-S)，对流项采用二阶精度的QUICK格式，扩散项采用中心差分格式。利用SIMPLE算法求解压力和速度耦合问题。利用所发展的程序研究了在不同孔隙率，不同的温度、浓度边界条件下，流场、温度场和浓度场以及Nu和Sh的变化规律。     

Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus

Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity.     

Free convection heat and mass transfer from a horizontal cylinder of elliptic cross section in micropolar fluids

This work examines the natural convection heat and mass transfer near a horizontal cylinder of elliptic cross section with constant wall temperature and concentration in a micropolar fluid. The transformed governing equations are then solved by the cubic spline collocation method. Results for local Nusselt and Sherwood numbers are presented as functions of vortex viscosity parameter and aspect ratio. The heat and mass transfer rates of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, the heat and mass transfer rates from an elliptical cylinder in Newtonian fluids are higher than those in micropolar fluids.     

Combined heat and mass transfer in natural convection flow from a vertical wavy surface in a power-law fluid saturated porous medium with thermal and mass stratification

This work studies the coupled heat and mass transfer by natural convection near a vertical wavy surface in a non-Newtonian fluid saturated porous medium with thermal and mass stratification. The surface of the vertical wavy plate is kept at constant wall temperature and concentration. A coordinate transformation is employed to transform the complex wavy surface to a smooth surface, and the obtained boundary layer equations are then solved by the cubic spline collocation method. Effects of thermal and concentration stratification parameters, Lewis number, buoyancy ratio, power-law index, and wavy geometry on the important heat and mass transfer characteristics are studied. Results show that an increase in the thermal and concentration stratification parameter decreases the buoyancy force and retards the flow, thus decreasing the heat and mass transfer rates between the fluid and the vertical wavy surface. It is shown that an increase in the power-law index, the thermal stratification parameter, or the concentration stratification parameter leads to a smaller fluctuation of the local Nusselt and Sherwood numbers with the streamwise coordinate. Moreover, the total heat transfer rate and the total mass transfer rate of vertical wavy surfaces are higher than those of the corresponding smooth surfaces.     

Local non-similarity solution of coupled heat—Mass transfer of a flat plate with uniform heat flux in a laminar parallel flow

The coupled heat and mass transfer problem of gas flow over a UHF flat plate with its wall coated with sublimable substance has been solved by local non-similarity method. Considerations have been given also to the effect of non-saturation of the sublimable substance in the oncoming flow and the normal injection velocity at the surface. Analytical results are given for local Nusselt and Sherwood numbers at the various locations.     

Natural convection from a vertical cone in a porous medium due to the combined effects of heat and mass diffusion with non-uniform wall temperature/concentration or heat/mass flux and suction/injection

An analysis has been carried out to study the non-Darcy natural convention flow of Newtonian fluids on a vertical cone embedded in a saturated porous medium with power-law variation of the wall temperature/concentration or heat/mass flux and suction/injection with the streamwise distance x. Both non-similar and self-similar solutions have been obtained. The effects of non-Darcy parameter, ratio of the buoyancy forces due to mass and heat diffusion, variation of wall temperature/concentration or heat/mass flux and suction/injection on the Nusselt and Sherwood numbers have been studied.     

An integral treatment for combined heat and mass transfer by natural convection along a horizontal surface in a porous medium

The heat and mass transfer characteristics of natural convection about a horizontal surface embedded in a saturated porous medium is analyzed. An integral procedure is derived to the heated horizontal surface, where surface temperature and surface concentration are power function of distance from the leading edge of porous plate. Local Nusselt number and local Sherwood number variations in the boundary layer are presented graphically and in the tables for the various values of problem parameters and it is found that the temperature and concentration fields near the plate increases with power law exponent n.     

