Estimation of Surface Temperature and Heat Flux Using Inverse Solution for One-Dimensional Heat Conduction

An analytical method has been developed for the inverse heat conduction problem using the Laplace transform technique when the temperatures are known at two positions within a finite body. On the basis of these known temperatures, a closed form to the inverse solution can be obtained to predict surface conditions. The method first approximates the measured temperatures with a half polynomial power series of time as well as a time lag, which takes for a monitor to sense the temperature change at the point. The expressions for the surface temperature and the surface heat flux are explicitly obtained in the form of the power series of time. The surface temperature and heat flux calculated for some representative problems show agreement with the known values. The method can be applied to the case where an initial temperature distribution exists.