MHD Effects on Non-Darcy Forced Convection Boundary Layer Flow past a Permeable Wedge in a Porous Medium with Uniform Heat Flux

A Y Y Bakier,A M M Rashad

doi:10.15388/na.2009.14.2.14523

Abstract

The steady two-dimensional laminar forced flow and heat transfer of a viscous incompressible electrically conducting and heat-generating fluid past a permeable wedge embedded in non-Darcy high-porosity ambient medium with uniform surface heat flux has been studied. The governing equations are derived using the usual boundary layer and Bossinesq approximations and accounting for the applied magnetic filed, permeability of porous medium, variable porosity, inertia and heat generation effects. These equations and boundary conditions are non-dimenstionalized and transformed using non-similarity transformation. The resulting non-linear partial differential equations are then solved numerically subject to the transformed boundary conditions by a finite difference method. Comparisons with previously published works are performed and the results are found to be in excellent agreement. Numerical and graphical results for the velocity and temperature profiles as well as the skin friction and Nusselt number are presented and discussed for various parametric conditions.

Highlights

Convective heat transfer from surfaces embedded in porous media has been the topic of several studies in recent year
We observe that if P r decreases, there is a corresponding decrease in the value of local Nusselt number for fixed value of m means the boundary layer thickness increasing with the increase of P r
We can observe that both skin friction coefficient and Nusselt number increases with the increase the values of M, Q, C, ε, but decreases with the increase of K

Summary

Introduction

Convective heat transfer from surfaces embedded in porous media has been the topic of several studies in recent year. MHD Effects on Non-Darcy Forced Convection Boundary Layer Flow past a Permeable Wedge a vertical heated surface in a porous medium has been studied by Mittal [16]. Hossain et al [25] investigated the same problem by having temperature dependent viscosity as well as thermal conductivity on the forced flow past a wedge and heat transfer of a viscous incompressible fluid with uniform surface heat flux. The aim of the present theoretical study is to investigate the effects of porosity, permeability of the porous medium, inertia and magnetic field on the flow and heat transfer of a viscous incompressible electrically conducting and heat-generating fluid past a permeable wedge embedded in fluid-saturated high-porosity ambient medium, using the extension of the Darcy-Forchheimer-Brinkman model, in the presence the magnetic field and internal heat generation effects.

Problem formulation

Numerical scheme

Results and discussion

Conclusions