Numerical predictions of two-dimensional conduction, convection, and radiation heat transfer. I. Formulation

Abstract

The research presented in this paper involves the detailed formulation of a Control-Volume Finite Element Method (CVFEM) for the solution of combined-mode heat transfer in participating media. The proposed numerical method accounts for emitting, absorbing, and scattering media in regularly- and irregularly-shaped geometries. In the proposed CVFEM, the calculation domain is divided into three-node triangular finite elements: the geometrical flexibility associated with finite element methods is preserved. Each element is further subdivided in such a way that upon assembly of all elements, complete control volumes are formed around each node in the calculation domain. To account for the directional nature of radiation heat transfer, a spherical envelope, surrounding each node in the calculation domain, is discretized in adjacent non-overlapping solid angles (or control angles). Element-based interpolation functions for the dependent variables, and the subdomain-type method of weighted residuals are used to derive algebraic approximations to the governing equations. Interpolation schemes that guarantee positive contributions to the coefficients in the algebraic discretization equations are used to approximate the convective and radiative fluxes across control-volume surfaces.