The flow of power law fluids between parallel plates with shear heating

Abstract

A mathematical model for the flow and heat transfer between two parallel plates is studied, using the power law model. The flow due to a pressure gradient and flow due to a moving upper plate are investigated. In the derivation the Navier-Stokes and energy equations is reduced in line with the lubrication theory to provide scalar differential equations. The velocity and temperature profiles are determined analytically and the results show that the power law index n = 1 compares favourably with Newtonian profiles. The temperature field is increasing when n increases. The Brinkman number Br, also shows a significance increase of the temperature field when Br increases. © 2006 WIT Press.