A three dimensional immersed boundary-based method for the free and combined convective heat transfer from spherical bodies

The objective of this study is to develop a relatively simple numerical technique that utilizes a three-dimensional immersed boundary method (IBM) to solve the three dimensional thermal interactions of spherical particles in a fluid. Firstly, the natural convection of an isolated isothermal sphere immersed in a viscous fluid is analyzed and a new correlation for the heat transfer rate is obtained for 0.5≤ Pr ≤200 and 1 ≤ Gr ≤500. The natural convection heat transfer rate and drag coefficients of a pair of spheres (bi-sphere) and spherical clusters immersed in air (Pr=0.72) were also investigated and found to be dependent on the separation between the spheres; an increase in the separation of two spheres in tandem or side-by-side within a certain range enhances the average heat transfer rate. The average heat transfer rate of a cluster of identical spheres with the same Grashof number was found to decrease as the number of spheres increased in a cluster. Furthermore, the mixed convection of a heated sphere at various flow incident angles has also been studied for laminar flows ranging from completely downward (opposing) to completely upward (assisting). Separate treatment for the heat transfer rate is required for the cross flow (at right angles), completely upward flow, and completely upward flow. Finally, the influence of the Grashof number on the settling velocity and heat transfer rate of a single or multiple isothermal spheres settling in a fluid-filled vertical channel has been investigated; an increase in the Grashof number decreases both the settling velocity and heat transfer rate of a single sphere or many spheres in sedimentation.