Vertical channel free convection for a power law fluid with a constant heat flux

The development of free convection in a purely viscous non-Newtonian fluid under the influence of a uniform wall heat flux is investigated. A finite difference solution is presented of the velocity and temperature profiles for the flow of an Ostwald-de Waele (power law) fluid between two symmetrically heated vertical plates. The flow, temperature and heat transfer characteristics of the channel are presented in a dimensionless manner as related to the generalized Grashof and Prandtl numbers and the fully developed flow range is established. The numerical solutions for the developing flow are shown to approach two classical asymptotes - fully developed duct free convection at low Rayleigh numbers and two independent vertical plates at high Rayleigh numbers. A comparison is made between the results of this theoretical investigation and previously published analytical and experimental work on Newtonian and non-Newtonian fluids. The results and their application to engineering problems are discussed. The changes caused by the addition of soluble substances to water cause significant variations in the mean flow between the plates and in the outlet temperature.