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International Heat Transfer Conference 15

ISSN: 2377-424X (online)
ISSN: 2377-4371 (flashdrive)

High-Order Numerical Implementation of Surface Radiation for the Coupling with Natural Convection in an Air-Filled Square Cavity

Ronnie Knikker
Univ Lyon, CNRS, INSA-Lyon, Universite Claude Bernard Lyon 1, CETHIL UMR5008, F-69621, Villeurbanne, France

Shihe Xin
Univ Lyon, CNRS, INSA-Lyon, Universite Claude Bernard Lyon 1, CETHIL UMR5008, F-69621, Villeurbanne, France

Ren Dai
University of Shanghai for Science and Technology

DOI: 10.1615/IHTC15.cnv.009092
pages 1638-1652


KEY WORDS: Computational methods, Convection, Radiation

Abstract

Natural convection in a cavities without radiation has been the subject of many investigations with many practical applications and it became a benchmark problem for testing CFD codes. Although surface radiation is far from negligible in natural convection in air-filled cavities, studies including the interaction between the two phenomena remain still sparse. The main purpose of this work is the development of accurate numerical methods for the study of the coupling of natural convection with surface radiation in air-filled cavities, in view also of providing a benchmark problem and reference solutions. Since the standard radiosity method using view factors can yield only second-order spatial accuracy, a new formulation using pointwise radiosity and integration by parts is proposed. The numerical implementation of the new formulation is based on appropriate quadratures for numerical integration and differentiation and is tested in a spectral Chebyshev collocation method and a fourth-order finite-difference method. Results obtained at RaH = 104 and 105 show respectively spectral and fourth-order convergence for the convective and radiative Nusselt numbers. The spectral implementation also confirms that a much coarser mesh can be employed for surface radiation compared to the one used for the solution of the Navier-Stokes equations, without decreasing the accuracy of the numerical results. This is an important observation for future 3D simulations in which the large number of surface elements becomes a major stumbling block.

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