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Rayleigh-Bénard convection instability in the presence of temperature variation at the lower wall

DOI: 10.2298/tsci120505169j

Keywords: direct numerical simulation of Navier-Stokes equation , Oberbeck-Boussinesq approximation , Rayleigh and Prandtl number , nonlinear stability analysis

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Abstract:

This paper analyzes the two-dimensional viscous fluid flow between two parallel plates, where the lower plate is heated and the upper one is cooled. The temperature difference between the plates is gradually increased during a certain time period, and afterwards it is temporarily constant. The temperature distribution on the lower plate is not constant in x-direction, and there is longitudinal sinusoidal temperature variation imposed on the mean temperature. We investigate the wave number and amplitude influence of this variation on the stability of Rayleigh-Benard convective cells, by direct numerical simulation of 2-D Navier-Stokes and energy equation.

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