Multi-layer transient heat conduction using transition time scales

The solution of multi-layer transient heat conduction problems may be simplified by analyzing the different transition times of the various layers of a composite slab. These transition times, in fact, allow the ‘disturbance’ effect of each layer on the eigenvalues of the composite slab to be analyzed and estimated. It was found that the eigenvalues may be obtained in the first approximation by merging in increasing order the suitable corrected eigenvalues of each layer for which explicit equations are available. The errors in the resulting dimensionless temperatures are of one order of magnitude larger than the deviations between the exact and approximate eigenvalues. In particular, when one of the two outer boundaries is kept at constant temperature and the transition times of the layers are quite different, the eigenvalues may be written down very simply as the eigenvalues of the layer whose exposed surface is not at prescribed temperature. In this paper the temperature solution for the case of a two-layer slab with interlayer thermal contact resistance is presented.