Effect of variable density on hydromagnetic mixed convection flow of a non-Newtonian fluid past a moving vertical plate Ahmed M. Salem, Mohamed Abd El-Aziz * , Emad M. Abo-Eldahab, Ibrahim Abd-Elfatah Department of Mathematics, Faculty of Science, Helwan University, 11795 Cairo, Egypt article info Article history: Received 4 December 2008 Received in revised form 2 June 2009 Accepted 4 June 2009 Available online 9 June 2009 PACS: 47.50.d 44.20.+b Keywords: Power-law fluid Mixed convection Variable density Magnetic field abstract The effect of temperature-dependent density on MHD mixed convection flow of power-law fluid past a moving semi-infinite vertical plate for high temperature differences between the plate and the ambient fluid is studied. The fluid density is assumed to decrease expo- nentially with temperature. The usual Boussinesq approximations are not considered due to the large temperature differences. The surface temperature of the moving plate was assumed to vary according to a power-law form, that is, T w (x)= T 1 + Ax c . The fluid is per- meated by a uniform magnetic field imposed perpendicularly to the plate on the assump- tion of small magnetic Reynolds number. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. The effects of various parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number are presented graphically and in the tabular form. The results show that application of Boussinesq approximations in a non-Newtonian fluid subjected to high temperature differences gives a significant error in the values of the skin-friction coefficient and the application of an external magnetic field reduces this error markedly in the case of shear-thickening fluid. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction The transfer of heat and momentum from a heated moving surface in an otherwise ambient medium occurs in many manufacturing processes such as rolling sheet drawn from a die, cooling and/or drying of paper and textile, manufacturing of polymeric sheets, sheet glass and crystalline materials, etc. [1,2]. When the material emerges from the die or roller, its temperature is higher than that of the surroundings. Generally, this high temperature is due to the external heating as in the case of hot extrusion. Plastic deformation of the material and the friction between the flowing material and the die also contribute to the heating. In the case of cold extrusion, a portion of heat generated is lost to the die and the remaining heat is dissipated to the environment. In many practical applications, the extruded material passes through a cooling bath as in the case of wire cutting discussed by Fisher [2]. Sakiadis [3] was the first to study the flow due to a solid surface moving with a constant velocity in an otherwise ambient fluid. Due to the entrainment of ambient fluid, this problem represents a different class of boundary layer problem which has a solution different from that of boundary layer flow over a stationary surface. The corresponding heat transfer problem was studied theoretically and experimentally by Tsou et al. [4], theoretically by Erickson et al. [5] and experimentally by Griffin and Thorne [6]. Jeng et al. [7] considered the flow and heat transfer charac- teristics over a moving surface in an ambient fluid. Moutsoglou and Chen [8] and Takhar et al. [9] examined the effect of buoyancy forces on an inclined surface moving in an ambient fluid. 1007-5704/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cnsns.2009.06.005 * Corresponding author. E-mail addresses: ah_marei@hotmail.com (A.M. Salem), m_abdelaziz999@yahoo.com (M. Abd El-Aziz). Commun Nonlinear Sci Numer Simulat 15 (2010) 1485–1493 Contents lists available at ScienceDirect Commun Nonlinear Sci Numer Simulat journal homepage: www.elsevier.com/locate/cnsns