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

Abstract 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.

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