Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient

Abstract

In this paper, differential transform method (DTM) is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient. Using DTM, the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally, the coefficients of power series are obtained based on the solution of this set of equations. DTM overcame on nonlinearity without using restrictive assumptions or linearization. Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters. DTM results are compared with special case of the problem that has an exact closed-form solution, and an excellent accuracy is observed.

Keywords

• Differential transform method
• Nonlinear heat transfer equation
• Power-law temperature dependent
• Temperature distribution
• Fin efficiency