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

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

Автор: Ryazhskikh V.I., Konovalov D.A., Ryazhskikh A.V., Boger A.A., Dakhin S.V.

Журнал: Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp

Рубрика: Математическое моделирование

Статья в выпуске: 3 т.10, 2017 года.

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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.

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Porous medium, convective heat transfer, rectangular channel, coefficient of hydraulic resistance, initial hydrodynamic section

Короткий адрес: https://sciup.org/147159441

IDR: 147159441   |   DOI: 10.14529/mmp170304

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