Abstract
Natural convection of a perfect gas in a porous medium between two coaxial horizontal cylinders of large length located in heat-conducting space is considered. The two-dimensional problem (thin porous ring) is investigated in a plane orthogonal of the axis of the cylinders. The dependence of the criterion of the onset of convection on the non-Boussinesq parameters is studied. In the steady-state case an analytic solution of the nonlinear problem is obtained and its asymptotic behavior is considered for large Rayleigh numbers and when the compressibility criterion tends to zero. The gas flow rate in the ring and other characteristics of convection are studied as functions of the gas compressibility criterion and a constant temperature gradient given far away from the contour.
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References
G.Z. Gershuni and E.M. Zhukhovitskii, Convective Stability of an Incompressible Fluid (Nauka, Moscow, 1972) [in Russian].
B. Gebhart, Y. Jaluria, R.L. Mahajan, and B. Sammakia, Buoyancy-Induced Flows and Transport, Hemisphere, Washington, etc. (1988).
A.V. Getling, “Formation of Three-Dimensional Structures of the Rayleigh-Bénard Convection,” Usp. Fiz. Nauk 161, No. 1, 1–80 (1991).
F. Bousset, D.V. Lyubimov, T.P. Lyubimova, and G.A. Sedel’nikov, “Three-dimensional Convection Regimes in a Cubical Cavity,” Fluid Dynamics 43, No. 1, 1–8 (2008).
K. Schwarzschild, “Uber das Gleichgewicht der Sonnenatmosphere,” Gott. Nach. 41, 1–24 (1906).
L.D. Landau and E.M. Lifshitz, Theoretical Physics. Vol. 6. Hydrodynamics (Nauka, Moscow, 1986) [in Russian].
A.A. Gorbunov, S.A. Nikitin, and V.I. Polezhaev, “Conditions of Rayleigh-Bénard Convection Onset and Heat Transfer in a Near-Critical Medium,” Fluid Dynamics 42, No. 5, 704–718 (2007).
V.I. Polezhaev and M.P. Vlasyuk, “Model of Penetrating Convection of a Compressible Gas in the Deep Atmosphere,” Dokl. Akad. Nauk SSSR 201, No. 4, 552–555 (1971).
V.I. Polezhaev and E.B. Soboleva, “Rayleigh-Bénard Convection in a Near-Critical Fluid in the Neighborhood of the Stability Threshold,” Fluid Dynamics 40, No. 2, 209–220 (2005).
M.M. Ramazanov, “Convection in an Obliquely Heated Thin Porous Elliptic Ring,” Fluid Dynamics 35, No. 6, 910–917 (2000).
M.M. Ramazanov, “Free Fluid Convection in a Closed Contour in a Heat-Conducting Half-Space,” Fluid Dynamics 40, No. 4, 613–622 (2005).
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Original Russian Text © M.M. Ramazanov, 2010, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2010, Vol. 45, No. 2, pp. 84–96.
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Ramazanov, M.M. Perfect gas convection in a porous medium between two coaxial horizontal cylinders of large length. Fluid Dyn 45, 241–253 (2010). https://doi.org/10.1134/S0015462810020092
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DOI: https://doi.org/10.1134/S0015462810020092