Predicting Dimensions of a Rectangular Fin Satisfying a Given Internal Heat Generation Using Inverse Method

This paper deals with a computational study to predict important dimensions of a rectangular fin used in gas turbine blade cooling for satisfying a prescribed internal heat generation. The heat transfer is assumed to occur by simultaneous conduction, convection and radiation. The effect of temperature-dependent thermal conductivity has been also taken into consideration. Rectangular fin geometry has been considered due to its simplicity and easiness of fabrication. Corresponding to known values of various thermo-physical parameters, at first using the fourth order implicit Runge-Kutta-based forward method, the relevant steady-state temperature distribution is evaluated. Forward method has been well-validated with three numerical schemes and experimental data. Thereafter, an inverse problem is solved using the genetic algorithm (GA) for predicting fin dimensions satisfying a prescribed temperature distribution corresponding to a fixed internal heat generation. The relevant objective function has been formulated using a three-point error minimization technique represented by square of residuals between guessed and available temperature distributions. The analysis has been done for three different fin materials such as Inconel, Hastelloy and Titanium. These materials are generally used in gas turbine blade applications due to their high melting point along with good fatigue, corrosion and creep properties. Effects of random measurement errors following a Gaussian profile are analyzed. The variations of relevant parameters are studied at different generations of GA. It is observed that for a given fin material, many feasible dimensions can sustain a given amount of internal heat generation which offer sufficient scopes to the fin designer. For the required amount of heat generation, the suitability of estimated parameters has been verified by the comparison between actual and reconstructed temperature distributions alongwith minimization of total fin volume. The present work is proposed to be useful in selecting appropriate dimensional fin configurations corresponding to a given material which can satisfy a fixed amount of internal heat generation.