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# Schmidt number

About: Schmidt number is a(n) research topic. Over the lifetime, 2571 publication(s) have been published within this topic receiving 56295 citation(s).

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Abstract: This paper deals wi th two l imit ing cases of laminar heat transfer over blunt-nosed bodies at hypersonic flight speeds, or high s tagnat ion temperatures: (a) thermodynamic equil ibrium, in which the chemical reaction rates are regarded as "very fas t" compared to the rates of diffusion across streamlines; (b) diffusion as rate-governing, in which the volume recombination rates within the boundary layer are "very s low" compared to diffusion across streamlines. In either case the gas density near the surface of a blunt-nosed body is m u c h higher than the density jus t outside the boundary layer, and the velocity and stagnation enthalpy profiles are m u c h less sensitive to pressure gradient than in the more familiar case of moderate temperature differences. In fact, in case (a), the nondimensionalized enthalpy gradient at the surface is represented very accurately by the "classical" zero pressure gradient value, and the surface heat-transfer rate distribution is obtained directly in terms of the surface pressure distribution. In order to i l lustrate the method , this solution is applied to the special cases of an unyawed hemisphere and an unyawed, b lunt cone capped by a spherical segment . In the opposite l imit ing case where diffusion is ratecontrolling the diffusion equation for each species is reduced to the same form as the low-speed energy equation, except that the Prandtl number is replaced by the Schmidt number . The simplifications introduced in case (a) are also applicable here, and the expression for surface heat transfer rate is similar; the maximum value of the ratio between the rate of heat transfer by diffusion alone and by heat conduction alone in the case of thermodynamic equil ibrium is given by: (Prandtl n o . / S c h m i d t no.)'. When the diffusion coefficient is es t imated by taking a reasonable value of a tom-molecule collision cross section this ratio is 1.30. Additional theoretical and (especially) experimental studies are clearly required before these s imple results are accepted.

786 citations

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Abstract: The paper describes the turbulence scheme implemented in the Meso-NH community research model, and reports on some validation studies. Since the model is intended to perform both large-eddy and mesoscale simulations, we have developed a full three-dimensional scheme, based on the original method of Redelsperger and Sommeria. A prognostic equation for the turbulent kinetic energy is used, together with conservative variables for moist non-precipitating processes. A particularity of the scheme is the use of variable turbulent Prandtl and Schmidt numbers, consistently derived from the complete set of second-order turbulent-moment equations. The results of three idealized boundary-layer simulations allowing detailed comparisons with other large-eddy simulation (LES) models are discussed, and lead to the conclusion that the model is performing satisfactorily.
The vertical flux and gradient computation can be run in isolation from the rest of the scheme, providing an efficient single-column parametrization for the mesoscale configuration of the model, if an appropriate parametrization of the eddy length-scale is used. The mixing-length specification is then the only aspect of the scheme which differs from the LES to the mesoscale configuration, and the numerical constants used for the closure terms are the same in both configurations. The scheme is run in single-column mode for the same three cases as above, and a comparison of single-column and LES results again leads to satisfactory results. It is believed that this result is original, and is due to the proper formulation of the parametrized mixing length and of the turbulent Prandtl and Schmidt numbers. In fact, a comparison of the parametrized mixing length with the length-scale of the energy-containing eddies deduced by spectral analysis of the LES shows interesting similarity.

695 citations

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Abstract: In this study, effect of thermal radiation on magnetohydrodynamics nanofluid flow between two horizontal rotating plates is studied. The significant effects of Brownian motion and thermophoresis have been included in the model of nanofluid. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer are reduced to a set of ordinary differential equations. These equations, subjected to the associated boundary conditions are solved numerically using the fourth-order Runge–Kutta method. The effects of Reynolds number, magnetic parameter, rotation parameter, Schmidt number, thermophoretic parameter, Brownian parameter and radiation parameter on heat and mass characteristics are examined. Results show that Nusselt number has direct relationship with radiation parameter and Reynolds number while it has reverse relationship with other active parameters. It can also be found that concentration boundary layer thickness decreases with the increase of radiation parameter.

636 citations

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Abstract: Detailed gas exchange measurements from two circular and one linear wind/wave tunnels are presented. Heat, He, CH4, CO2, Kr, and Xe have been used as tracers. The experiments show the central importance of waves for the water-side transfer process. With the onset of waves the Schmidt number dependence of the transfer velocity k changes from k ∝ Sc−⅔ to k ∝ Sc−½indicating a change in the boundary conditions at the surface. Moreover, energy put into the wave field by wind is transferred to near-surface turbulence enhancing gas transfer. The data show that the mean square slope of the waves is the best parameter to characterize the free wavy surface with respect to water-side transfer processes.

605 citations

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Abstract: This paper concerns the laminar flows which arise in fluids due to the interaction of the force of gravity and density differences caused by the simultaneous diffusion of thermal energy and of chemical species. Species concentration levels are assumed small, as is typical for many processes in water and in atmospheric air. The usual Boussinesq approximations yield a set of equations which are shown to have solutions of similarity form for combined buoyancy effects, for vertical flows adjacent to surfaces and in plumes. This similarity is of the same form as that found for single buoyancy mechanism flows. The resulting equations were integrated for air and water for various practical values of the Schmidt number and for multiple buoyancy effects aiding and opposing. The results show many interesting effects on velocity, heat and mass transfer, and on laminar stability. A comparison of the results with those of integral method analysis shows the limits and reasons for failure of these approximate calculations in the more complicated of such combined buoyancy mechanism flows.

525 citations