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DOI: 10.1615/ICHMT.2014.IntSympConvHeatMassTransf.620
pages 815-828

Semen G. Martyushev
Faculty of Mechanics and Mathematics, Tomsk State University, Tomsk, 634050, Russia

Igor V. Miroshnichenko
Faculty of Mechanics and Mathematics Tomsk State University, 634050 Tomsk, Russia

Mikhail A. Sheremet
Department of Theoretical Mechanics, Tomsk State University, 634050, Tomsk, Russia; Institute of Power Engineering, Tomsk Polytechnic University, 634050, Tomsk, Russia


This paper presents a numerical analysis of an effect of the radiative heat transfer and conjugate parameters on transient natural convection in a cubical cavity having heat-conducting solid walls of finite thickness with a heat source located at the bottom of the cavity in conditions of convective heat exchange with an environment for different surface emissivities and solid wall thermal conductivities, Pr = 0.7 and Ra = 105. The domain of interest filled by a transparent medium has gray and diffuse walls. The three-dimensional natural convection equations, using the Boussinesq approximation for the treatment of buoyancy term in the momentum equation, are expressed in dimensionless form using the vector potential functions, vorticity vector and temperature. The governing differential equations are solved by a finite difference method. An analytical approach is used for the thermal radiation modelling with an implicit boundary condition for convective and radiative heat transfer at solid-fluid interfaces. Main attention was paid to the effects of a dimensionless time 0 ≤ τ ≤ 100, an emissivity of internal surfaces of the solid walls 0 ≤ ε < 1, and a thermal conductivity ratio 1 ≤ k1,2 ≤ 15 on the velocity and temperature fields.

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