Finite Volume Method for Thermal Analysis of Longitudinal Trapezoidal Fin with Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient

This paper investigates the thermal performance of a longitudinal trapezoidal fin using the Finite Volume Method, considering temperature-dependent thermal conductivity and heat transfer coefficient. The governing energy equation is developed by incorporating nonlinear thermal parameters and transforming these to dimensionless forms. The domain is discretized into control volumes and the energy balance is applied to each node to develop a system of algebraic equations. The effect of parameters like effectiveness factor, fin steepness, thermal conductivity and scale factor on temperature distribution is then studied. The results provide insights into optimizing fin geometry and thermal properties for efficient heat dissipation in engineering applications, while the temperature gradients along the fin length offers useful information for design. The Finite Volume Method ((FVM) proves advantageous in handling irregular geometries and conserving local balances. Overall, this comprehensive numerical approach enables accurate prediction of the intricate thermal response of longitudinal trapezoidal fins.