Infinite Prandtl number convection. (English) Zbl 0935.76083

Constantin, Peter; Doering, Charles R.

J. Stat. Phys. 94, No. 1-2, 159-172 (1999).

Summary: We prove an inequality of the type \(N\leq CR^{1/3}(1+ \log_+R)^{2/3}\) for the Nusselt number \(N\) in terms of the Rayleigh number \(R\) for the equations describing three-dimensional Rayleigh-Bénard convection in the limit of infinite Prandtl number.

MSC:

76R10	Free convection
76F35	Convective turbulence
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

heat transport; Nusselt number; Rayleigh number; three-dimensional Rayleigh-Bénard convection