Hristov J.2024-07-102024-07-102024-07-102024-07-102012-07-011631-072110.1016/j.crme.2012.03.002SCOPUS_ID:84863190919https://rlib.uctm.edu/handle/123456789/245A heat-balance integral method employing a parabolic profile with a variable (self-adapting) exponent has been developed. The parabolic profile satisfies both the boundary conditions and the heat-balance integral at any value of the exponent, while the optimal solution requires minimization of the mean-squared error defined by the domain parabolic equation. The concept of a variable exponent results in simple relationships involving the LambertW function and the initial values defined through the profile calibration at x= 0. Two simple 1-D problems with classic solutions are developed to demonstrate the method. © 2012 Académie des sciences.enShort Survey