Boundary layer nomenclature

The Schmidt number is the ratio of kinematic viscosity to molecular diffusivity. Considering liquids in general and dissolution media in particular, the values for the kinematic viscosity usually exceed those for diffusion coefficients by a factor of 103 to 104. Thus, Prandtl or Schmidt numbers of about 103 are usually obtained. Subsequently, and in contrast to the classical concept of the boundary layer, Re numbers of magnitude of about Re > 0.01 are sufficient to generate Peclet numbers greater than 1 and to justify the hydrodynamic boundary layer concept for particle-liquid dissolution systems (Re Pr = Pe). It can be shown that [(9), term 10.15, nomenclature adapted]... 

We shall employ a simplified analysis of the ablation problem utilizing the coordinate system and nomenclature shown in Fig. 12-18. The solid wall is exposed to a constant heat flux of (q/A)0 at the surface. This heat flux may result from combined convection- and radiation-energy transfer from the highspeed boundary layer. As a result of the high-heat flux the solid body melts, and a portion of the surface is removed at the ablation velocity V . We assume that a steady-state situation is attained so that the surface ablates at a constant... 

Prandtl Z-M<7w/g (1875-1953) Ger. phys., founder of modern hydrodynamics and aerodynamics, proved sound barrier, boundary layer on moving surfaces in liquids, Prandtl number named after him Presl Jan Svatopluk (1791-1849) Czech, chem., originator of modern nomenclature in chemistry and botany Priestley Joseph (1733-1804) Brit, chem., phlogistonist, explained some composites of air, history of electricity and light Prigogine Ilya (1917-2003) Rus. bom Belgian phys. chemist, inventor of nonequilibrium thermodynamics, propagator of the theory of chaos ( La nouvelle alliance avec la nature )... 

The vectors k are 3D, 2D, or ID for a crystal, slab, or periodic polymer respectively. Keep in mind that the nomenclature nD refers to the number of cartesian directions in which nuclei have periodic ordering. The electron density is three-dimensional, as is r, whatever the system periodicity. Thus, when we treat an ultra-thin film (UTF) with GTOFF, we are not doing a super-cell calculation on a fictitious crystal consisting of the UTF interspersed by layers of vacuum . GTOFF can do such super-cell calculations but more importantly, it can handle the UTF as a fi ee-standing object periodic in two Cartesian directions and of finite thickness in the third direction (conventionally z), subject to vacuum boundary conditions in z. Note also that a 2D GTOFF calculation does not require inversion s)mimetry with respect to z, hence can treat an even number of nuclear planes as readily as an odd number. 

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