Abstract:
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 thermophysical 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
