Numerical Study of Transient and Steady-State Anisotropic Cylindrical Pin Fin Thermal Behavior

Abstract

This paper deals with the transient thermal analysis of two-dimensional cylindrical anisotropic pin fin that contains tip convection and subjected to a prescribed temperature at the fin base. The heat conduction equation contains a dual second-order derivation, which precludes solving the equation by direct application of common exact methods. Therefore, an appropriate canonical mapping is selected as a solution to cancel the dual derivation of temperature in the mapped equations. The alternating-direction implicit finite difference method (ADI) performs the integration of the mapped equations in the novel space, which involve a complicate geometry. Applying the inverse spatial transformation provides transient temperature profile in the real geometry for full-field configuration. The established numerical code has been validated successfully with the analytical solutions of the usual fins (orthotropic and isotropic). The anisotropy effect is investigated by means of various contour plots of the temperature profile as well as heat transfer rate from the fin base and the effectiveness for different parameters of study (kr/kz, krz/kz , and Bir) in transient and steady-state heat conduction. The numerical code allows the study of the thermal behavior of anisotropic, orthotropic, and isotropic cylindrical pin fin according to the geometrical and physical parameters, as well as the thermal conditions to which the pin fin is subjected. A parametric study is performed in view to compare the thermal behavior of the various pin fin kinds submitted to the same conditions.