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

A. mathematical model for the flow and heat transfer in an accelerating liq uid film of a non-Newtonian power-law fluid is presented. The thermal bound ary layer equation permits exact similarity solutions only in the particula r case when the power-law index n is equal to unity, i.e. for Newtonian fil ms. To this end, the heat transfer problem is solved by means of a local no nsimilarity approach with n and local Prandtl number Pr-x being the only pa rameters. A critical Prandtl number Pr-x* is introduced, which is a monoton ically increasing function of n. The nonsimilar heat transfer problem is in tegrated numerically for several parameter combinations in the ranges 0.2 l ess than or equal to n less than or equal to 2.0 and 0.001 less than or equ al to Pr-x less than or equal to 1000 and the calculations for n = 1 compar ed favourably with earlier results for Newtonian liquid films. For high Pra ndtl numbers, the temperature gradient at the wall is controlled by the wal l gradient of the streamwise velocity component, which is practically indep endent of n for dilatant fluids (n > 1.0) but increases significantly with increasing pseudoplasticity (n < 1.0). For Pr-x much less than 1, on the ot her hand, the wall gradient of the temperature field increases slowly with n and this modest variation is ascribed to the displacement effect caused b y the presence of the momentum boundary layer. Curve-fit formulas far the t emperature gradient at the wall are provided in order to facilitate rapid a nd yet accurate estimates of the local heat transfer coefficient and the Nu sselt number. (C) 1998 Elsevier Science Ltd. All rights reserved.