Problem Description

The problem to be considered is shown schematically in Figure  5.1. A three-dimensional box $(0.5 \times 0.5 \times 0.5)$ has a hot wall at 473 K and all other walls at 293 K. Gravity acts downwards. The medium contained in the box is assumed to be absorbing and emitting, so that the radiant exchange between the walls is attenuated by absorption and augmented by emission in the medium. All walls are black. The objective is to compute the flow and temperature patterns in the box, as well as the wall heat flux, using the surface-to-surface (S2S) model available in ANSYS FLUENT.

The working fluid has a Prandtl number of approximately 0.71, and the Rayleigh number based on $L$ (0.5) is $5 \times 10^{8}$. This means the flow is most likely laminar. The Planck number $k/(4\sigma LT^3_0)$ is 0.003, and measures the relative importance of conduction to radiation.

Figure 5.1: Schematic of the Problem