Unsteady Heat Transfer From a Sphere at Small Peclet Numbers

In a recent paper by Michaelides and Feng (1994) it was discovered that there are history terms in the unsteady heat conduction equation from a small sphere. The history terms are analogous to the terms found in the equation of motion of the sphere, which sometimes are called “Basset terms.” An analysis is presented here for the unsteady heat transfer from a sphere, when its surface temperature undergoes a step change. The singular perturbation technique is used to obtain short and longtime solutions, first in the vicinity of the sphere and then far from the sphere. The solution obtained is for finite but low Peclet numbers. It appears that in the case of the step temperature, change, the history terms are reduced to an analytical expression of the error function.