Estimation of critical dimensions for a trapezoidal-shaped steel fin using hybrid differential evolution algorithm

This paper deals with the inverse prediction of parameters in a trapezoidal fin with temperature-dependent thermal conductivity and heat transfer coefficient. Three critical dimensions along with the relevant heat transfer coefficient at the fin base have been simultaneously predicted for satisfying a given temperature distribution on the surface of the trapezoidal fin. The inverse problem is solved by a hybrid differential evolution-nonlinear programming (DE-NLP) optimization method. For a given fin material which is considered to be stainless steel, it is found from the present study that many feasible dimensions exist which satisfy a given temperature distribution, thereby providing flexibility in selecting any dimensions from the available alternatives by appropriately regulating the base heat transfer coefficient. A very good estimation of the unknown parameters has been obtained even for temperature distribution involving random measurement errors which is confirmed by the comparisons of the reconstructed distributions. It is concluded that for a given fin material, the hybrid DE-NLP algorithm satisfactorily estimates feasible dimensions of a trapezoidal fin even with random measurement error of 11 %.