Laminar forced convection of a rotating sphere immersed in a uniform viscous flow

In a large number of applications, heat transfer rates are calculated through correlations that typically have a small range of applicability and have a significant margin of error. Therefore, models usually are greatly simplified to meet the restrictions of the correlation. For example, heat transfer from a sphere is a classical problem that has been studied extensively, but very rarely has the possibility of rotation of the sphere or angle of rotation have been considered.

The purpose of this study is to implement a Direct Numerical Simulation with an Immersed Boundary (DNS-IB) to investigate the heat transfer effects as a result of a particle rotating at different angles. The particle Reynolds numbers based on either the free-stream velocity or its angular velocity ranged from 0-300, while the angles of rotation that were investigated were from 0°-90°. It was observed that the particle's angle of rotation only had a significant effect on the rate of heat transfer at high rotational Reynolds numbers. The Nusselt number also appeared to increase with an increase in the angle of rotation, reaching a maximum at about 40°. At angles greater than 40°, the Nusselt number appeared to be negatively affected by the angle of rotation. At a rotational and free-stream Reynolds number of 200, the Nusselt number dropped by 11.4% by changing the angle of rotation from 45° to 90°. It was also determined that the Nusselt number increased in an almost linear fashion as the angle of rotation and rotational Reynolds number increased. An increase of 13.1% was observed by changing the angle of rotation from 0° to 45°, followed by a decrease of 18.2% by changing the angle of rotation from 45° to 90°. For different values of the free-stream velocity it was observed that at 40° the Nusselt was a maximum while at a rotational angle of 90° it was a minimum for a particle Reynolds number of 50. Consequently, it was concluded that if the particle's rotational Reynolds number is below 50, the angle of rotation is insignificant and the flow can be modeled as forced convection.

Prior to this study, there was no available published data regarding heat transfer effects as a result of the angle rotation; therefore, the methodology was validated with different pieces of published literature, which allowed the results for this study to be regarded as reliable data.