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The temperature profile for fins with temperature-dependent thermal conductivity and heat transfer coefficients will be considered. Assuming such forms for these coefficients leads to a highly nonlinear partial differential equation (PDE) which cannot easily be solved analytically. We establish a numerical balance rule which can assist in getting a well-balanced numerical scheme. When coupled with the zero-flux condition, this scheme can be used to solve this nonlinear partial differential equation (PDE) modelling the temperature distribution ina one-dimensional longitudinal triangular fin without requiring any additional assumptions or simplifications of the fin profile

A Numerical Well-Balanced Scheme for One-Dimensional Heat Transfer in Longitudinal Triangular Fins