The Heat-Balance Integral Method (HBIM) of Goodman under classic prescribed temperature boundary conditions has been studied towards it optimization. Because the parabolic profile satisfies both the boundary conditions and the heat-balance integral at any value of the exponent the calibration is of a primary importance in generation of the approximate solution. The simple 1-D heat conduction problem, enabling one to demonstrate the HBIM performance with the entropy generation minimization (EGM) concept in calibration of a parabolic temperature profile with unspecified exponents, has been developed. The EGM concept provides constraints that impose addition boundary conditions at the approximate parabolic profile. Additionally, entire domain optimizations based on the mean-squared error concept has been performed in two versions – the method Myers and through a similarity transformed diffusion equation.
Jordan Hristov 1
@article{CRMECA_2012__340_7_485_0,
author = {Jordan Hristov},
title = {The heat-balance integral: 1. {How} to calibrate the parabolic profile?},
journal = {Comptes Rendus. M\'ecanique},
pages = {485--492},
publisher = {Elsevier},
volume = {340},
number = {7},
year = {2012},
doi = {10.1016/j.crme.2012.03.001},
language = {en},
}
Jordan Hristov. The heat-balance integral: 1. How to calibrate the parabolic profile?. Comptes Rendus. Mécanique, Volume 340 (2012) no. 7, pp. 485-492. doi : 10.1016/j.crme.2012.03.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.03.001/
[1] The heat balance integral and its application to problems involving a change of phase, Trans. ASME, Volume 80 (1958) no. 1–2, pp. 335-342
[2] On high-order polynomial heat-balance integral implementations, Thermal Science, Volume 13 (2009) no. 2, pp. 11-25
[3] Application of heat-balance integral method to conjugate thermal explosion, Thermal Science, Volume 13 (2009) no. 2, pp. 73-80
[4] On the Goodman heat-balance integral method for Stefan-like problems, Thermal Science, Volume 13 (2009) no. 2, pp. 91-96
[5] How good is Goodmanʼs heat-balance integral method for analyzing the rewetting of hot surfaces?, Thermal Science, Volume 13 (2009) no. 2, pp. 97-112
[6] Heat-balance integral method for heat transfer in superfluid helium, Thermal Science, Volume 13 (2009) no. 92, pp. 121-132
[7] Entropy generation analysis in error estimation of an approximate solution: A constant surface temperature semi-infinite conductive problem, Thermal Science, Volume 13 (2009) no. 2, pp. 133-140
[8] Analysis of phase-change in finite slabs subjected to convective boundary conditions: Part I – Melting, Int. Rev. Chem. Eng., Volume 1 (2009) no. 1, pp. 87-99
[9] Analysis of phase-change in finite slabs subjected to convective boundary conditions: Part II – Freezing, Int. Rev. Chem. Eng., Volume 1 (2009) no. 1, pp. 100-108
[10] Application of integral methods to transient nonlinear heat transfer, Adv. Heat Transfer, Volume 1 (1964), pp. 51-122
[11] A comprehensive analysis of conduction-controlled rewetting by the heat balance integral method, Int. J. Heat Mass Transfer, Volume 49 (2006), pp. 4978-4986
[12] An inverse Stefan problem relevant to boilover: Heat balance integral solutions and analysis, Thermal Science, Volume 11 (2007) no. 2, pp. 141-160
[13] The heat-balance integral method by a parabolic profile with unspecified exponent: Analysis and benchmark exercises, Thermal Science, Volume 13 (2009) no. 2, pp. 22-48
[14] W. Braga, M. Mantelli, A new approach for the heat balance integral method applied to heat conduction problems, in: 38th AIAA Thermophysics Conference, Toronto, Ontario, June 6–9, 2005, paper AIAA-2005-4686.
[15] Optimizing the exponent in the hear balance and refined integral methods, Int. Comm. Heat Mass Transfer, Volume 36 (2009), pp. 143-147
[16] The heat balance integral method, Int. J. Heat Mass Transfer, Volume 16 (1973), pp. 2424-2428
[17] Conduction of Heat in Solids, Oxford University Press, Oxford, UK, 1992
[18] Research note on a parabolic heat-balance integral method with unspecified exponent: An entropy generation approach in optimal profile determination, Thermal Science, Volume 13 (2009) no. 2, pp. 49-59
[19] On the minimum entropy production in steady state heat conduction processes, Energy, Volume 29 (2004), pp. 2441-2460
[20] The Fractional Calculus, Academic Press, New York, 1974
[21] Fractional-diffusion solutions for transient local temperature and heat flux, J. Heat Transfer, Volume 122 (2000), pp. 372-376
[22] Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhauser, Boston, 1997
[23] W.F. Braga, Integral method and electrical analogy to solution of heat transfer in ablating solids, MsS Thesis, Federal University of Santa Catarina, Florianópolis, Brazil, 2002 (in Portuguese).
[24] The heat-balance integral: 2. Parabolic profile with a variable exponent: the concept, analysis and numerical experiments, C. R. Mecanique, Volume 340 (2012) no. 7, pp. 493-500
[25] Stokes flows of a Newtonian fluid with fractional derivatives and slip at the wall, Int. Rev. Chem. Eng., Volume 3 (2011), pp. 822-826
[26] Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative, Appl. Math. Model., Volume 33 (2009), pp. 4184-4191
[27] Development of heavy metal sorption isotherm using fractional calculus, Int. Rev. Chem. Eng., Volume 3 (2011), pp. 814-817
[28] Starting radial subdiffusion from a central point through a diverging medium (a sphere): heat-balance integral method, Thermal Science, Volume 15 (2011), p. S5-S20
[29] Modeling of granular material mixing using fractional calculus, Int. Rev. Chem. Eng., Volume 3 (2011), pp. 818-821
[30] A research note on a solution of Stefan problem with fractional time and space derivatives, Int. Rev. Chem. Eng., Volume 3 (2011), pp. 810-813
[31] Relevance of a thermal contact resistance depending on the solid/liquid phase change transition for sprayed composite metal/ceramic powder by direct current plasma jets, C. R. Mécanique, Volume 336 (2008) no. 7, pp. 592-599
[32] Analytical solution of unsteady heat conduction in a two-layered material in imperfect contact subjected to a moving heat source, Int. J. Thermal Sciences, Volume 49 (2010) no. 2, pp. 311-318
[33] Thermal impedance at the interface of contacting bodies: 1-D example solved by semi-derivatives, Thermal Science, Volume 16 (2012) no. 2 | DOI
Cité par Sources :
Commentaires - Politique