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Symmetry Analysis for MHD Viscous Flow and Heat Transfer over a Stretching Sheet

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ABSTRACT
This work deals with the boundary layer flow and heat transfer of an electrically conducting viscous fluid over a stretching sheet. Lie-group method is applied for determining the symmetry reductions for the governing equations by reducing the number of independent variables in the given system of partial differential equations by one, leading to a system of non-linear ordinary differential equation. The resulting system is then solved numerically using shooting method coupled with Runge-Kutta scheme. Effects of various values of physical parameters on the horizontal and vertical velocities, temperature profiles, wall heat transfer and the wall shear stress (skin friction), have been studied and the results are plotted. Furthermore, a comparison between the present results with existing numerical and homotopy methods has been reported and we found that they are in a good agreement.
 
Cite this paper
Hassan, H. (2015) Symmetry Analysis for MHD Viscous Flow and Heat Transfer over a Stretching Sheet. Applied Mathematics, 6, 78-94. doi: 10.4236/am.2015.61009.
 
References
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[21]Boutros, Y.Z., Abd-el-Malek, M.B., Badran, N.A. and Hassan, H.S. (2007) Lie-Group Method Solution for Two-Dimensional Viscous Flow between Slowly Expanding or Contracting Walls with Weak Permeability. Applied Mathematical Modelling, 31, 1092-1108.
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[23]Abd-el-Malek, M.B. and Hassan, H.S. (2010) Symmetry Analysis for Steady Boundary-Layer Stagnation-Point Flow of Rivlin-Ericksen Fluid of Second Grade Subject to Suction. Nonlinear Analysis: Modelling and Control, 15, 379-396.
 
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[26]Abd-el-Malek, M.B. and Hassan, H.S. (2014) Lie Group Method for Solving the Problem of Fission Product Behavior in Nuclear Fuel. Mathematical Methods in the Applied Sciences, 37, 420-427.
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[27]Hassan, H.S., Mahrous, S.A., Sharara, A. and Hassan, A. (2014) A Study for MHD Boundary Layer Flow of Variable Viscosity over a Heated Stretching Sheet via Lie-Group Method. Applied Mathematics & Information Sciences, in Press.
 
[28]Abd-el-Malek, M.B., Badran, N.A., Hassan, H.S. and Abbas, H.H. (2015) New Solutions for Solving Boussinesq Equation via Potential Symmetries Method. Applied Mathematics and Computation, 251, 225-232.
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[29]Abd-el-Malek, M.B., Badran, N.A., Hassan, H.S. and Abbas, H.H. (2014) Lie Group Method for Studying the Thermophoresis and Heat Generation Effect on Free-Convection Laminar Boundary-Layer Flow over a Vertical Flat Plate. Submitted for Publication.
 
[30]Abd-el-Malek, M.B. and Hassan, H.S. (2014) Solution of N-Dimensional Radially Symmetric Non-Linear Diffusion Equation via Symmetry Analysis. Submitted for Publication.
 
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http://dx.doi.org/10.1016/j.cnsns.2003.12.008                                                                     eww150113lx
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