Stable branch and hysteresis effect of steady cubic convection

Abstract

Both spatially-averaged kinetic energy K and influx-averaged Nusselt number Nuinflux are numerically investigated concerning the three-dimensional thermal convection in a cubic cavity heated from a bottom wall and chilled from its opposite top wall. Nuinflux represents the total influx of heat normalised by an area. Assuming incompressible fluid with a Prandtl number of 7.1 (water) in a Rayleigh-number range of 1.0×104– 1.0×105, the authors solve the three-dimensional Navier-Stokes equations with the Boussinesq approximation, using the finite difference method. As a result, in the Rayleigh-number range, hysteresis effects appear accompanying various steady flow structures. Hence, there can exist multiple values of K and multiple values of Nuinflux for the same Ra due to the different steady flow structures. As Rayleigh number gradually increases or decreases, there exist four stable branches. On the branches, the authors reveal the relation between K and flow structure and the relation between Nuinflux and flow structure. Besides, a steady flow structure becomes oscillatory on one branch, as Rayleigh number gradually increases.

Keywords

• rayleigh-bénard convection
• natural convection
• heat transfer
• convective stability
• hysteresis effect