Convection gravity-driven

Laminar Free Convection. Sparrow and Gregg [33] were the first to use the boundary layer method to study laminar, gravity-driven film condensation on a vertical plate. They improved upon the approximate analysis of Nusselt by including fluid acceleration and energy convection terms in the momentum and energy equations, respectively. Their numerical results can be expressed as ... 

Fundamental studies on the kinetics of crystal nudeation and growth in glassy melts under the influence of surface tension-driven (Marangoni) convection that, under Ig conditions, would be superseded by gravity-driven (B nard or Rayleigh) convection. 

For gravity driven free convection the velocity v is not known a priori therefore one has to use relations with a dimensionless group containing the acceleration of gravity. This is expressed by the Grashof number Gr, or by the Rayleigh number Ra ... 

Under accident conditions, with the valves opened, water is drawn from the upper surface of the pool, allowed to cool in the heat exchanger, and returned to the bottom of the pool by means of a gravity-driven convection current. Likewise, cooler air is drawn through the heat exchangers from the bottom of the shroud, with the heated air escaping at the top of the shroud. 

Before reviewing the common theories, we should identify exaetly what we want to predict. Almost always, we want to predict the mass transfer eoeffieient fe as a funetion of the diffusion coefficient D and the fluid velocity v. In many cases, eonveetion will be foreed, i.e., the velocity will be caused by mechanical forces like pressure drop imposed from outside the system. In occasional cases, convection will be free, the eonsequenee of gravity driven flows often caused by the mass transfer itself. While we will diseuss both eases, we will stress forced convection because it is more important and more common in chemical processing. 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

Convection driven by body forces, e.g., gravity, acting on fluid subject to thermal expansion. 

The prior art discussion relates that current crystal growing techniques suffer from some limitations in their operation. Specifically, the temperature driven crystallization method requires precise time-temperature regulation and that the earth s gravity field causes convection currents that can interfere in crystal growth. 

Natural convection is the motion that results from the interaction of gravity with density differences within a fluid. The differences may result from gradients in temperature, concentration, or composition. This chapter deals with the heat transfer associated with natural convection driven by temperature gradients in a newtonian fluid. 

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