A Duhamel Integral Based Solution for the Sideways Heat Equation Applied to the Non-intrusive Temperature Measurement

In the present study, an inverse heat conduction problem is considered, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Considering the problem of an intrinsic thermocouple attached to a slab, and no thermal contact, a transfer function is proposed. It is based on Duhamel Integral and the measured response is approximated by a quasi-periodical function. The derived transfer function is the product of two transfer functions, for the slab and for the intrinsic thermocouple respectively. To validate the present model, a comparison with actual measurements is carried out. It was found that the present model can predict the inner temperatures more accurately than the previous model, which did not take into account the effect of the thermocouple.