Natural Rayleigh Benard Convection of Bingham Fluid in Enclosure Cavity with Sinusoidal Profiles

In this study, two-dimensional steady-state simulations of laminar natural convection of Rayleigh Benard in square enclosure were performed.The enclosure is considered to be completely filled with a yield stress fluid obeying viscoplastic model Bingham.The vertical lateral walls are thermally isolated, whereas sinusoidal temperature distributions with different amplitudes and phases are imposed over the horizontal walls.Fluid flow and heat transfer characteristics are systematically studied over a wide range of Phase deviation ϕ (0-π) and amplitude ration Ɛ (0-1).We have fixed the Rayleigh number (Ra = 10 5 ), Prandtl number (Pr = 7), and finally the Bingham number (Bn = 0.5).The Navier-Stokes equations, the mass and energy conservation equations, are solved numerically using CFD software FLUENT 15.The results shows that the Nusselt number decreases with the increase of the Bingham number, and for the large values of the latter the heat transfer is done by conduction.It is also noteworthy that the increase in the phase difference and the amplitude ratio leads to the increase in the heat transfer.