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

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 nn value exponent temperature profile is used. The obtained re...

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Bibliographic Details
Published in:Journal of thermophysics and heat transfer 2011-07, Vol.25 (3), p.443-449
Main Authors: Mantelli, Marcia B. H, Braga, Walber F
Format: Article
Language:English
Subjects:
Benchmarking
Boundary conditions
Exponents
Heat balance
Heat transfer
Integrals
Mathematical models
Temperature profiles
Online Access:Get full text
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Summary: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 nn 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 nn 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 nn exponent temperature profile heat balance integral method solutions. [PUBLISHER ABSTRACT]
ISSN:0887-8722
1533-6808
DOI:10.2514/1.T3658