Boundary Layer Flow through Darcy–Brinkman Porous Medium in the Presence of Slip Effects and Porous Dissipation

Muhammad Salman Kausar,Babar Ahmad,Mustafa Mamat,Abid Hussanan

doi:10.3390/sym11050659

Muhammad Salman Kausar, Babar Ahmad + Show 2 more

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https://doi.org/10.3390/sym11050659

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Abstract

This paper aims to examine the Darcy–Brinkman flow over a stretching sheet in the presence of frictional heating and porous dissipation. The governing equations are modeled and simplified under boundary layer approximations, which are then transformed into system of self-similar equations using appropriate transformations. The resulting system of nonlinear equations was solved numerically under velocity and thermal slip conditions, by fourth-order Runge–Kutta method and built-in routine bvp4c in Matlab. Under special conditions, the obtained results were compared with the results available in the literature. An excellent agreement was observed. The variation of parameters was studied for different flow quantities of interest and results are presented in the form of tables and graphs.

Highlights

The porous medium is a continuous solid phase having void spaces/pores in it
Industrial and engineering applications of flows through porous medium have attracted the attention of researchers
The aim of this paper is to investigate the Darcy–Brinkman flow over a permeable stretching sheet in the presence of viscous and porous dissipation under the velocity and thermal slip conditions

Summary

Introduction

The porous medium is a continuous solid phase having void spaces/pores in it. Industrial and engineering applications of flows through porous medium have attracted the attention of researchers. “Flow is linearly dependent on the pressure gradient and the gravitational force” is known as Darcy Law. This law is generally accepted as the macroscopic equation of motion for the Newtonian fluids in porous media at small Reynolds numbers and when the medium is close-packed (lower permeability). When the pore distribution in the medium is sparse and the pores are large, the porous medium will have large voids, giving rise to viscous shear in addition to Darcy’s resistance.

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