In this paper an inverse numerical study of a conductive, convective and radiative rectangular fin is carried out with temperature-dependent thermal conductivity. At first, an implicit Runge-Kutta method-based solution is obtained for calculating the temperature distribution, and then an inverse problem is solved for estimation of unknown thermo-physical properties. The convection–conduction parameter, variable conductivity parameter and radiative parameter have been simultaneously predicted for satisfying a prescribed temperature distribution. This is achieved by minimizing a least squares-based objective function using a hybrid differential evolution-nonlinear programming optimization algorithm. The results obtained from the forward method are compared with Adomian decomposition and homotopy analysis methods which are found to be satisfactory. It is observed that many feasible combinations of parameters exist which satisfy the same temperature distribution, thus providing an opportunity for selecting any combination from the available alternatives. The effect of convection–conduction parameter on the temperature distribution is observed to be more than other parameters. A case study of different fin materials is also carried out for demonstrating the application of the present methodology.
Numerical study of temperature dependent thermal conductivity and homogeneous-heterogeneous reactions on Williamson fluid flow