Recurrence formula for the temperature distributions in plates undergoing heat treatment

Abstract

The recurrence formula giving the temperature distribution in the unsteady state is determined for an isotropie solid bounded by two parallel planes in the following symmetrical case: The surfaces are submitted to a succession of different cooling and/or heating rates, some of which - if not all of them - are applied during times that are too short to attain their corresponding steady states prior to applying the next cooling or heating rate. The initial temperature is assumed to be uniform at the moment of the application of the first cooling or heating rate only. In the most general case, the initial conditions at the application of any cooling or heating rate are expressed by an unsteady state distribution equation involving all the previous rates. Depending on the magnitude of the applied rates, these conditions can occur in thin plates as well as in very thick ones.