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.