A general mathematical method is presented suitable for the “lumping” of many damped linear systems when the response function and the forcing function can be related by a convolution integral. The method is illustrated by application to transient heat conduction in slabs and cylindrical rods. An ordinary differential equation (equation 26) relating the mean temperature of these bodies to their surface temperature is derived, and then applied to the solution of several problems. Agreement with exact results is found to be excellent except for very rapid transients. Means for estimating error are provided in the paper.

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