Optimization of non-symmetric convective–radiative annular fins by differential quadrature method

The shape optimization of non-symmetric, convective–radiative annular fins is performed based on two-dimensional heat transfer analysis. The formulations are general so that the spatial and temperature dependent geometrical and thermal parameters can easily be implemented. The thermal conductivity of the fin is assumed to vary as a linear function of the temperature. The convective–radiative condition at the external surfaces of the fin and the effective convective condition at the fin base are considered. The differential quadrature method (DQM), as a simple, accurate and computationally efficient numerical tool, is used to solve the nonlinear two-dimensional heat transfer equation and the related nonlinear boundary conditions in the polar coordinate system. The accuracy of the method is demonstrated by comparing its results with those of the finite difference method. It is shown that by using fewer grid points, highly accurate results are obtained. Less computational effort of the method with respect to the finite difference method is shown.