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 D Cxm and the wall temperature distribution of the form Tw D T1 C Ax is presented, where x denotes the distance from the slit from which the surface emerges and C and A are constants, m and 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 D 1=3 or the power-law index n D 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.