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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2017, Volume 10, Issue 3, Pages 40–53 (Mi vyuru385)  

This article is cited in 1 scientific paper (total in 1 paper)

Mathematical Modelling

Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus

V. I. Ryazhskikha, D. A. Konovalova, A. V. Ryazhskikha, A. A. Bogerb, S. V. Dakhina

a Voronezh State Technical University, Voronezh, Russian Federation
b Military Educational Scientific Center of the Military — Air Forces "Military Air Academy named after Professor N.E. Zhukovsky and Yu.A. Gagarin", Voronezh, Russian Federation

Abstract: In the three-dimensional statement, we consider the Brinkman equation together with the equation of heterogeneous heat transfer for an unidirectional flow of the Newtonian fluid under laminar regime through horizontal porous channel having a constant rectangular cross-section with known thermal flows at the boundary and small values of the Darcy numbers. Due to the linearity of the formulated system of model equations, we obtain analytical solution of the system using the Laplace and Fourier integral transformation. The obtained solution allows to estimate the length of the input hydrodynamic section, the coefficient of hydraulic resistance, and the local Nusselt numbers. The results obtained for the hydrodynamic subproblem with a large porosity and thermal subproblem with a stationary temperature field agree with the classical data.

Keywords: porous medium; convective heat transfer; rectangular channel; coefficient of hydraulic resistance; initial hydrodynamic section.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.577.21.0202 (RFMEFI57715X0202)
The paper was supported by the Ministry of Education and Science of the Russian Federation under the Federal Target Program (Agreement №14.577.21.0202, the unique identifier is RFMEFI57715X0202).


DOI: https://doi.org/10.14529/mmp170304

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Bibliographic databases:

UDC: 621.1.016.4(03)
MSC: 76S05
Received: 05.05.2017
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Citation: V. I. Ryazhskikh, D. A. Konovalov, A. V. Ryazhskikh, A. A. Boger, S. V. Dakhin, “Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:3 (2017), 40–53

Citation in format AMSBIB
\Bibitem{RjaKonRya17}
\by V.~I.~Ryazhskikh, D.~A.~Konovalov, A.~V.~Ryazhskikh, A.~A.~Boger, S.~V.~Dakhin
\paper Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 3
\pages 40--53
\mathnet{http://mi.mathnet.ru/vyuru385}
\crossref{https://doi.org/10.14529/mmp170304}
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\elib{https://elibrary.ru/item.asp?id=29930356}


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    This publication is cited in the following articles:
    1. V. I. Ryazhskikh, A. V. Keller, A. V. Ryazhskikh, A. V. Nikolenko, S. V. Dakhin, “Matematicheskaya model razgonnogo laminarnogo techeniya nyutonovskoi zhidkosti v anizotropnom poristom kanale pryamougolnogo secheniya”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 13:3 (2020), 17–28  mathnet  crossref
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