Temperature Profiles for Diffusion Problem Precise Solutions Using Heat Balance Integral Method

摘要

In the present paper, the heat balance integral method is applied for the solution of semi-infinite solid heat conduction problems subjected to prescribed polynomial type time-variable temperature or heat flux boundary conditions. A real n value exponent temperature profile is used. The obtained results are compared with literature classical solutions. For the first time in the literature, an algebraic expression for the n exponent, which depends on the boundary conditions applied to the problem, is proposed. Although the heat balance integral method is much easier to implement, the precision obtained using the proposed temperature profile is of the same order of magnitude of the classical literature solutions. The temperature distributions obtained from a numerical benchmark test case are used in the comparison with the present solutions. This study also discusses the restrictions of the real n exponent temperature profile heat balance integral method solutions.