Forward and inverse solutions of a conductive, convective and radiative cylindrical porous fin

Abstract

This paper deals with the numerical study of a conductive, convective and radiative cylindrical porous fin. At first, Runge–Kutta method-based numerical solution is obtained for calculating the temperature distribution, and then an inverse problem is solved for estimation of unknown parameters. Five critical parameters such as the porosity, emissivity, solid thermal conductivity, thickness and the permeability have been simultaneously predicted for satisfying a prescribed temperature distribution on the surface of the porous fin. This is achieved by solving an inverse problem using the hybrid evolutionary–nonlinear programming optimization algorithm. The effect of random measurement errors between ±10% has been considered. The estimated values of non-dimensional entities such as porosity and surface emissivity are found to be approximately within the range, 0.28–0.92 and 0.27–0.75, respectively. Additionally, the thermal conductivity, thickness and the permeability are found to be almost between 17 and 140W/mK, 8.7×10−4 to 0.007m and 2×10−11 to 5×10−8m2, respectively. The present study reveals that many feasible combinations of available materials satisfy the same temperature field, thus providing an opportunity for selecting any combination from the available alternatives. Moreover, the hybrid method is found to perform better and yield relatively faster convergence than individual methods. The sensitivity analysis reveals that the effect of fin permeability on the temperature field is considerably high than other parameters.