Bounds on heat transfer for Bénard–Marangoni convection at infinite Prandtl number

Logarithmic bounds for infinite Prandtl number rotating convection

Convection refers to fluid motion that is induced by buoyancy. In thermal convection buoyancy is due to temperature differences and one of the interesting questions is how much of the total heat transfer is due to convection. The natural measure of this quantity is the Nusselt number, N , and many experiments and numerical simulations have been performed to discern the relationship between N an...

Bifurcation of Infinite Prandtl Number Rotating Convection

We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park [15, 16, 17] under various boundary conditions. By thoroughly investigating We prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor ΣR which consists of only on...

Internal heating driven convection at infinite Prandtl number

On upper bounds for infinite Prandtl number convection with or without rotation

Bounds for the bulk heat transport in Rayleigh-Benard convection for an infinite Prandtl number fluid are derived from the primitive equations. The enhancement of heat transport beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the nondimensional temperature difference across the layer (the Rayleigh number Ra) according to Nu ≤ c Ra where c < 1 is an absolute co...

Effects of vertical boundaries on infinite Prandtl number thermal convection

The physics of thermomechanical coupling of the continental lithosphere and its surrounding mantle is studied using a simple hydrodynamic model in which a fluid is heated from below and is bounded by rigid side walls. Rayleigh numbers up to 10 are considered. A series of finite-element stability analyses is employed to characterize systematically the nature of convective instability in such a s...