Regular solid bodies with uniform surface heat flux: Curve-fitted surface temperatures versus time in the small time subregion

The present study considers the behavior of surface temperatures in regular solid bodies (plate, cylinder, and sphere) with constant initial temperature and heated with uniform heat flux in the early time subregion. First, the dimensionless surface temperatures are evaluated numerically in the entire dimensionless time domain with a symbolic algebra software owning automatic convergence control. Second, a regression analysis is applied to the gathered data for the dimensionless surface temperatures versus the dimensionless time in the dimensionless time subregion 0 < τ ≤ τ_cr (τ_cr is the critical dimensionless time that sets the borderline for the "large time" subregion). As a direct outcome, compact correlation asymptotes are retrieved for prediction of the dimensionless surface temperatures in the plate, cylinder, and sphere confined to the dimensionless time subregion 0 < τ ≤ τ_cr. Interestingly, agreement with the exact analytical surface temperature distributions expressible by the standard infinite series for the "all time" domain is considered excellent.