Heat transfer in gravity-driven film flow of power-law fluids

A mathematical model for the flow and heat transfer in an accelerating liquid film of a non-Newtonian power-law fluid is presented. The thermal boundary layer equation permits exact similarity solutions only in the particular case when the power-law index n is equal to unity, i.e. for Newtonian films. To this end, the heat transfer problem is solvede by means of a local similarity approach with n and the local Prandtl number being the only parameters.The nonsimilar heat transfer problem is integrated numerically for several parameter combinations. For high Prandtl numbers, the temperature gradient at the wall is controlled by the wall gradient of the streamwise velocity component, which is practically independent of n for dilatant fluids but increases significantly with increasing pseudo-plasticity. For small Prandtl numbers, the wall gradient of the temperature field increases slowly with n. Curve-fit formulas for the temperature gradient at the wall are provided in order to facilitate rapid and yet accurate estimates of the local heat transfer coefficient and the Nusselt numb er.