Joop's World: A Mathematical Analysis of Heat Transfer in an Earth Analog Model

The purpose of this experiment is to identify a greenhouse effect in the simple earth analog model: a uniformly heated sphere in a closed chamber. By filling the chamber with different gases, we can compare the effects of different gas properties on the overall heat transfer of the system. The goal is to determine the influence of each component of heat transfer on the overall system and investigate how this affects the average temperature of the sphere. Ultimately, we hope to be able to relate these results to the global climate system, specifically how changes in atmospheric gases affect average global temperature. We used a series of mathematical computations to determine the magnitude of the various methods of heat transfer and found convection to be an important component. We then concluded that the properties of each gas had a significant effect on convection in the chamber. From these results, we were also able to show the existence of the greenhouse effect.