Abstract :

An exact semi-analytical development using the ray tracing method followed by numerical

simulations of radiation and coupling conduction-radiation heat transfer is applied to a gray

semi-transparent medium, enclosed in a 2D rectangular enclosure with a square and centered

obstacle. This work is subdivided into three parts: the first deals with the study of radiation

with black surfaces, the second takes into account, the diffuse reflection, the third analyzes the

combined conduction-radiation in the presence of black surfaces. The obstacle is contained

within the enclosure and participates to heat transfer through its surfaces at imposed

temperatures. The participating medium absorbs and emits radiation, and its initial temperature

is imposed constant. The objective of this work, is to evaluate the qualitative and quantitative

behavior from radiative quantities, such as the temperature field and the radiative flux in the

medium, which remain of great importance in engineering. The geometric configuration of the

semi-transparent medium according to the different sizes of the enclosure and of the obstacle

reveals the existence of several sub-zones, such that, the modeling of incident radiation differs

with regard to the heat ray pathlengths. In the first part, the radiative transfer equation is solved

by means of special Bickley-Naylor functions, followed by a numerical analysis with Gauss

quadratures that gives precise results. The one of the temperature profile and the heat flow are

compared with the literature, numerical simulations showing the influence of the obstacle on

the distribution of radiative quantities are presented and the latter inform the validity of this

analysis. In the second part, the radiosity technique is introduced to precisely determine the

exact semi-analytical expressions of the radiosity temperatures at the boundary surfaces, as well

as the resulting heat flux in the semi-transparent medium. The numerical results show an

extremely significant effect of surface emissivities on the radiative behavior of the internal

environment. In the third part, we add to the radiation a conductive transfer modeled by centered

finite differences. The results obtained were compared with the literature and analyzed

according to the characteristic parameters.