External forced flow

In this section we will focus on the heat and mass transfer from or to the surface of a body with external flow. Neighbouring bodies should not be present or should be so far away that the boundary layers on the bodies over which the fluid is flowing can develop freely. Velocities, temperatures and concentrations shall only change in the boundary layer and be constant in the flow outside of the boundary layer. A forced flow, which we will consider here, is obtained from a pump or blower. Local heat and mass transfer coefficients are yielded from equations of the form 

In many cases the shape of the body over which the fluid is flowing and with that the flow pattern are so involved that the functional relationship between the quantities can only be found experimentally. This requires the measurement of the heat and mass flows transferred at the body or a geometrically similar model and also the associated temperature and concentration differences. This then allows the calculation of the heat and mass transfer coefficients as 

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Some empirical equations for heat and mass transfer in external forced flow... 

Newtonian behavior the rate of shear is small compared to the rate constant for the flow process. When molecular displacements occur very much faster than the rate of shear (7 < kj ), the molecules show maximum efficiency in dissipating the applied forces. When the molecules cannot move fast enough to keep pace with the external forces, they couple with and dissipate those forces to a lesser extent. Thus there is a decrease in viscosity from its upper, Newtonian limit with increasing 7/kj. The rate constant for the flow process is therefore seen to define a standard against which the rate of shear is to be judged large or small. In the next section we shall consider a molecular model in terms of which this rate constant can be analyzed. 

The creation terms embody the changes in momentum arising from external forces in accordance with Newton s second law (F = ma). The body forces arise from gravitational, electrostatic, and magnetic fields. The surface forces are the shear and normal forces acting on the fluid diffusion of momentum, as manifested in viscosity, is included in these terms. In practice the vector equation is usually resolved into its Cartesian components and the normal stresses are set equal to the pressures over those surfaces through which fluid is flowing. 

Rheology. The rheology of foam is striking it simultaneously shares the hallmark rheological properties of soHds, Hquids, and gases. Like an ordinary soHd, foams have a finite shear modulus and respond elastically to a small shear stress. However, if the appHed stress is increased beyond the yield stress, the foam flows like a viscous Hquid. In addition, because they contain a large volume fraction of gas, foams are quite compressible, like gases. Thus foams defy classification as soHd, Hquid, or vapor, and their mechanical response to external forces can be very complex. 

Convective heat transfer is classified as forced convection and natural (or free) convection. The former results from the forced flow of fluid caused by an external means such as a pump, fan, blower, agitator, mixer, etc. In the natural convection, flow is caused by density difference resulting from a temperature gradient within the fluid. An example of the principle of natural convection is illustrated by a heated vertical plate in quiescent air. 

Viscous Drag. The velocity, v, with which a particle can move through a Hquid in response to an external force is limited by the viscosity, Tj, of the Hquid. At low velocity or creeping flow (77 < 1), the viscous drag force is /drag — SirTf- Dv. The Reynolds number (R ) is deterrnined from... 

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. 

The performance of an axial fan is based on the external force to drive the propeller, whose blades change the direction of airflow when flowing from the inlet edge to the outlet edge. 

As a fluid is deformed because of flow and applied external forces, frictional effects are exhibited by the motion of molecules relative to each other. The effects are encountered in all fluids and are due to their viscosities. Considering a thin layer of fluid between two parallel planes, distance y apart as shown in Figure 3.4 with the lower plane fixed and a shearing force F applied to the other, since fluids deform continuously under shear, the upper plane moves at a steady velocity ux relative to the fixed lower plane. When conditions are steady, the force F is balanced by an internal force in the fluid due to its viscosity and the shear force per unit area is proportional to the velocity gradient in the fluid, or ... 

The flow is induced in the following way. External forces are applied on the particles of each reservoir In order to ke p the average y velocities of the reservoirs constant. The Imposed motion of the reservoirs shears the liquid slab. The work supplied In order to keep the reservoirs moving eventually Is dissipated and heats up the liquid. In order to remove this extra heat from the system the velocities of the reservoir molecules are scaled at each time step so as to keep the average reservoir temperatures constant. The Imposed shear rate Is obviously... 

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