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.     

A study on heat transfer in a second‐grade fluid through a porous medium with the modified differential transform method

This study investigates the boundary‐layer flow and heat transfer characteristics in a second‐grade fluid through a porous medium. The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the differential transform method (DTM) and the DTM‐Padé. The DTM‐Padé is a combination of the DTM and the Padé approximant. The convergence analysis elucidates that the DTM does not give accurate results for large values of independent variables. Hence the DTM is not applicable for the solution of boundary‐layer flow problems having boundary conditions at infinity. Comparison between the solutions obtained by the DTM and the DTM‐Padé with numerical solution (fourth‐order Runge–Kutta with shooting method) illustrates that the DTM‐Padé is the most effective method for solving the problems that have boundary conditions at infinity. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21030     

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     

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     

Entropy generation in an asymmetrically cooled slab with temperature‐dependent internal heat generation

The paper presents an entropy generation analysis for steady conduction in a slab with temperature‐dependent volumetric internal heat generation. The slab experiences asymmetric convective cooling on its two faces. The exact analytical solution for the temperature distribution is used to compute dimensionless local and total entropy generation rates in the slab. The total entropy generation rate depends on five dimensionless parameters: reference heat generation temperature Q, the heat generation–temperature variation parameter a, the temperature asymmetry parameter λ, and Biot numbers Bi₁ and Bi₂. Graphs illustrating the effect of these five parameters on the local and total entropy generation rates are presented and discussed. It is found that the total entropy generation in the slab can be minimized with a suitable choice of the cooling parameters. The paper corrects the flawed entropy results published recently. The present results for the special case of uniform internal heat generation confirm the results presented in a 2003 paper. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20404     

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