Series solution of convective radiative conduction equation of the nonlinear fin with temperature dependent thermal conductivity

In this study, differential transform method (DTM) is used to evaluate the analytical solution of the nonlinear fin problem with temperature dependent thermal conductivity. Results are presented for the dimensionless temperature distribution and fin efficiency for a range of values of the problem parameters. Using DTM, the differential equation and related boundary conditions are 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. Results of this method are compared with the variational iteration method (VIM) and numerical solutions. Here, it is shown that the results of DTM are more accurate than the VIM with lesser calculation cost, which is the main innovation of the current study.