Analytic solution for transient heat flow in a shocked composite slab

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Abstract
An analytical solution and computational procedure has been obtained for transient heat flow in a three‐slab finite‐length composite solid with symmetry about the center. Each material has different initial temperatures and there are constant temperatures on the boundaries. The solutions are of interest in thermal quenching procedures and in the shock compression of sandwich configurations of materials. The results of a computation corresponding to the temperatures reached in shock‐wave compression indicate that there is significant heat flow into a metal foil, which is sandwiched between two epoxy layers, in less than 1 μsec of heat flow. This paper presents a mathematical discussion of the heat‐flow problem along with sample computational results. One conclusion from these results is that they demonstrate the important effect of heat flow on electrical resistance changes in certain geometries of shock‐wave compression of metals.