Element Differential Method for Non-Fourier Heat Conduction in the Convective-Radiative Fin with Mixed Boundary Conditions

Fin is an efficient and straightforward way to enhance heat transfer rate. When the heat source varies dramatically in a very short time, non-Fourier heat conduction should be considered. In the paper, taking advantage of numerical stability and no integral and easy-to-implement features of an element differential method, a numerical model is developed to evaluate the fin efficiency of the convective-radiative fin within non-Fourier heat conduction. In this fin, heat is generated by an internal heat source and dissipated by convection and radiation. Both periodic and adiabatic boundary conditions are considered. The accuracy and efficiency of the element differential method is validated by several numerical examples with analytical solutions. The results indicate that the element differential method has high precision and flexibility to solve non-Fourier heat conduction in convective-radiative fin. Besides, the effects of Vernotte number, dimensionless periodicity, thermal conductivity coefficient, and emissivity coefficient on dimensionless fin tip temperature, instantaneous fin efficiency, and average fin efficiency are comprehensively analyzed.