Forced convection external

In many diffusion problems of practical importance in the pharmaceutical sciences, such as intrinsic dissolution studies and drug release from solid dosage forms, the medium under consideration is not at rest. In addition to concentration changes due to diffusion, there are concentration changes by convection. External forces, such as pressure gradients and temperature differences, can cause convective flows. Although convection can also be caused by diffusion itself, our discussion is limited to convection caused by external forces, since convection produced by diffusion is negligible (less than 10%) for most pharmaceutical problems. 

MOMEN- TUM BALANCE Rate of change of momentum per unit volume Rale of change of momenium by convection per unit volume Rale of change of momentum by molecular transfer (viscous transfer) per volume Generation per volume (External forces) (Ex gravity) Empirically determined flux specified (3)< Velocity specified (1.2b) ... 

Natural convection is self-induced and is created by the density differences, which are temperature related the boiling of water in a kettle is an example of free convection. Forced convection is caused by an external force being applied by mechanical means such as a fan or pump the cooling of a warm bottle in cool flowing water is an example of forced convection. 

Filtration of Liquids Depending on the specific electrochemical reactor type, the filtration rate of a liqnid electrolyte throngfi tfie separator should be either high (to secure a convective snpply of snbstances) or very low (to prevent mixing of the anolyte and catholyte). The filtration rate that is attained under the effect of an external force Ap depends on porosity. For a separator model with cylindrical pores, the volnme filtration rate can be calcnlated by Poiseuille s law ... 

Convection—the transport of mass or energy as a result of streaming in the system produced by the action of external forces. These include mechanical forces (forced convection) or gravitation, if there are density gradients in the system (natural or free convection). 

In the example above, if the drop of dye is not carefully placed at the bottom of the beaker, the water is disturbed and convection currents are set up. Consequently, it can be observed that the dye is transported to the upper part at a much faster rate. It generally takes less time for the solution to achieve a uniform color because of convection caused by external forces. 

If there is an external force acting in the same direction on solute molecules, the velocity of these molecules is vz and the resulting flux is cvz. Therefore, the total flux, nz, due to both diffusion and convection is... 

Forced Convection, where the flow is induced by external forces, e.g. from a pump or a fan. 

Forced Convection. In forced convection, flow is generated by some external means, e.g. a pump, and heat transfer coefficients would be expected to be a function of... 

The boundary layer problem is difficult to solve exactly. There are several approximate methods to solve the problem. This chapter looks at external forced convection, that is, flow outside and around a solid body like a plate. The next chapter discusses flows inside a solid structure such as a pipe, or between two plates. 

Diffusion, which occurrs in essentially all matter, is one of the most ubiquitous phenomena in nature. It is the process of transport of materials driven by an external force field and the gradients of pressure, temperature, and concentration. It is the net transport of material that occurs within a single phase in the absence of mixing either by mechanical means or by convection. The rates of different technical as well as many physical, chemical, and biological processes are directly influenced by diffusive mass transfer, and also the efficiency and quality of processes are governed by diffusion [1]. 

C WTiat is external forced convection How does it differ from internal forced convection fian a heat transfer system involve both internal and external convection at the same time Give an example. 

To this point we have limited onr consideration to mass diffitsion in a station aiy medium, and thus the only ntotion involved was the creeping motion of molecules in the direction of decreasing concentration, and there was no motion of the mixture as a whole. Many practical problems, such as the evaporation of water from a lake under the iiifliience of the wind or the mixing of two fluids as they flow in a pipe, involve diffusion in a moving medium where the hoik motion i.s caused by an external force. Mass diffusion in such c.nses is complicated by the fact that chemical species are transported both by diffusion and by the bulk motion of the medium (i.e., convection). The velocities and mass flow rates of species in a moving medium consist of two components one due to molecular diffusion and one due to convection (Fig. 14-29). 

Very often fluid motion near the solid is not only the result of the temperature gradient, but also the result of some outside forces. In such cases, heat transfer is by forced convection. Here, a pressure gradient appears as a result of an external force exerted by a pump, for example. Fluid mixing takes place as a result of the... 

The basic concept of diffusion refers to the net transport of material within a single phase in the absence of mixing (by mechanical means or by convection). Both experiment and theory have shown that diffusion can result from pressure gradients (pressure diffusion), temperature gradients (thermal diffusion), external force fields (forced diffusion), and concentration gradients. Only the last type is considered in this book that is, the discussion is limited to diffusion caused by the concentration difference between two points in a stagnant solution. This process, called molecular diffusion, is described by Pick s laws. His first law relates the flux of a chemical to the concentration gradient ... 

Limtitng consideration to the steady state, the equation of convective diffiLsion in the absence of an external force field can be expressed in dimensionless fomi as follows... 

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