Application of Adomian decomposition method and inverse solution for a fin with variable thermal conductivity and heat generation

Abstract

In this work, our aim is to demonstrate the application of the Adomian decomposition method (ADM) to solve a non linear heat transfer problem for a rectangular fin with temperature dependent internal heat generation and thermal conductivity. Next, for satisfying a prescribed temperature field, inverse predictions of the internal heat generation and the condition responsible for insulated boundary (represented by a constant) were done using ADM alongwith the genetic algorithm (GA). For obtaining the required temperature field, a forward problem is solved using ADM, where Newton–Raphson method is used for estimating the relevant constant representing the fin tip temperature. It is found from the present study that with accurate temperature data, even for different runs of GA, estimation of two unknowns remain nearly unique. The investigation has been done for various searching range of GA, and different number of temperature measurement points. It is finally observed that for correct reconstruction of the temperature field, an accurate measurement of the temperature field is found to be necessary.