General exact solution of the fin problem with variable thermal conductivity

Abstract

In this paper, Lie point symmetry method is used to obtain the general exact solution of the second order nonlinear ordinary differential equation which governing heat transfer in rectangular fin with variable thermal conductivity. Some new forms of thermal conductivity are introduced and the associated exact solution is obtained in each case. The general relation among the fin efficiency, thermal conductivity and thermo-geometric parameter is obtained.

Keywords

• Exact solution
• Fin
• Thermal conductivity
• Heat transfer
• Lie point symmetry