The study of how heat moves around a sphere is one of the most crucial problems in fluid dynamics and thermal sciences. The main objective of this study is to show that CFD simulations for heat transfer over a sphere are correct by comparing the outcomes with mathematical models. In particular, we will look into the Nusselt number, a parameter that doesn’t have any units and describes the ratio of convective to conductive heat transfer at a border. This process of validation greatly matters for building trust in CFD methods for more difficult heat transfer problems and for learning more about how heat moves around spherical objects in different flow conditions.

Figure 1: Heat Transfer around a sphere

Simulation Process

A 1-cm sphere is placed in a rectangular domain. The grid features a thin boundary layer on sphere walls that gradually increase in size, leading to 1398307 elements. The Nusselt number for the flow passing over a sphere is calculated analytically based on the following equation ( considering the acceptable range of Reynolds number):

In our case problem, Reynolds is 11190.

Post-processing

The mathematical formulation shows that the Nusselt number for a Reynolds number of 11,190 is 129, but the CFD simulation gives a value of 121.86. This difference is about 5.2%, which is satisfactory in engineering models. The fact that the two methods agreed on a lot of things says that the CFD model does a good job of showing how heat moves around the sphere. The CFD modeling may have slightly underestimated the problem for different reasons, such as the mesh resolution, the choice of turbulence model, or the way the boundary conditions are set up. This makes it a useful tool for further research and more complicated shapes where analytical answers might not be easy to find.