The effect of container capacitance on the thermal response of plane walls, infinite cylinders, and spheres subjected to sudden changes in ambient temperature is analyzed. A series solution is presented for each geometry which can be obtained by the method of separation of variables. The first three eigenvalues necessary for the numerical evaluation of the series are tabulated for each configuration. Analytical curves are presented which enable the engineer to determine whether the exact solution must be used or whether an additional approximation can be made which allows a simplification to results commonly found in heat transfer textbooks.

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