Convection drag coefficient

Treatment of liquid drops is considerably more complex than bubbles, since the internal motion must be considered and internal boundary layers are difficult to handle. Early attempts to deal with boundary layers on liquid drops were made by Conkie and Savic (C8), McDonald (M9), and Chao (C4, W7). More useful results have been obtained by Harper and Moore (HIO) and Parlange (PI). The unperturbed internal flow field is given by Hill s spherical vortex (HI3) which, coupled with irrotational flow of the external fluid, leads to a first estimate of drag for a spherical droplet for Re 1 and Rep 1. The internal flow field is then modified to account for convection of vorticity by the internal fluid to the front of the drop from the rear. The drag coefficient. 

The shape of a drop moving under the influence of gravity may be affected by interfacial motions the drop may also wobble and move sideways (S27, W3). In one system (S22) the terminal velocity was reduced yielding a drag coefficient nearly equal to that of a solid particle. Interfacial convection tends to increase the rate of mass transfer above that which would occur in the absence of interfacial motion. The interaction between mass transfer and interfacial convection has been treated by Sawistowski (S7) and Davies (D4, D5). 

A number of fundamental parameters that describe iontophoretic transport in Nation (e.g., convective flow velocities, solute drag coefficient) can be evaluated from the SECM experiment. Consider, the overall iontropho-retic flux of a neutral molecular permeant ... 

Hamlin BS, Ristenpart WD (2012) Transient reduction of the drag coefficient of charged droplets via the convective reversal of stagnant caps. Phys Eluids 24 012101... 

Y 1-2F) J where Cd is the drag coefficient inside the convective IBL 3/ is the lapse rate above the boundary layer or upwind conditions F is an entrainment coefficient, which ranges from 0 to 0.22 6>iand and 6>sea are the potential air temperatures over land and water, respectively and X is the distance or fetch downwind from the shoreline. The dependency of h on has been predicted by dimensional analysis and by the modynamic approaches. 

Comparison of Eqs. (3) and (5) indicates that the height of the convective IBL over a coast is higher than that over anoceanforagivenfetchand temperature difference. This is mainty due to the higher drag coefficient ( 10 x 10 ) across the shorehne on land than that ( 1.5 x 10 )aeross an oceanic front at sea. 

Figure 3 illustrates some additional capability of the flow code. Here no pressure gradient is Imposed (this is then drag or "Couette flow only), but we also compute the temperatures resulting from Internal viscous dissipation. The shear rate in this case is just 7 — 3u/3y — U/H. The associated stress is.r — 177 = i/CU/H), and the thermal dissipation is then Q - r7 - i/CU/H). Figure 3 also shows the temperature profile which is obtained if the upper boundary exhibits a convective rather than fixed condition. The convective heat transfer coefficient h was set to unity this corresponds to a "Nusselt Number" Nu - (hH/k) - 1. 

What are the mechanisms and the transport coefficients of water fluxes (diffusion, convection, hydraulic permeation, electro-osmotic drag) ... 

A 2-m X 3-m flat plate is suspended in a room, and is subjected to air flow parallel to its surfaces along its 3-m-long side. The free stream temperature and velocity of air are 20°C and 7 m/s. The total drag force acting on the plate is measured to be 0.86 N. Determine the average convection heal transfer coefficient for the plate (Fig. 5-36). 

SOLUTION A flat plate is subjected to air flov/, and the drag force acting on it is measured. The average convection coefficient is to be determined. Assumptions I Steady operating conditions exist. 2 The edge effects are negligible. 3 The local atmospheric pressure is 1 atm. 

B Develop an intuitive understanding of friction drag and pressure drag, and evaluate the average drag and convection coefficients in external flow, a Evaluate the drag and heat transfer associated with flow over a flat plate for both laminar and turbulent flow,... 

When (he average drag and convection coefficients are available, the drag force can be determined from Eq. 7-1 and the rate of heat transfer to or from an isothermal surface can be determined from... 

In multiphase reactor simulations, the momentum, heat and species mass balances may thus contain several terms that can be placed in this framework. However, in these problem solvers, the generalized proportionality coefficient K is usually derived from the steady drag force, and the convective heat and mass transfer fluxes, respectively. 

Processes involving water transport and transformation. What are the relevant mechanisms and transport coefficients of water fluxes (diffusion, convection, hydraulic permeation, electroosmotic drag) What are relevant mechanisms and rates of phase changes (between liquid water, water vapor, surface water, water in membrane) These mechanisms and relevant parameters are amenable to evaluation by ex situ diagnostics. The statistical theory of random composite media [136-138] and percolation theory [44-46] provides various tools for assessing effective parameters of transport and interfacial processes, as discussed in Section 8.4. 

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