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The heat-balance integral method of Goodman has been thoroughly analyzed inthe case of a parabolic profile with unspecified exponent depending on theboundary condition imposed. That the classical Good man's boundary conditionsdefining the time-dependent coefficients of the prescribed temperature profiledo not work efficiently at the front of the thermal layers if the specificparabolic profile at issue is employed. Additional constraints based onphysical assumption enhance the heat-balance integral method and form a robustalgorithm defining the parabola exponent . The method has been compared byresults provided by the Veinik's method that is by far different from the Goodman's idea but also assume forma tion of thermal layer penetrating the heatbody. The method has been demonstrated through detailed solutions of 4 1-Dheat-conduction problems in Cartesian co-ordinates including a sphericalproblem (through change of vari ables) and over-specified boundary condition atthe face of the thermal layer.

The heat-balance integral method by a parabolic profile with unspecified exponent: Analysis and Benchmark Exercises