Inverse Estimation of Boundary Heat Flux for Heat Conduction Model

Mathematical model of direct and inverse problems isdeveloped for the flat plate probe which is subjected to timedependentheat flux at one end, while the other end is kept insulated.The direct solution, which is concerned with determination of thetemperature distribution in the probe, is developed using an approachbased on the method of variation of parameters. The direct solution isused to solve the inverse heat conduction problem (IHCP) for anyassumed heat flux. In this paper, the piecewise linear interpolationmodel for heat flux is used. The inverse algorithm is developed usingthe Levenberg-Marquardt method. Different test cases for known heatflux profile are used to validate the inverse algorithm. A satisfactoryagreement between exact and estimated heat flux profiles is achieved.The algorithm is used to estimate the heat flux for a flat plate probedeveloped at Ohio University.