Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet

A theoretical analysis of the laminar boundary-layer flow and heat transfer of power-law non-Newtonian fluids over a stretching sheet with the sheet velocity distribution of the form Uw = Cxm and the wall temperature distribution of the form Tw = T∞ + Ax is presented, where x denotes the distance from the slit from which the surface emerges and C and A are constants, m and γ denote, the sheet velocity exponent and the temperature exponent, respectively. Within the framework of the boundary layer approximations, the nonlinear boundary layer momentum equation and the energy equation are reduced to a set of ordinary differential equations. It is found that when the velocity exponent m = 1/3 or the power-law index n = 1, the similarity solutions are in existence for both the momentum equation and the energy equation. Analytical approximations with high accuracy for the reduced velocity and temperature profiles are obtained using a new procedure based on the homotopy analysis method. Besides, the effects of the parameters m, n and the Prandlt number Pr on the flow are investigated. © 2009 Elsevier Ltd. All rights reserved.