Numerical study of grey‐body surface radiation coupled with fluid flow for general geometries using a finite volume multigrid solver

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Abstract
The paper presents a numerical technique for the simulation of the effects of grey‐diffusive surface radiation on fluid flow using a finite volume procedure for two‐dimensional (plane and axi‐symmetric) geometries. The governing equations are solved sequentially, and the non‐linearities and coupling of variables are accounted for through outer iterations (coefficients updates). In order to reduce the number of outer iterations, a multigrid algorithm was implemented. The radiating surface model assumes a non‐participating medium, semi‐transparent walls and constant elementary surface temperature and radiation fluxes. The calculation of view factors is based on the analytical evaluation for the plane geometry and numerical integration for axi‐symmetric geometry. Ashadowing algorithm was implemented for the calculation of view factors in general geometries. The method for the calculation of view factors was first tested by comparison with available analytical solutions for a complex geometric configuration. The flow prediction code combined with radiation heat transfer was verified by comparisons with analytical one‐dimensional solutions. Further test calculations were done for the flow and heat transfer in a cavity with a radiating submerged body. As an example of the capabilities of the method, transport processes in metalorganic chemical vapour deposition (MOCVD) reactors were simulated.