Estimation of Surface Temperature and Heat Flux over a Hollow Cylinder and Slab using an Inverse Heat Conduction Approach

Abstract

A non-iterative approximation of the inverse heat conduction problem has been developed through energy balance between the control volumes. The heat flow domain along the surface normal was divided into three control volumes and studied in three cases, specifically on a heated hollow metallic cylinder cooled in crossflow of air, a heating flat plate in still air, and a heated flat plate when cooled in still air with random air blows. The time derivatives of temperature and heat flux estimates at the surface appearing in derived equations were evaluated by approximate expressions. Both estimates were obtained from the derived equations by simultaneous measurement of temperature-time histories at two locations: one at the inner surface and the other anywhere within the control volume along the surface normal. The deviation was checked by real-time simultaneous measurement of temperature-time history at the outer surface along the normal surface. Comparison between the estimated surface temperature-time history using the derived equations and the real-time measurement showed deviations within 0.5 % for the cylinder, within 0.03 % for the plate in still air and within 0.5 % when air blows were given. Heat fluxes estimated using these time histories were correspondingly arrived at consistent and close approximations for all cases. Estimates from the derived equations were compared with reported equations from the literature, and a wind tunnel experiment for the validation of circumferential distribution of heat transfer was conducted, for which they also showed reasonably good agreements.