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Russia Tomsk
Section  Mechanics 
Title  Numerical analysis of conjugate natural convection and thermal surface radiation in a cube filled with diathermanous medium 
Author(s)  Martyushev S.G.^{a}, Miroshnichenko I.V.^{a}, Sheremet M.A.^{ab} 
Affiliations  Tomsk State University^{a}, Tomsk Polytechnic University^{b} 
Abstract  Mathematical simulation of convectiveconductiveradiative heat transfer in a cubical cavity filled with diathermanous medium has been carried out. The domain of interest is a closed volume having heatconducting 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 boundaryvalue problem has been formulated in dimensionless variables such as “vector potentialvorticity vectortemperature’’ 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 netradiation method in the form of Poljak. The formulated transient boundaryvalue 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 solidfluid interface have been obtained. The comparison between the obtained threedimensional results and the twodimensional data has been conducted. It has been found, that on the basis of a threedimensional model it is possible to analyze the formation of intensive transverse flows from two vertical surfaces which are absent in a twodimensional model. It has been also shown, that the solution of convectiveradiative heat transfer problems in the conjugate statement leads to essential changes in distributions of local and integral parameters in comparison with the nonconjugate 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. 
Keywords  conjugate natural convection, thermal surface radiation, Boussinesq approximation, closed cubical cavity, solid walls of finite thickness, mathematical simulation 
UDC  536.24 
MSC  76R10, 80A20 
DOI  10.20537/vm140208 
Received  12 February 2014 
Language  Russian 
Citation  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. 111120. 
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