Abstract
This paper presents the solution of coupled radiative transfer equation with heat conduction equation in complex three-dimensional geometries. Due to very different time scales for both physics, the radiative problem is considered steady-state but solved at each time iteration of the transient conduction problem. The discrete ordinate method along with the decentered streamline-upwind Petrov-Galerkin method is developed. Since specular reflection is considered on borders, a very accurate algorithm has been developed for calculation of partition ratio coefficients of incident solid angles to the several reflected solid angles. The developed algorithms are tested on a paraboloid-shaped geometry used for example on concentrated solar power technologies.
Highlights
The study of the thermal and radiative heat transfer in semitransparent media plays an important role for industrial applications such as thermal insulation [1], photo-thermal therapy [2], glass forming [3] [4], porous media [5] and many others [6]
The coupling takes into account of the steady-state radiative transfer equation (RTE), as well as the transient heat conduction equation (HCE)
The radiative transfer equation is written as follow: s.∇I ( x, s) + β I ( x, s) =σ s ∫4π Φ ( s, s′) I ( x, s′) ds′ + κ Ib (T (t, x))
Summary
The study of the thermal and radiative heat transfer in semitransparent media plays an important role for industrial applications such as thermal insulation [1], photo-thermal therapy [2], glass forming [3] [4], porous media [5] and many others [6]. The coupling takes into account of the steady-state radiative transfer equation (RTE), as well as the transient heat conduction equation (HCE). Such a transient coupling is well derived in [9] [10]. (2016) 3D Radiative Transfer Equation Coupled with Heat Conduction Equation with Realistic Boundary Conditions Applied on Complex Geometries. A discrete ordinate method for angular discretization, combined with SUPG, a decentered finite element scheme for space discretization, allow the solution of the RTE. The temperature evolution inside the medium of concern greatly changes
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