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Chin. Phys. B, 2013, Vol. 22(3): 030202    DOI: 10.1088/1674-1056/22/3/030202
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Melting phenomenon in magneto hydro-dynamics steady flow and heat transfer over a moving surfacein the presence of thermal radiation

Reda G. Abdel-Rahman, M. M. Khader, Ahmed M. Megahed
Department of Mathematics, Faculty of Science, Benha University, Benha 13518, Egypt
Abstract  The Lie group method is applied to present an analysis of the magneto hydro-dynamics (MHD) steady laminar flow and the heat transfer from a warm laminar liquid flow to a melting moving surface in the presence of thermal radiation. By using the Lie group method, we have presented the transformation groups for the problem with a part from the scaling group. The application of this method reduces the partial differential equations (PDEs) with their boundary conditions governing the flow and heat transfer to a system of nonlinear ordinary differential equations (ODEs) with appropriate boundary conditions. The resulting nonlinear system of ODEs is solved numerically using an implicit finite difference method (FDM). The local skin-friction coefficients and the local Nusselt numbers for different physical parameters are presented in a table.
Keywords:  Lie group method      magneto hydro-dynamics      melting phenomenon      Newtonian fluid radiation      finite difference method  
Received:  04 July 2012      Revised:  27 August 2012      Accepted manuscript online: 
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  47.15.-x (Laminar flows)  
  44.40.+a (Thermal radiation)  
  44.10.+i (Heat conduction)  
Corresponding Authors:  M. M. Khader     E-mail:  mohamedmbd@yahoo.com

Cite this article: 

Reda G. Abdel-Rahman, M. M. Khader, Ahmed M. Megahed Melting phenomenon in magneto hydro-dynamics steady flow and heat transfer over a moving surfacein the presence of thermal radiation 2013 Chin. Phys. B 22 030202

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