Heat Transfer of the Falling Film Flow of Non-Newtonian Power-Law Fluids

Abstract

A deep study is done on heat transfer from an inclined plane surface to an accelerating liquid film of a non-Newtonian power-law fluid. The new similarity analysis method for the accompanying hydrodynamic problem was adopted in combination with a local pseudo-similarity method. The resulting transformed problem turned out to involve only two independent parameters, namely the power-law index and the local Prandtl number. All other related physical properties and parameters are combined into the induced local Reynolds number, and the dimensionless velocity components. Accurate numerical results are obtained for combinations of local Prandtl number from 0.001 to 1000 and the power-law index n in the range $0.2\le n\le 2$. Special treatment for the low and high local Prandtl number cases is essential in order to maintain the numerical accuracy. The calculated results obtained both by using local similarity and local pseudo-similarity methods are practically indistinguishable for $n = 1$ over the entire local Prandtl number range. Furthermore, it is found that the wall temperature gradient which depends on local Prandtl number and power-law index is the only one no-given condition for evaluation of heat transfer. With increasing the local Prandtl number, the heat transfer coefficient increases, but with increasing the power-law increase, the heat transfer coefficient decreases. A set of accurate curve-fit formulas for the wall temperature gradient is provided, so that the rapid estimates of the heat transfer rate for any combination of the local Prandtl number and power-law index within the parameter ranges considered are realized.