Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 40-53
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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.
@article{VYURU_2017_10_3_a3,
author = {V. I. Ryazhskikh and D. A. Konovalov and A. V. Ryazhskikh and A. A. Boger and S. V. Dakhin},
title = {Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {40--53},
publisher = {mathdoc},
volume = {10},
number = {3},
year = {2017},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/}
}
TY - JOUR AU - V. I. Ryazhskikh AU - D. A. Konovalov AU - A. V. Ryazhskikh AU - A. A. Boger AU - S. V. Dakhin TI - Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2017 SP - 40 EP - 53 VL - 10 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/ LA - en ID - VYURU_2017_10_3_a3 ER -
%0 Journal Article %A V. I. Ryazhskikh %A D. A. Konovalov %A A. V. Ryazhskikh %A A. A. Boger %A S. V. Dakhin %T Analytical solution to the problem of convective heat transfer in a porous rectangular channel for thermal boundary conditions of the second genus %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2017 %P 40-53 %V 10 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/ %G en %F VYURU_2017_10_3_a3
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 Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 3, pp. 40-53. http://geodesic.mathdoc.fr/item/VYURU_2017_10_3_a3/