Inverse Heat Transfer Study of a Nonlinear Straight Porous Fin Using Hybrid Optimization

Gas turbine blades are subjected to excessive heating load and for safe operation they must be properly cooled for protecting the blade material from damage. This involves external film cooling and internal pin-fin cooling. Cooling using fins are used for gas turbine blades by passing cold air over small extended surfaces. However, it is found that compared to conventional solid fins, for same weight, the usage of porous fins gives better thermal performance. In order to satisfy a given temperature distribution, the fin designer needs to determine various important properties and parameters, which requires solution of inverse problems. These parameters are generally thermo-physical properties for selecting suitable material and dimensions. In this work, an inverse heat transfer study of a porous rectangular fin using a hybrid Differential Evolution (DE)-nonlinear programming (NLP) algorithm has been carried out. The energy exchange in the porous fin is governed by conductive, convective and radiative heat transfer alongwith mass diffusion through the porous media, which makes the problem nonlinear. The fluid medium is assumed to be air. Using DE-NLP algorithm, four important parameters such as porosity, thermal conductivity of solid, length and thickness of the porous fin have been estimated for satisfying a given temperature distribution. Initially, the prescribed temperature distribution is calculated by solving a forward problem based on an implicit Runge-Kutta method working on Lobatto technique. Effects of random measurement errors, comparison of number of iterations and reconstruction distributions for the hybrid DE-NLP and individual NLP, DE schemes are performed. It is observed that the hybrid DE-NLP method converges faster than other two methods working separately. For all measurement errors, a very good reconstruction of the temperature distribution is observed using DE-NLP algorithm. In addition to this, it is found that many feasible combinations of the parameters can satisfy a given temperature distribution, which offers flexibility in selecting various parameters by adjusting the fin size, solid thermal conductivity and porosity.