A novel revision of Goodman’s profile and its application to a one-phase Stefan problem

Due to its extreme simplicity the heat balance integral method (HBIM), introduced by Goodman for addressing transport problems, has attracted lots of attention in recent times. Specifically, the subtle objective of most of these has been that of significant improvement of its accuracy while retaining simplicity. A crucial factor in achieving this is the choice of test functions/profiles, of which holds little structure in current literature. It is shown, by elementary methods, how seemingly disjoint sets of earlier proffered profiles relate. Further, novel test profiles, due to pertinent generators, are introduced and shown to yield remarkably accurate approximate solutions to a benchmark Stefan (melting) problem.

► A sequential framework based on fundamental solutions is introduced in the implementation of the heat balance integral method.
► Pertinent generating functions related to the fundamental solutions of the state equation are exploited.
► Application of resulting novel profiles to a Stefan melting problem shows remarkable accuracy.