Transient Formulations for a Heat-Generating Fin with a Temperature-Dependent Heat Transfer Coefficient and Thermal Conductivity

This project investigates transient heat transfer phenomena within a heat-generating fin, considering the complexities introduced by temperature-dependent heat transfer coefficients and thermal conductivity. The core challenge involves addressing a highly nonlinear governing equation, which is subject to both Dirichlet and Neumann boundary conditions at the domain extremities. A robust numerical methodology is employed, leveraging an integral representation of the governing equation. This representation is formulated through Green’s second identity, incorporating a free-space Green function to facilitate an element-driven discretization approach. The temporal derivative is approximated using finite difference schemes, leading to a system of discrete equations characterized by their recursive nature. To ensure the physical consistency and continuity of scalar

variables, compatibility conditions and boundary conditions are rigorously enforced at the interfaces between adjacent elements. The resulting system of discrete equations is subsequently solved and assembled numerically to determine the transient evolution of scalar variables over time. The formulation's convergence and accuracy are validated through comprehensive numerical tests, with results benchmarked against established literature to confirm reliability. This research contributes to advanced thermal system analysis, particularly for components operating under dynamic and non-linear thermal conditions.

Message: Hi FE, I need help with “Transient Formulations for a Heat-Generating Fin with a Temperature-Dependent Heat Transfer Coefficient and Thermal Conductivity” in “Thermal & Fluid Sciences”