Numerical and Analytical Study of Two Dimensional Heat Transfer Thorough an Annular Fin of Variable Thickness

Ziad M Al-Makhyoul

doi:10.33899/rengj.2011.27888

Abstract

This paper included an analytical study of a two dimensional (radial and transverse) heat flow through annular fin variable thickness analytically depending on the group of resistances by derivating the major equations of conduction and convection. The total resistance equation of fin is derived to be general and simple model to calculate the heat flow and to study the effect of fin parameters on it. A numerical solution is added to prove the validity of the analytical solution by using a grid generation transformation-algebraic method to regulating the irregular mesh on the fin surface. Finally, the results show a good agreement between the two solutions using a wide range of fin parameters and this study is supposed to facilitate the designing of fin to the designer. Key words: Annular fin , Total resistance, heat transfer coefficient

Highlights

Annular fins find numerous applications in compact heat exchangers: in specialized installations of single and double-pipe heat exchangers, in electrical apparatus in which generated heat must be efficiently dissipated, on cylinders of air cooled internal-combustion engines
Higges [1] studied the heat transfer from annular fins of triangular profile with variable heat transfer coefficient from the base to the tip. He found that the increase in the heat transfer coefficient will cause the decrease in the efficiency of the fin
Simplifying assumptions like arc idealization and the insulated fin tip condition have been relaxed and a linear variation of the convective heat transfer coefficient along the fin surface has been taken into account

Summary

Introduction

Annular fins find numerous applications in compact heat exchangers: in specialized installations of single and double-pipe heat exchangers, in electrical apparatus in which generated heat must be efficiently dissipated, on cylinders of air cooled internal-combustion engines. Kahwaji and Al-Makhyoul [5] derived analytically the total resistance model by using the variable heat transfer coefficient in two dimensional heat flow for annular fin constant thickness by using a finite difference method using SOR technique. The above literature indicated that [1 and 2] were concerned with the heat flow through extended surface by using either charts or a computer program, while the researchers [3 to 6] were concerned with the studying of the heat transfer calculations depending on total resistance model for annular and longitudinal fins with constant thickness and their results were good. Every term of the general equation is converted to calculate the coordinate ( , ) and the equations can be written as:

Where Jac is Jacobian matrix and the derivatives

4.Results and Discussions

Length of Fin

Num The