Surface Temperature and Heat Transfer Conditions in the Ablation of Shear Thinning and Shear Thickening Liquids

Abstract

The heat and mass transfer conditions for the ablation of Newtonian liquids have been described in a number of excellent articles. However, little attention has been paid to the behavior of non-Newtonian liquids for which the viscosity is not only a function of temperature but also of shear rate. This is astonishing since many excellent ablators behave in a non-Newtonian manner, especially when they contain foreign particles such as gas bubbles. The purpose of this paper is to study changes in heat and mass transfer if the ablator has a shear rate dependent viscosity. As a result of this study it will be shown that deviations from normal Newtonian behavior increase with increasing shear stress and decreasing bluntness of the cone. Surface temperatures are calculated as a function of Mach number, degree of non-Newtonian viscosity parameter, nose radius, and altitude. Numerical results are given for a model substance with the physical characteristics of Pyrex glass but with a hypothetically varying degree of non-Newtonian viscosity behavior.