Heat Conduction Transient 1D

The app estimates the time it takes to the middle of a slab/plate to reach a specified temperature Tf between its initial uniform temperature Ti and that of a fluid to which it was suddenly exposed T∞, given the thermal conductivity k and diffusivity α of the slab material, and the average heat transfer coefficient h associated to the fluid and slab configuration.

The most ordinary use of this kind of estimate is in metallic alloys heat treatment.

The estimation is based on the analytic solution for the unidimensional transient heat conduction equation obtained by the separation of variables method. Only the first term of the Fourier series involved is used, an approximation valid when the nondimensional time (Fourier number) is above 0.2. The theoretical details are available at Heat Conduction textbooks, like those written by Carlslaw and Jaeger or by Hahn and Özişik and in general Heat and Mass Transfer textbooks like those written by Incropera et al. or by Çengel and Ghajar.