Profound temperature peaks are observed in regions of high velocity shear in a 2D dusty plasma experiment with laser-driven flow. These are attributed to viscous heating, which occurs due to collisional scattering in a shear flow. Using measurements of viscosity, thermal conductivity, and spatial profiles of flow velocity and temperature, we determine three dimensionless numbers: Brinkman, Br =...

Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number. The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of t...

We investigate the behavior of the magnetic Prandtl number (ratio of microscopic viscosity to resistivity) for accretion sources. Generally this number is very small in standard accretion disk models, but can become larger than unity within ∼ 50 Schwarzschild radii of the central mass. Recent numerical investigations suggest a marked dependence of the level of MHD turbulence on the value of the...

This is the rst of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space. In this paper we prove short time existence theorems for the Euler and Prandtl equations with analytic initial data in either two or three spatial dimensions. The main technical tool in this analysis is the abstract Cauchy-Kowalewski theorem. For the Euler equations, the pro...

Abstract. We prove local existence and uniqueness for the two-dimensional Prandtl system in weighted Sobolev spaces under the Oleinik’s monotonicity assumption. In particular we do not use the Crocco transform. Our proof is based on a new nonlinear energy estimate for the Prandtl system. This new energy estimate is based on a cancellation property which is valid under the monotonicity assumptio...

We present measurements of the Nusselt number N as a function of the Rayleigh number R and the Prandtl number sigma in cylindrical cells with aspect ratios gamma = 0.5 and 1.0. We used acetone, methanol, ethanol, and 2-propanol with Prandtl numbers sigma = 4.0, 6.5, 14.2, and 34.1, respectively, in the range 3x10(7) less, similarR less, similar10(11). At constant R, N(R,sigma) varies with sigma...

In the lines of the recent paper [5], we establish various ill-posedness results for the Prandtl equation. By considering perturbations of stationary shear flows, we show that for some linearizations of the Prandtl equation and some C∞ initial data, local in time C∞ solutions do not exist. At the nonlinear level, we prove that if a flow exists in the Sobolev setting, it cannot be Lipschitz cont...

Effect of the capillary meniscus on the instability of large Prandtl number Czochralski melt flow is studied experimentally. The measurements are conducted in two experimental facilities by two independent non-intrusive optical techniques. The quantitative results are presented as dependencies of the critical Grashof number (critical temperature difference) on the meniscus height for different ...

We simulate the evolution of an initially weak magnetic field in forced turbulence for a range of Prandtl numbers. The field grows exponentially with the Kulsrud-Anderson k 3/2 spectrum until the magnetic energy approaches the viscous-scale kinetic energy, where the magnetic forces then backreact on the velocity. Further growth proceeds more slowly until a saturated state is reached where the m...

The onset of square convective cells in fluid layers heated from below is investigated. Amplitude equations are deduced from the Boussinesq equations and a standard stability analysis is performed. Square cells are shown to be preferred when the instability is mainly capillarity driven. The influence of the Prandtl and Biot numbers are examined. At small Pr, the Biot number has not very much in...