Solution of a coupled inverse heat conduction–radiation problem for the study of radiation effects on the transient hot wire measurements

Abstract

The transient hot wire technique has recently become one of the most widely used methods for measuring thermal properties of materials. This method, based on an ideal theory assuming the hot wire as an infinitely thin and long heat source surrounded by an infinite medium, is also restricted to exclusively conductive heat transfer media. In this work, a numerical solution and an experimental apparatus are presented in order to study the effect of radiation in transient hot wire measurements. A more rigorous numerical analysis of the transient combined conduction and radiation heat transfer in a cylindrical hot wire cell is carried out, where absorption and emission of radiation by the medium and radiation emitted by the wire surface are taken into account. The discrete ordinates method is used to solve the radiative transfer equation, while an implicit finite-difference scheme is employed for handling the energy equation. Results show that the classical parallel hot wire method is accurately applied only for sufficiently large or nearly zero absorption coefficients. Based on a sensitivity analysis, an inverse conduction–radiation problem for simultaneously estimating the thermal conductivity, the heat capacity, the absorption coefficient and the heat transfer coefficient is successfully solved with the Levenberg–Marquardt method where the thermal conductivity and the heat capacity, simultaneously obtained from a non-linear fitting procedure based on the hot wire method, are used as initial guesses. This inverse investigation is validated using a real set of experimental temperature measurements. Such an experimental inverse analysis is presented as a useful tool to evaluate the accuracy of the thermal properties obtained with the hot wire method, and to discuss their errors with respect to the order of the absorption coefficient.