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

Abstract

Numerical calculations and scalar transport analyses are carried out for transient heat transfer in a heat generating fin with a temperature-dependent heat transfer and conduction coefficients. The highly nonlinear governing equation, satisfies the Dirichlet and Neumann boundary conditions at both ends of the problem domain.Integral representation of the governing equation over the discretized problem domain is achieved via the Green’s second identity together with the so called free- space Green function . This element-driven approach togetherwith the finite difference approximation of the temporal derivative result in discrete equations which are recursive in nature. At the boundaries of any of the adjacent elements, compatibility conditions and/or boundary conditions are enforced to guarantee scalar continuity. After the resulting system of discrete equations are numerically solved and assembled, they yield the transient history of the scalar variables at any particular point in time. Several numerical tests are carried out to ensure the convergence and accuracy of the formulation by comparing numerical results with those found in literature.