1D heat transfer through a flat plate submitted to step changes in heat transfer coefficient

The thermal response of an infinite flat plate is considered, when the heat transfer coefficients on both the exposed surfaces undergo step changes. The configuration is a simplified model for the heat transfer through the separating wall in the Isochoric Counter-Current Heat Exchanger. The step change in the second surface appears with a time delay with respect to the first. The plate temperature, surface heat fluxes and accumulated energy perturbations are evaluated for both the thermally thick and thin cases and the corresponding results are compared. The results show a significant influence of both the delay time and the Biot numbers perturbations. It is shown that for a specific combination of Biot number magnitudes the plate is brought suddenly into a steady state condition and as soon as the second step appears. In addition, an inner point may be defined where the final steady state temperature perturbation becomes zero, separating the plate into two oppositely thermally stressed regions.