Analysis of Combined Conductive and Radiative Heat Transfer in a Two Dimensional Square Enclosure using the Finite Volume Method

Abstract

An efficient tool to deal with multidimensional radiative heat transfer is in strong demand to analyse the various thermal problems combined either with other modes of heat transfer or with combustion phenomena. Combined conduction and radiation heat transfer without heat generation is investigated. Analysis is carried out for both steady and unsteady situations.
Two-dimensional gray Cartesian enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperature.
The finite volume method is used to solve the energy equation and the finite volume method is used to compute the radiative information required in the solution of energy equation. The Implicit scheme is used to solve the transient energy equation. Transient and steady state
temperature and heat flux distributions are found for various radiative parameters.
In the last two decade, finite volume method (FVM) emerged as one of the most attractive method for modeling steady as well as transient state radiative transfer. The finite
volume method is a method for representing and evaluating partial differential equations as algebraic equations. Similar to the finite difference method, values are calculated at discrete places on a meshed geometry. "Finite volume" refers to the small volume surrounding each node point on a mesh. In the finite volume method, volume integrals in a partial differential
equation that contain a divergence term are converted to surface integral using divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume.
Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative.
In the present work the boundaries are assumed to be gray and the medium scatters isotropically. The current study examines the finite volume method (FVM) for coupled radiative and conductive heat transfer in square enclosures in which either a non-scattering or scattering
medium is included. Implicit Scheme has been used for solving the coupled conductive and radiative heat transfer equation. The transient temperature distributions are studied for the effects of various parameters like the extinction coefficient, the scattering albedo and the
conduction radiation parameter for both constant. The effect of radiative parameters on the system to reach the steady state is also studied.