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, 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, 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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