Prandtl number

Abstract: The dynamic subgrid-scale (SGS) model of Germano et al. (1991) is generalized for the large eddy simulation (LES) of compressible flows and transport of a scalar. The model was applied to the LES of decaying isotropic turbulence, and the results are in excellent agreement with experimental data and direct numerical simulations. The expression for the SGS turbulent Prandtl number was evaluated using direct numerical simulation (DNS) data in isotropic turbulence, homogeneous shear flow, and turbulent channel flow. The qualitative behavior of the model for turbulent Prandtl number and its dependence on molecular Prandtl number, direction of scalar gradient, and distance from the wall are in accordance with the total turbulent Prandtl number from the DNS data.

Abstract: The problem of laminar fluid flow which results from the stretching of a flat surface in a nanofluid has been investigated numerically. This is the first paper on stretching sheet in nanofluids. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented which depends on the Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. The variation of the reduced Nusselt and reduced Sherwood numbers with Nb and Nt for various values of Pr and Le is presented in tabular and graphical forms. It was found that the reduced Nusselt number is a decreasing function of each dimensionless number, while the reduced Sherwood number is an increasing function of higher Pr and a decreasing function of lower Pr number for each Le, Nb and Nt numbers.

Abstract: This chapter contains sections titled: Theory of Free Turbulence, Prandtl's Old Theory of Free Turbulence, Application of Prandtl's Old Theory of Free Turbulence to Heat and Diffusion Problems, Theory of the Boundary Layer of a Two-Dimensional Turbulent Jet of Incompressible Fluid, Tollmien's Plane Turbulent Source, Tollmien's Axially Symmetric Turbulent Source, Distribution of Temperature and Constituent Concentration in the Main Region of a Jet According to Prandtl's Old Theory of Free Turbulence, Taylor's Free Turbulence Theory and Its Application, Prandtl's New Theory of Free Turbulence and Its Applications, Reichardt's Theory of Turbulent Mixing and Its Application, Determination of the Temperature Profile in a Jet on the Basis of the New Prandtl-Gortler Theory of Turbulence and Reichardt's Theory

Abstract: The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.