Instability of Rayleigh-Bernard Convection Affected by Upper Wall Temperature Variation
This paper represents the analysis of Rayleigh-Bernard convection between two parallel plates. Lower wall is being cooled while upper is heated according to periodic spatial distribution. This process has been modeled using Navier-Stokes equations, equation of continuity and energy equation. Solution of the differential equations has been obtained using pseudo spectral numeric method. For discretization in homogeneous direction, Fourier-Galerkin model has been used, while for discretization in inhomogeneous direction Chebyshev collocation method is applied. Time discretization has been performed using Adams-Bashworth two step method of second order. The results of numeric simulation have been presented by figures where vorticity fields, stream-function and velocity are shown for six different time steps.