Numerical Study for Simulation the MHD Flow and Heat-Transfer Due to a Stretching Sheet on Variable Thickness and Thermal Conductivity with Thermal Radiation

Mohamed M. Khader^1,2, Mohammed M. Babatin¹, Ali Eid³, Ahmed M. Megahed²

¹Department of Mathematics and Statistics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.
²Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt.
³Department of Physics, College of Science, Al-Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia.

DOI: 10.4236/am.2015.612180                

Abstract

The main aim of this article is to introduce the approximate solution for MHD flow of an electrically conducting Newtonian fluid over an impermeable stretching sheet with a power law surface velocity and variable thickness in the presence of thermal-radiation and internal heat generation/absorption. The flow is caused by the non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The obtaining PDEs are transformed into non-linear system of ODEs using suitable boundary conditions for various physical parameters. We use the Chebyshev spectral method to solve numerically the resulting system of ODEs. We present the effects of more parameters in the proposed model, such as the magnetic parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter and the Prandtl number on the flow and temperature profiles are presented, moreover, the local skin-friction and Nusselt numbers. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted. The obtained numerical results confirm that the introduced technique is powerful mathematical tool and it can be implemented to a wide class of non-linear systems appearing in more branches in science and engineering.

Keywords

Newtonian Fluid, Stretching Sheet, Variable Thermal Conductivity, Thermal Radiation, Chebyshev Spectral Method

Conflicts of Interest

The authors declare no conflicts of interest.

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