Numerical Method for Optimum Performances of Fin Profiles

Abstract

In the present work, we present a numerical method able to capture the optimum thermal performances of finned surfaces of high and low conductivity. The bidimensional temperature distribution on the longitudinal section of the fin is calculated by restoring to the finite volumes method. The heat flux dissipated by a generic profile fin is compared with the heat flux removed by the rectangular profile fin with the same length and volume. In this study it is shown that a finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation, in order to determine the sinusoidal parameter values which optimize the fin effectiveness. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the ‘Stokes theorem’. The heat flux dissipated by generic profile fin is compared with the heat flux removed by rectangular profile with the same length and volume. The numerical method is then applied to the case of sinusoidal profiles fin that represent problems with complex geometries, which make the heat transfer fluxes as high as possible under different conditions. The optimum profile is finally shown for different sinusoidal profiles.