Abstract
In a recent research, the authors established an approximation to the modified error function (MEF)
φδ$$ {\varphi}_{\delta } $$ for a small positive thermal conductivity coefficient
δ>0$$ \delta >0 $$, leaving the problem open for the general case
−1<δ<∞$$ -1<\delta <\infty $$. The approximation represents an approximate solution to the Stephan problem with linear thermal conductivity in a semi‐infinite body, which converges to the classical MEF as
δ→0+$$ \delta \to {0}&#x0005E;{&#x0002B;} $$. In this paper, a new approximation to the MEF is found for
−1<δ<∞$$ -1<\delta <\infty $$ and converges to the classical MEF as
δ→0±$$ \delta \to {0}&#x0005E;{\pm } $$. A comparative analysis shows that our proposed approximation gives a better estimate than the one in this recent reasearch by Ceratani et al.