Radial conduction effects in transient heat transfer experiments

Abstract

[Introduction]: Convective heat transfer data is frequently obtained from transient surface temperature measurements. Thin film resistance gauges, thermocouples, and thermochromic liquid crystals, are used in various situations to measure the surface temperature history. By assuming that uniform semi-infinite flat plate conditions apply, it is possible to express the instantaneous surface heat flux as an analytical function of the transient surface temperature[ll. Various approaches can be used to account for the presence of multi-layered substrates and finite thickness substrate effects (Schultz and Jones; Doorly and Oldfield; Guo et al), however, the effects of surface curvature are usually, neglected. - If the heat transfer data is obtained on the premise that flat plate conditions apply. then error will be introduced if the surface is actually curved. Intuitively, the magnitude of such errors will depend on how far the heat penetrates into the substrate relative to the radius of curvature of the surface. Maulardc4) derived expressions to evaluate the accuracy of the flat plate assumption in cases where the surface under consideration is curved. However, his theoretical results do not provide a convenient means of accurately accounting for surface curvature effects in the routine analysis of experimental data. The current work presents simple analytical curvature corrections for heat transfer results inferred on the assumption that flat plate conditions prevailed during the experiment. Conditions of arbitrary surface heat flux are easily accommodated with the present analysis. The accuracy of the first-order correction analysis is demonstrated by comparing results from the approximate curvature analysis with exact results for a variety of configurations under constant convective heat transfer coefficient conditions. The practical utility of the radial heat conduction modelling is evident from a number of studies in which it has already been employed (Buttsworth and Jones); Hoffs et a1; Fletcher). Nevertheless, data from a recent heat transfer probe experiment is also considered as a further practical demonstration of the present analysis.