Solution of the Rayleigh problem for a power law non-Newtonian conducting fluid via group method Mina B. Abd-el-Malek a,*,1 , Nagwa A. Badran a , Hossam S. Hassan b a Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt b Department of Basic and Applied Science, Arab Academy for Science and Technology and Maritime Transport, P.O. Box 1029, Alexandria 21614, Egypt Received 5 October 2001; received in revised form 8 March 2002; accepted 3 April 2002 Abstract An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an im- pulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent. We will study the non-stationary flow of an electrically conducting non-Newtonian fluid of infinite extent in a transverse external magnetic field. The rheological model of this fluid is given by the well-known expression for a power law fluid [Ing. Arch. 41 (1972) 381] s ij ¼pd ij þ kj 1 2 I 2 j ðn1Þ=2 e ij ; where s ij is the shear stress, p is the pressure, d ij is the Kronecker symbol, k the coefficient of consistency, I 2 the second strain rate invariant, e ij the strain rate tensor and n is a parameter characteristic of the non- Newtonian behavior of the fluid. For n ¼ 1, the behavior of the fluid is Newtonian, for n > 1, the behavior is dilatant and for 0 < n < 1, the behavior is pseudo-plastic. The equation of motion of the semi-infinite flat plate in the infinite power law non-Newtonian fluid after an impulsive end loading and maintaining con- stant velocity thereafter is ou ot  c o oy ou oy  2 " # ðn1Þ=2 ou oy 8 < : 9 = ; þ MH 2 u ¼ 0; where uðy ; tÞ is the velocity of the fluid flow in the horizontal direction, V is the steady state velocity of the plate, t is the time, y is the coordinate normal to the plate, n is constant, c (¼ k=q) is constant, k is the * Corresponding author. Tel.: +20-3-391-8715; fax: +20-2-797-5643. E-mail addresses: minab@aucegypt.edu (M.B. Abd-el-Malek), hossams@aast.edu (H.S. Hassan). 1 Present address: Department of Mathematics, The American University in Cairo, Cairo 11511, Egypt. 0020-7225/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0020-7225(02)00037-X International Journal of Engineering Science 40 (2002) 1599–1609 www.elsevier.com/locate/ijengsci