Conductive-radiative heat transfer in a 2D semi-transparent medium with a square centered obstacle

Abstract

The present paper deals with an exact semi-analytical formulation of a combined conductiveradiative heat transfer, applied to a two-dimensional semi-transparent medium carrying a square centered obstacle. The gray participating medium with black boundaries absorbs, emits but does not scatter radiation. One intends to evaluate the temperature and radiative heat flux distributions within the semi-transparent medium. The radiative transfer equation has been solved using an exact analytical expansion of Bickley-Naylor and Altaç angular integrated Bickley-Naylor functions, then solved numerically with Gauss quadrature. Energy equation has been directly discretized and approximated numerically using the centered finite differences method and consequently the dimensionless temperature has been obtained after an iterative scheme. The results of radiative quantities obtained have been verified with benchmark with an excellent agreement, both for simple and complex geometries. Simulations have been performed to obtain results for different sizes of the centered obstacle and the optical thickness. The effects of the conduction-radiation parameters, discrete directions and the size of the obstacle have also been investigated.

Determination of the surfaces radiosity temperatures in a square cavity with a square inner centred obstacle and a non-isothermal absorbing-emitting medium

“…-Contribution incoming from the southern obstacle's surface: (25) where the internal contribution ℵ 𝐸 is expressed by, in the general case of an non-isothermal medium:…”

“…In the previous works, although the semi-transparent medium is both emitting-absorbing and scattering, it is generally isothermal at an imposed constant temperature and no real heat transfer occurs, the main problem being in the effective resolution of the RTE and applying it to the flux calculation. We recently examined the case of a centred square opaque obstacle inside a square cavity containing an emittingabsorbing medium at radiative equilibrium by using an exact analytical method [24] which proved its robustness, both at radiative equilibrium and in situation of radiation/conduction coupling [25]. Although quite complex to implement due to difficult calculations, it is to our best knowledge the only one method which efficiently points out the major rule of the ratio ℎ 𝐻 in the radiative behaviour of the whole device and produces smooth accurate results for the different values of the previous ratio.…”