Mean action time as a measure for fin performance in one dimensional fins of exponential profiles

The aim of this paper is to numerically solve the one dimensional time dependent heat transfer equation while considering different types of exponential profiles. We consider non-linear thermal conductivity via the power law and employ a numerical relaxation scheme due to its simplicity. Furthermore, we obtain the mean action time and propose it as a novel means of analysing the fin performance. Our results are validated through comparing with benchmark results and our new index for fin performance is shown to provide meaningful insight.