Mixed convection heat transfer from a vertical plate to non-Newtonian fluids

Abstract

The nonsimilar boundary-layer analysis of steady laminar mixed-convection heat transfer between a vertical plate and non-Newtonian fluids is extended and unified. A mixed-convection parameter ζ is proposed to replace the conventional Richardson number, Gr/Re 2/(2− n) and to serve as a controlling parameter that determines the relative importance of the forced and the free convection. The value of mixed-convection parameter lies between 0 and 1. In addition, the power-law model is used for nonNewtonian fluids with exponent n < 1 for pseudoplastics; n = 1 for Newtonian fluids; and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection, from the pure forced-convection limit to the pure free-convection limit, and the whole domain of non-Newtonian fluids, from pseudoplastics to dilatant fluids. The effects of the mixed-convection parameter, the power-law viscosity index, and the generalized Prandtl number on the velocity profiles, the temperature profiles, as well as on the wall skin friction and heat transfer rate are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.