Constructing a new geometric numerical integration method to the nonlinear heat transfer equations

In this paper, we construct a new geometric integration method which is based on the Lie group SL(2,R) to solve the nonlinear longitudinal convective-radiative-conduction fin equation. SL(2,R)-shooting method and related algorithm to find a high accuracy solutions are discussed. Finally, effects of thermal conductivity parameter, surface emissivity parameter, convection-conduction and radiation-conduction parameters are illustrated on the performance of fins.