The heat-balance integral: 2. Parabolic profile with a variable exponent: The concept, analysis and numerical experiments

Jordan Hristov

doi:10.1016/j.crme.2012.03.002

The heat-balance integral: 2. Parabolic profile with a variable exponent: The concept, analysis and numerical experiments

Jordan Hristov ¹

¹ Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 1756 Sofia, 8 Kl. Ohridsky Blvd., Bulgaria

Comptes Rendus. Mécanique, Analytical and innovative solutions for heat transfer problems involving phase change and interfaces, Volume 340 (2012) no. 7, pp. 493-500.

Résumé

A heat-balance integral method employing a parabolic profile with a variable (self-adapting) exponent has been developed. The parabolic profile satisfies both the boundary conditions and the heat-balance integral at any value of the exponent, while the optimal solution requires minimization of the mean-squared error defined by the domain parabolic equation. The concept of a variable exponent results in simple relationships involving the LambertW function and the initial values defined through the profile calibration at $x = 0$ . Two simple 1-D problems with classic solutions are developed to demonstrate the method.

Publié le : 2012-05-03

DOI : 10.1016/j.crme.2012.03.002

Mots-clés : Heat-balance integral, Parabolic profile, Variable exponent, LambertW function

Affiliations des auteurs :

Jordan Hristov ¹

¹ Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 1756 Sofia, 8 Kl. Ohridsky Blvd., Bulgaria

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Jordan Hristov. The heat-balance integral: 2. Parabolic profile with a variable exponent: The concept, analysis and numerical experiments. Comptes Rendus. Mécanique, Analytical and innovative solutions for heat transfer problems involving phase change and interfaces, Volume 340 (2012) no. 7, pp. 493-500. doi : 10.1016/j.crme.2012.03.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.03.002/

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Jordan Hristov A non-linear diffusion problem with power-law diffusivity: An approximate solution experimenting with a modified sinc function, Mathematical Modelling and Numerical Simulation with Applications, Volume 4 (2024) no. 5-Special Issue: ICAME'24, p. 6 | DOI:10.53391/mmnsa.1545438
E.P. Canzian; F. Santiago; A.V. Brito Lopes; M.R. Barbosa; A.G. Barañano On the application of the double integral method with quadratic temperature profile for spherical solidification of lead and tin metals, Applied Thermal Engineering, Volume 219 (2023), p. 119528 | DOI:10.1016/j.applthermaleng.2022.119528
E.P. Canzian; F. Santiago; A.V. Brito Lopes; A.G. Barañano Spherical solidification: An application of the integral methods, International Journal of Thermal Sciences, Volume 177 (2022), p. 107575 | DOI:10.1016/j.ijthermalsci.2022.107575
Petro Babak; Apostolos Kantzas Estimation of Gas Absorption and Diffusion Coefficients for Dissolved Gases in Liquids, Industrial Engineering Chemistry Research, Volume 58 (2019) no. 2, p. 1019 | DOI:10.1021/acs.iecr.8b02343
V. A. Kot Parabolic Profile in Heat-Conduction Problems. 1. Semi-Bounded Space with a Surface of Constant Temperature, Journal of Engineering Physics and Thermophysics, Volume 91 (2018) no. 6, p. 1391 | DOI:10.1007/s10891-018-1873-1
S.C. Gupta Quasi-Analytical Solutions and Methods, The Classical Stefan Problem (2018), p. 311 | DOI:10.1016/b978-0-444-63581-5.00012-9
Bibliography, The Classical Stefan Problem (2018), p. 683 | DOI:10.1016/b978-0-444-63581-5.09990-5
Jordan Hristov Integral solutions to transient nonlinear heat (mass) diffusion with a power-law diffusivity: a semi-infinite medium with fixed boundary conditions, Heat and Mass Transfer, Volume 52 (2016) no. 3, p. 635 | DOI:10.1007/s00231-015-1579-2
V. A. Kot Method of Boundary Characteristics, Journal of Engineering Physics and Thermophysics, Volume 88 (2015) no. 6, p. 1390 | DOI:10.1007/s10891-015-1324-1

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