On the approximation of the modified error function

Abstract

In a recent research, the authors established an approximation to the modified error function (MEF) for a small positive thermal conductivity coefficient , leaving the problem open for the general case . 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 . In this paper, a new approximation to the MEF is found for and converges to the classical MEF as . A comparative analysis shows that our proposed approximation gives a better estimate than the one in this recent reasearch by Ceratani et al.