Finite element analysis of couple stress micropolar nanofluid flow by non‐Fourier's law heat flux model past stretching surface

Numerical analysis has been done to investigate magnetohydrodynamics nonlinear convective flow of couple stress micropolar nanofluid with Catteneo‐Christov heat flux model past stretching surface with the effects of heat generation/absorption term, chemical reaction rate, first‐order slip, and convective boundary conditions. The coupled highly nonlinear differential equation governing the steady incompressible laminar flow has been solved by a powerful numerical technique called finite element method. The impacts of diverse parameters on linear velocity, angular velocity (microrotation), temperature, concentration profile, local skin friction coefficient, local wall couple stress, local Nusselt number, and Sherwood number are presented in graphical and tabular form. The result pointed out that the enhancement in material parameter β increases the velocity of the fluid while the couple stress parameter K has quite opposite effect. Heat and mass transfer rate of the fluid are enhanced by increasing material parameter while couple stress parameter shows the opposite influence. Moreover, heat and mass transfer rate are higher with the Catteneo‐Christov heat flux model than Fourier's law of heat conduction. The accuracy of the present method has been confirmed by comparing with previously published works.     

Integral treatment of coupled heat and mass transfer by natural convection from a cylinder in porous media

This paper deals with the study of the buoyancy induced heat and mass transfer from a slender body of revolution embedded in a saturated porous medium. The study has reported the important case of a cylinder with linear temperature and concentration distributions. The governing parameters for the problem under study are buoyancy ratio (N) and Lewis number (Le). The numerical values of local Nusselt and local Sherwood numbers have also been computed for a wide range of N and Le. The results pertaining to the variations of local Nusselt number, local Sherwood number, N and Le with one another have been studied graphically, and it has been concluded that the local Nusselt number decreases while the local Sherwood number increases along with N > 0 for increasing Lewis number. The local Nusselt number decreases while the local Sherwood number increases along with Le for positive values of N. Also the boundary layer thickness ratio decreases along with Le for N > = 0. In this study, an integral method of Von-Karman type has been used in order to obtain mathematical expressions for local Nusselt and local Sherwood numbers.     

Mixed convection with heat and mass transfer in horizontal tubes

This paper presents the influence of the Lewis number on laminar mixed convective heat and mass transfer in a horizontal tube with uniform heat flux and uniform concentration at the fluid–solid interface. The results of this numerical study show that, for these boundary conditions, the effect of the Lewis number on the Sherwood number is most important near the tube inlet. In the case of the Nusselt number and the wall shear stress, this effect is limited to the intermediate region between the entrance and the fully developed regions.     

Flow and heat transfer in a porous medium saturated with a Sisko nanofluid over a nonlinearly stretching sheet with heat generation/absorption

This work is focused on steady flow and heat transfer in a porous medium saturated with a Sisko nanofluid (non‐Newtonian power‐law) over a nonlinearly stretching sheet in the presence of heat generation/absorption. Nonlinear PDEs are transformed into a system of coupled nonlinear ODEs with related boundary conditions using similarity transformation. The reduced equations are then solved numerically using the Runge–Kutta–Fehlberg fourth–fifth order method (RKF45) with Maple 14.0 software. The solutions depend on the power‐law index n and the effect of pertinent parameter such as the Brownian motion parameter, thermophoresis parameter, Lewis number, the permeability, and the heat generation/absorption on the dimensionless velocity, temperature, and nanoparticles volume fraction and also on the skin friction, local Nusselt, and Sherwood numbers are produced for values of the influence parameter. A rapprochement of the numerical results of the actual study with formerly published data detected an excellent agreement.     

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.     

Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium

The heat and mass transfer characteristics of free convection about a permeable horizontal cylinder embedded in porous media under the coupled effects of thermal and mass diffusion are numerically analyzed. The surface of the horizontal cylinder is maintained at a uniform wall temperature and uniform wall concentration. The transformed governing equations are obtained and solved by Keller box method. Numerical results for the dimensionless temperature profiles, the dimensionless concentration profiles, the Nusselt number and the Sherwood number are presented. Increasing the buoyancy ratio N and the transpiration parameter f_w increases the Nusselt number and the Sherwood number. For thermally assisting flow, when Lewis number Le increases, the Nusselt (Sherwood) number decreases (increases). Whereas, for thermally opposing flow, both the Nusselt number and the Sherwood number increase with increasing the Lewis number.