Subregion of validity of the lumped-based model for transient, radiative cooling of spherical bodies to a zero temperature sink

Abstract

Transient radiative cooling of small spherical bodies having large thermal conductivity has not been critically examined in the open literature from a demarcation point of view as compared with the transient convective cooling. For a sink temperature at zero absolute, a comparative study involving the distributed- and the lumped-based models have been presented where the controlling parameter is the radiation-conduction parameter, N rc. The family of curves for the relative errors associated with the surface-to-center temperatures followed a normal distribution in semilog coordinates. Viable quantitative thresholds can be extracted from the figures and for a maximum allowable 5% relative error, the magnitude of N rc must be 0.15.