A new upper bound on the rate of vertical heat transport is established in 3 dimensions for stress-free velocity boundary conditions on horizontally periodic plates. For large (but finite) Prandtl numbers this bound is an improvement over the ‘ultimate’ Ra scaling and in the limit of infinite Pr, agrees with the bound of Ra recently derived in that limit. keywords: Rayleigh-Bénard convection, B...

We study the effects of severe non-Boussinesq conditions on thermal convection at the moderate Rayleigh numbers of Ra = 2× 108 and 2× 109 by resorting to direct numerical computations of the full governing equations. We illustrate the effects by considering low temperature gaseous helium. The properties of helium are allowed to depend on the temperature around the mean of 5.4K. The Nusselt numb...

In this paper availability model for a linear (circular) consecutive-k-out-of-n:F system (or C(k, n:F) system) of nonidentical components has been considered. It is assumed that both the working time and repair time of each component are Rayleigh distributed. The estimate of the parameters from the Rayleigh distribution can be represented by triangular fuzzy numbers. A numerical example is solv...

Thermally driven flows are ubiquitous in nature. An important and longstanding question is how heat transfer depends on the control parameters of flow. In this Letter, author presents a theoretical analysis that answers such for large aspect-ratio turbulent thermal convection fluid between two vertical walls maintained at different temperatures. This yields dependence flux wall shear stress Ray...

Simulations were carried out using penalty finite element analysis with bi-quadratic elements to investigate the influence of uniform and non-uniform heating of bottom wall within a trapezoidal enclosure of various inclination angles ðuÞ. Parametric study has been carried out for a wide range of Rayleigh number ðRaÞ ð10 6 Ra 6 10Þ, Prandtl number ðPrÞ ð0:026 6 Pr 6 988:24Þ and Darcy number ðDaÞ...

We consider double-diffusive convection between two parallel plates and compute bounds on the flux of the unstably stratified species using the background method. The bound on the heat flux for Rayleigh–Bénard convection also serves as a bound on the double-diffusive problem (with the thermal Rayleigh number equal to that of the unstably stratified component). In order to incorporate a dependen...

Movies of the breakup of viscous and viscoelastic drops in the high speed airstream behind a shock wave in a shock tube have been reported by Joseph, Belanger and Beavers [1999]. A Rayleigh-Taylor stability analysis for the initial breakup of a drop of Newtonian liquid was presented in that paper. The movies, which may be viewed at http://www.aem.umn.edu/ research/Aerodynamic_Breakup, show that...

We report measurements of the Nusselt number, Nu, in turbulent thermal convection in a cylindrical container of aspect ratio 4. The highest Rayleigh number achieved was Ra=2× 10. Except for the last half a decade or so of Ra, experimental conditions obey the Boussinesq approximation accurately. For these conditions, the data show that the logNu–logRa slope saturates at a value close to 1/3, as ...

To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version complete Boussinesq equations containing only one horizontal wavenumber. In light later observations robust large-scale circulation sweeping through convecting enclosures at high Rayleigh numbers, it is perhaps not an implausible point view from which to reexamine high-Rayleig...