Abstract
Investigations into the convective transport of heat in porous materials are of interest for many applications in connection with the problem of increasing the efficiency of thermal insulation. In [1–5], convection in Isotropic porous media was considered. However, in many cases porous materials have an essential anisotropy of their permeability. Convective heat transfer has been inadequately studied for this case. In [6], the linearized equations were used to study the convection between infinite horizontal planes with a filling of an anisotropic material; the value of the critical Rayleigh number was found, and this agreed satisfactorily with experimental data. In the present paper, we investigate numerically convection between two infinite coaxial cylinders with an anisotropic porous filling, using the equations of convection in the Darcy—Boussinesq approximation [1–3]. The permeability tensor in the annular region is constructed from its principal values, which can be found experimentally. A method of calculation is developed and a parametric study made of the structure of the flow and of the local and averaged characteristics of the heat transfer, which are of interest for the design of thermal insulation.
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C. W. Horton and F. T. Rogers, “Convection current in a porous medium,” J. Appl. Phys.,16, No. 6 (1945).
M. Combarnous, “Convection naturelle et convection mixte dans une couche poreuse horizontale,” Rev. Gen. Iherm.,9, No. 108 (1970).
M. P. Vlasyuk and V. I. Polezhaev, “Natural convection and heat transfer in permeable porous materials,” Preprint No. 77, Institute of Applied Mathematics, USSR Academy of Sciences, Moscow (1975).
V. A. Brailovskaya, “Numerical investigation of natural convection in porous cylindrical layers,” in: Mathematical Models of Liquid Flows. Proc. Sixth All-Union Seminar on Numerical Methods in the Mechanics of Viscous Fluids, Kungur, 1976 [in Russian], Novosibirsk (1978).
V. A. Brailovskaya, G. B. Petrazhitskii, and V. I. Polezhaev, “Natural convection and heat transport in porous layers between horizontal coaxial cylinders,” Zh. Prikl. Mekh. Tekh. Fiz., No. 6 (1978).
G. Gastinel and M. Combarnous, “Critere d'apparition de la convection naturelle dans une couche poreuse anisotrope horizontale,” C.R. Acad. Sci. Ser. B,278, No. 15 (1974).
F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1966).
V. A. Brailovskaya and G. B. Petrazhitskii, “Thermal laminar convection of a fluid in an annular region for given heat flux,” Zh. Prikl. Mekh. Tekh. Fiz., No. 3 (1977).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 59–64, January–February, 1980.
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Brailovskaya, V.A., Kogan, V.R. & Polezhaev, V.I. Influence of anisotropy of the permeability on the convection and heat transfer in a porous annular layer. Fluid Dyn 15, 48–52 (1980). https://doi.org/10.1007/BF01089812
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DOI: https://doi.org/10.1007/BF01089812