Abstract
The unsteady, laminar hydro magnetic flow of an incompressible, viscous and electrically conducting Newtonian fluid over a contracting sheet embedded in a porous medium has been investigated. The flow takes place between two parallel flat sheets that are made of an electrically non-conducting material. The fluid is subjected to transverse magnetic field that cuts perpendicularly across the flow in the positive direction of the z-axis. The contracting sheet has a permeable surface while the surface of other sheet is impermeable, each sheet has an isothermal surface and both sheets are kept at different temperature of TW andT∞ such that the temperature differences within the flow are sufficiently small. The effect of varying various parameters on the velocity and temperature profiles has been discussed. The coupled non-linear partial differential equations governing the flow have been solved numerically using the finite difference method because of its accuracy, stability and convergence. The results that are obtained are then presented graphically and observations have been discussed. Changes in various parameters have been observed to alter the velocity profiles and temperature profiles. AMS Subject Classification: 76D05
Highlights
The study of heat transfer in the boundary layer flow has many applications in engi-Received: March 12, 2013 §Correspondence author c 2015 Academic Publications, Ltd. url: www.acadpubl.euM
In the past most researchers have studied wide variety of flow situations. Some of these studies can be found in work of [11] studied flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/ absorption and suction/ blowing. [3] investigated numerical steady free convection flow through a porous medium around a rectangular isothermal body. [10] analyzed the effects of magnetic field on the viscoelastic fluid flow and heat transfer over a non isothermal stretching sheet with internal heat generation. [16] investigated the effects of buoyancy force on the parallel flows bounded above by a rigid permeable plate which may be moving or stationary, and below, by a permeable bed
The flow region was divided into two zones: one zone made up of laminar flow and governed by Naiver Stokes equations, and the other zone was governed by Darcy’s law. [1] carried out an analytical study of a two dimensional unsteady MHD free convective flow past a vertical porous plate immersed in a porous medium with hall current, thermal diffusion and heat source
Summary
The study of heat transfer in the boundary layer flow has many applications in engi-Received: March 12, 2013 §Correspondence author c 2015 Academic Publications, Ltd. url: www.acadpubl.euM. In the past most researchers have studied wide variety of flow situations. Some of these studies can be found in work of [11] studied flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/ absorption and suction/ blowing. [10] analyzed the effects of magnetic field on the viscoelastic fluid flow and heat transfer over a non isothermal stretching sheet with internal heat generation. [1] carried out an analytical study of a two dimensional unsteady MHD free convective flow past a vertical porous plate immersed in a porous medium with hall current, thermal diffusion and heat source The flow region was divided into two zones: one zone made up of laminar flow and governed by Naiver Stokes equations, and the other zone was governed by Darcy’s law. [1] carried out an analytical study of a two dimensional unsteady MHD free convective flow past a vertical porous plate immersed in a porous medium with hall current, thermal diffusion and heat source
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