The method of matched asymptotic expansions, which has been used in previous studies of steady natural convection flow, is extended here to transient natural convection flow at high Prandtl number (Pr). Second-order expansion solutions, valid for large Prandtl numbers, are presented for the transient natural convection flow near a vertical surface which undergoes a step change in temperature. T...

This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water s...

We use DNS to study the effect of Prandtl number on mixing in weakly density stratified Kelvin-Helmholtz (KH) billows at low to moderate Reynolds numbers. The time evolution of the density field of the flow and the mixing are significantly influenced by the Prandtl number. By increasing the Prandtl number, the final amount of mixing increases for Reynolds that are too low to sustain three-dimen...

A numerical study of the onset of convection in rotating, internally heated, selfgravitating fluid spheres is presented. The exploration of the stability of the conduction state versus the Taylor and the Prandtl numbers supplies a detailed idea of the laws that fulfil the four types of solutions obtained at low Prandtl numbers. The main result found is that axisymmetric (torsional) modes of con...

Direct numerical simulation of a fully developed turbulent channel flow with passive scalar transport has been carried out at four Reynolds numbers, 180, 395, 640 and 1020, based on the friction velocity and the channel half width. The molecular Prandtl numbers are 0.025 and 0.71 where the working fluids are assumed to be mercury and air, respectively. It is shown that for both Prandtl numbers,...

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh-B enard convection at large Prandtl number. In particular, we show that the global attractors to the Boussinesq system for Rayleigh-B enard convection converge to that of the in nite Prandtl number model for convection as the Prandtl number approaches in nity. This o ers partial justi cation of the in ni...

This is the third in a series of our study of Rayleigh-Bénard convection at large Prandtl number. Here we investigate whether stationary statistical properties of the Boussinesq system for Rayleigh-Bénard convection at large Prandtl number are related to those of the infinite Prandtl number model for convection that is formally derived from the Boussinesq system via setting the Prandtl number t...

We compute the spectra and fluxes of the velocity and temperature fields in Rayleigh-Bénard convection in turbulent regime for a wide range of Prandtl numbers using pseudospectral simulations on 512(3) grids. Our spectral and flux results support the Kolmogorov-Obukhov (KO) scaling for zero Prandtl number and low Prandtl number (P=0.02) convection. The KO scaling for the velocity field in zero-...