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Section
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Mechanics
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Title
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Numerical analysis of conjugate natural convection and thermal surface radiation in a cube filled with diathermanous medium
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Author(-s)
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Martyushev S.G.a,
Miroshnichenko I.V.a,
Sheremet M.A.ab
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Affiliations
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Tomsk State Universitya,
Tomsk Polytechnic Universityb
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Abstract
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Mathematical simulation of convective-conductive-radiative heat transfer in a cubical cavity filled with diathermanous medium has been carried out. The domain of interest is a closed volume having heat-conducting solid walls of finite thickness with diffuse grey inner surfaces. The outer surfaces of two vertical walls are isothermal while the other walls are adiabatic. The boundary-value problem has been formulated in dimensionless variables such as “vector potential-vorticity vector-temperature’’ in the Boussinesq approximation and taking into account the diathermancy of the continuous medium. An analysis of surface thermal radiation has been conducted on the basis of the net-radiation method in the form of Poljak. The formulated transient boundary-value problem has been solved by finite difference method in a wide range of the Rayleigh number, thermal conductivity ratio and surface emissivity. Correlations for the average convective and radiative Nusselt numbers at the characteristic internal solid-fluid interface have been obtained. The comparison between the obtained three-dimensional results and the two-dimensional data has been conducted. It has been found, that on the basis of a three-dimensional model it is possible to analyze the formation of intensive transverse flows from two vertical surfaces which are absent in a two-dimensional model. It has been also shown, that the solution of convective-radiative heat transfer problems in the conjugate statement leads to essential changes in distributions of local and integral parameters in comparison with the non-conjugate model, which first of all is related to a more correct description of the thermal radiation in diathermanous media due to taking into account the thermal conduction of the solid walls.
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Keywords
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conjugate natural convection, thermal surface radiation, Boussinesq approximation, closed cubical cavity, solid walls of finite thickness, mathematical simulation
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UDC
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536.24
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MSC
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76R10, 80A20
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DOI
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10.20537/vm140208
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Received
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12 February 2014
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Language
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Russian
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Citation
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Martyushev S.G., Miroshnichenko I.V., Sheremet M.A. Numerical analysis of conjugate natural convection and thermal surface radiation in a cube filled with diathermanous medium, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2014, issue 2, pp. 111-120.
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References
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- Steinberg D.S. Cooling techniques for electronic equipment, San Francisco: Wiley, 1991, 512 p.
- Martyushev S.G., Sheremet M.A. Conjugate natural convection combined with surface thermal radiation in an air filled cavity with internal heat source, Int. J. Thermal Sciences, 2014, vol. 76, pp. 51-67.
- Smith T.F., Weber S.W., Beckermann C. Combined conduction, natural convection, and radiation heat transfer in an electronic chassis, J. Electronic Packaging, 1991, vol. 113, no. 4, pp. 382-391.
- Martyushev S.G., Sheremet M.A. Mathematical simulation of natural convection and thermal surface radiation in differentially heated parallelepiped, Proceedings of 7th Siberian Conference on Parallel and High-Performance Computing, Tomsk, Tomsk State University, 2013, pp. 50-51 (in Russian).
- Colomer G., Costa M., Coonsul R., Oliva A. Three-dimensional numerical simulation of convection and radiation in a differentially heated cavity using the discrete ordinates method, Int. J. Heat Mass Transfer, 2004, vol. 47, pp. 257-269.
- Albanakis C., Bouris D. 3D conjugate heat transfer with thermal radiation in a hollow cube exposed to external flow, Int. J. Heat Mass Transfer, 2008, vol. 51, pp. 6157-6168.
- Martyushev S.G., Sheremet M.A. Numerical analysis of conjugate convective-radiative heat transfer in an enclosure filled with diathermanous medium, Vestn. Udmurt. Univ. Mat. Mekh. Komp'yut. Nauki, 2012, no. 3, pp. 114-125 (in Russian).
- Martyushev S.G., Miroshnichenko I.V., Sheremet M.A. Numerical analysis of spatial transient conjugate convective-radiative heat transfer in a closed volume with heat source, Journal of Engineering Physics and Thermophysics, 2014, vol. 87, no. 1, pp. 124-134.
- Siegel R., Howell J.R. Thermal radiation heat transfer, London: Taylor and Francis, 2002, 868 p.
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