THEORETICAL EVALUATION OF NEW PHASE DELAY METHODS FOR MEASURING LOCAL HEAT TRANSFER COEFFICIENTS

Abstract

A one-dimensional analytical solution has been derived for unsteady heat conduction within a semi infinite body, of high thermal resistance, that is subject to a surface heat flux that varies periodically with time. The heat flux is assumed to be generated within a thin isothermal coating. The model predicts that a phase delay will develop between the heat flux and the coating thermal response. This phase delay is independent upon the material properties of the substrate and coating, on the heat flux driving frequency, and on the local heat transfer, coefficient. With the exception of this last quantity the other parameters are known a priori, hence if the phase delay can be measured experimentally it can then be used to determine the local heat transfer coefficient. Absolute values of the local coating temperature and local heat flux are not required. Hence calibration of the devices for measuring these quantities should not be required. In contrast to the overall surface temperature, it is predicted that the phase delay angle will attain a steady-state value within a few heat flux cycles, thus reducing the time required obtaining a measurement. Furthermore, the one-dimensional mathematical model that has been developed reduces to those used in previous experimentally validated techniques, when appropriate constants in the boundary condition are used.