When objects get hot, they give off heat without touching each other – this is radiation heat transfer. In our study, we look at how this happens inside a triangle-shaped hollow space (cavity) where the inside surfaces have different abilities to emit radiation (variable emissivity). This is important because in many real-world applications like solar collectors, building insulation, and electronic cooling systems, understanding how heat moves through radiation in enclosed spaces matters a lot. Our simulation explores how changing the surface properties affects how heat spreads inside the triangular cavity. Unlike most studies that focus on simple square or rectangular spaces, our triangle-shaped cavity creates unique radiation patterns as heat bounces off the angled surfaces. By tracking how different emissivity values change temperature patterns, we can better understand radiation heat transfer in more complex shapes that match real-world engineering problems.

Figure 1: Triangular cavity schematic

Simulation Process

The production of the geometry model and structured grid is not challenging compared to the solver settings. As the title of the project suggests, various wavelength Intervals for three bands are included. This requires the usage of the non-grey sub-model provided in Discrete Ordinates (DO) radiation module. Given the transient nature of the natural convection phenomenon, a pseudo-transient solver is utilized.

Post-processing

The temperature contour image shows heat distribution inside our triangular cavity, ranging from 300K (cool blue areas) to nearly 979K (hot red regions). The circular heat source in the center creates a hot spot that reaches maximum temperature, with heat gradually spreading upward in a plume-like pattern. This upward movement happens because hot air rises naturally due to buoyancy forces. The temperature decreases as we move away from the heat source, with most of the cavity remaining relatively cool (green-blue colors), showing how radiation and natural convection work together to distribute heat.

Figure 2: temperature contour shows heat distribution

The velocity streamline visualization reveals the complex air movement patterns inside the cavity, with speeds ranging from 0 to 0.719 meters per second. Several distinct circulation zones (vortices) form as the heated air rises from the circular source and cooler air moves to replace it. The highest velocities (yellow-red colors) appear along the cavity walls and in the rising plume above the heat source. Interestingly, the flow creates asymmetric patterns despite the symmetric geometry, a hallmark of natural convection systems. These flow patterns directly influence how heat transfers throughout the cavity, with the variable emissivity of different surfaces affecting both the radiation exchange and resulting air movement patterns. The multiple small vortices near cavity corners show how the triangular shape creates unique flow structures that wouldn’t exist in simpler geometries.

Figure 3: Velocity streamlines in the cavity