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 heatnconduction problems subjected to prescribed polynomial type time-variable temperature or heat flux boundarynconditions. A real n value exponent temperature profile is used. The obtained results are compared with literaturenclassical solutions. For the first time in the literature, an algebraic expression for the n exponent, which depends onnthe boundary conditions applied to the problem, is proposed. Although the heat balance integral method is muchneasier to implement, the precision obtained using the proposed temperature profile is of the same order ofmagnitudenof the classical literature solutions. The temperature distributions obtained from a numerical benchmark test casenare used in the comparison with the present solutions. This study also discusses the restrictions of the real n exponentntemperature profile heat balance integral method solutions.