Figure 1: Stefan’s Law in action.

The original ray-tracing radiation solver in our Energy2D software suffers from performance problems as well as inaccuracies (no, light particles do not travel that slowly as shown in it). After some sleepless nights, I finally implemented a real radiation solver, coupled it with the heat and fluid solvers, and supported both the convex and concave shapes (see this short paper for the mathematics and the algorithms). At last, Energy2D is capable of simulating all three heat transfer mechanisms in a decent way.

Figure 2: Radiation in a box.

Able to simulate heat, fluid, radiation, particles, and any combination of them, Energy2D is now one step closer towards a full multiphysics capacity. Despite the fact that all these complex calculations are done in real time on a single computer, the software still runs at a pretty amazing speed on an average Windows tablet (such as the Surface Pro). I guess this is why our industry friends love it (although Energy2D is mostly designed for K-12 students, to my surprise, quite a number of engineers are using it to do conceptual product design). Who doesn’t like a CFD tool for dummies that can save time from the long preprocessor-solver-postprocessor cycle?

Figure 1 shows a simulation that illustrates radiation heat transfer. As you can see, energy can “jump” from a high-temperature object (a radiator) to a low-temperature one without heating the medium between them (unlike the cases of conduction and convection). Users

Figure 3. Radiation in a circle.

can adjust the temperature of the radiator on the left and investigate how the radiation heat transfer increases with respect to the temperature, as per Stefan-Boltzmann’s Law. The image also shows the view factor field used in the computation. The simulation provides many subtleties. For example, if you observe carefully, you can find that the radiation barrier used to separate the left compartment from the right one increases the heating on the right side of the upper left object and the left side of the upper right object — because it reflects the radiation from the two radiators at the lower part of the box to the two sides!

Figures 2 and 3 show radiation among different shapes in an enclosed space. They show how accurate the radiation solver may be. The radiation heating on the side walls seems to make sense. In Figure 2, the upper one gets the most radiation energy because it is the closest to the radiator. The right one gets the least because part of it is blocked from the radiator by the other object in a box. A further test case using a symmetric setup shows its accuracy.