On the basis of the Oberbeck–Boussinesq equations, this study formulates the problem of a Newtonian fluid motion in a rectangular cavity under the Stokes hydrodynamic approximation. The thermal and hydrodynamic subproblems are presented, and an analytical solution of the model equations is obtained using integral Fourier transforms with thermal boundary conditions of the second kind. As an application example, this study analyzes the dynamics of hydrothermal fields during liquid nitrogen storage, taking into account the incoming heat through the wetted surface.
Similar content being viewed by others
References
R. F. Barron, Cryogenic Systems [in Russian], Moscow, Énergoatomizdat (1989).
L. A. Bol’shov, P. S. Kondratenko, and V. F. Strizhov, “Free convection of heat-generating liquid” [in Russian], Uspekh. Fiz. Nauk, 171, No. 10, 1051–1070 (2001).
N. Ben-Cheikh, B. Ben-Beya, and T. Lili, “Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below,” Int. Commun. Heat Mass Transfer., 34, 369–379 (2007).
M. Mobedi, U. Ozkol, and B. Sunden, “Visualization of diffusion and convection heat transport in a square cavity with natural convection,” Int. J. Heat Mass Transfer., 53, 99–109 (2010).
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics, Springer (1965).
V. I. Ryazhskikh and V. A. Sumin, “Theoretical evaluation of the effect of soluble impurities in liquefied gases on the intensity of mixing during their storage in cryogenic tanks” [in Russian], Airospace Forces. Theory and Practice, No 4 (4), 35–42 (2017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Khimicheskoe i Neftegazovoe Mashinostroenie, Vol. 58, No. 10, pp. 22–27, October, 2022.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Ryazhskikh, V.I., Sumin, V.A. Analysis of Free-Convection Hydrothermal Fields in a Rectangular Cavity under Thermal Boundary Conditions of the Second Kind. Chem Petrol Eng 58, 846–854 (2023). https://doi.org/10.1007/s10556-023-01171-y
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10556-023-01171-y