Approximate solution of one-dimensional heat diffusion problems via hybrid profiles

This paper presents hybrid temperature profiles, a combination of an exponential and a polynomial, capable of providing highly accurate but approximate solutions to one-dimensional heat diffusion problems by the use of the heat balance integral method. After establishing their capability in the case of two test problems, namely, an initially isothermal semi-infinite medium subject to either a specified heat flux or temperature at its surface, two typical applications are considered. These show that the hybrid profile-heat balance integral combination is an excellent approximation that may be used as a first step before launching on a numerical solution in cases that do not have available analytical solutions. © 1987.