A Three Dimensional Immersed Boundary Method for Free Convection From Single Spheres and Aggregates

A novel numerical technique that utilizes a three-dimensional Immersed Boundary Method (IBM) to solve the thermal interactions between spherical particles in a fluid is developed. At first, the natural convection of an isolated isothermal sphere immersed in a viscous fluid is analyzed and a new correlation for the heat transfer rate from a single sphere is obtained for 0.5≤Pr≤200 and 0 ≤ Gr ≤500. Secondly, the free convection heat transfer rate of a pair of spheres (bi-sphere) and spherical clusters immersed in air (Pr=0.72) were investigated using this numerical technique. The interactions depend on the separation distance between the spheres. It was observed that an increase in the separation of two spheres in tandem or side-by-side within a certain range may enhance the average heat transfer rate, when the interparticle distance is more than five radii. The average heat transfer rate of a cluster of touching, identical spheres with the same Grashof number was found to decrease as the number of spheres increased in the cluster.