A new method for predicting thermal flow stability: application to a heated rotating disk

Abstract

In this paper, an approximate analytical formulation is used to develop criteria for predicting thermal flow stability of a heated rotating disk reactor. For fluid flow directed vertically onto a heated horizontal rotating disk, gravitationally induced thermal recirculation results if the density difference between the disk and the incoming gas stream overcomes the stabilizing influence of the viscous forces. From both a fundamental and a practical standpoint, one would like a simple rule that predicts the flow regimes that are free of thermal recirculations. The new stability criteria are based on a variable property similarity transform that makes it possible to obtain approximate analytical solutions to the flow-governing equations. Stability criteria are developed by integrating and combining various terms of the resulting approximate equations. The new stability criteria developed herein are compared to existing criteria as well as to experimental results.