Velocity convective

In Eq. (22), r is the spherical co-ordinate starting at the center of the drop. The variable represents the convective velocity due to the moving surface of the expanding drop. Within a reference framework centered on the moving drop surface, this is given by... 

Fig. 2.9.10 Maps of the temperature and of the experimental data. The right-hand column convection flow velocity in a convection cell in refers to numerical simulations and is marked Rayleigh-Benard configuration (compare with with an index 2. The plots in the first row, (al) Figure 2.9.9). The medium consisted of a and (a2), are temperature maps. All other random-site percolation object of porosity maps refer to flow velocities induced by p = 0.7 filled with ethylene glycol (temperature thermal convection velocity components vx maps) or silicon oil (velocity maps). The left- (bl) and (b2) and vy (cl) and (c2), and the hand column marked with an index 1 represents velocity magnitude (dl) and (d2).

This value is close to the formal electrode potential and independent of the convection velocity. The plot of log(/d — j)/j versus E is linear with the slope nF/2.303RT. 

In a stagnant solution, free convection usually sets in as a density gradient develops at the electrode upon passing current. The resulting convective velocity, which is zero at the wall, enhances the transfer of ions toward the electrode. At a fixed applied current, the concentration difference between bulk and interface is reduced. For a given concentration difference, the concentration gradient of the reacting species at the electrode becomes steeper (equivalent to a decrease of the Nernst layer thickness), and the current is thereby increased. 

A third, rather unusual way of generating the limiting-current condition is possible in situations controlled by forced convection. The current is held at a known level while the convective velocity is diminished in a controlled manner, for example, by decreasing the rate of rotation of the electrode, until the electrode potential increases steeply (H9). 

Velocity and temperature gradients are confined to the surface layer defined by z < I-. Above L the wind velocity and potential temperature are virtually uniform with height. Venkatram (1978) has presented a method to estimate the value of the convective velocity scale w,. On the basis of this method, he showed that convective conditions in the planetary boundary layer are a common occurrence (Venkatram, 1980). In particular, the planetary boundary layer is convective during the daytime hours for a substantial fraction of each year ( 7 months). For example, for a wind speed of 5 m sec , a kinematic heat flux Qo as small as O.PC sec can drive the planetary boundary layer into a convective state. 

Venkatram, A. (1978). Estimating the convective velocity scale for diffusion applications. Boundary Layer Meteorol. 15, 447-452. 

Fig. 9. Droplet radii data for 1-dodecanol from which the charge and convective velocity data are determined (from Bridges, 1990).

This assumes that the concentration at any value of x is not a function of radius. Ca is the concentration of reacting species A, u the mean convective velocity, which is assumed to be neither a function of axial or radial position, and Ta is the reaction rate of A based on unit volume. If nth-order power law kinetics pertain, i.e. 

Convective Velocity component flux rate = normal to surface (g/s) (m/s)... 

It is difficult to solve the system of Eqs. (39)—(41) for these boundary conditions. However, certain simplifying assumptions can be made, if the Prandtl number approaches large values. In this case, the thermal boundary layer becomes very thin and, therefore, only the fluid layer near the plate contributes significantly to the heat transfer resistance. The velocity components in Eq. (41) can then be approximated by the first term of their Taylor series expansions in terms of y. In addition, because the nonlinear inertial terms are negligible near the wall, one can further assume that the combined forced and free convection velocity is approximately equal to the sum of the velocities that would exist when these effects act independently. Therefore, for assisting flows at large Prandtl numbers (theoretically for Pr -> oo), Eq. (41) can be rewritten in the form ... 

The natural convection velocity is given by Eq. (68b). The order-of-magnitude analysis provides the following algebraic equation ... 

Postprocess the solution, either with a short special purpose program or in a spreadsheet, to calculate the thermophoretic velocity at each point. (This velocity has the opposite sign of the convective velocity from the flow simulation.)... 

Now, strong stellar wind blows on the photosphere of early type stars (cf. de Jager 1980), so that mass outward flow vHin(i up to 1 cm/sec exists in the edge of core. The precise consideration is required to determine whether the convective velocity of C is more effective for dredge-up than vwind or not. Quantative results will be shown in the seperate paper. 

So much for the background. The question now is whether we can visualize the solution before going to the computer. This is particularly necessary as we have a delta function as initial condition. However, the equation looks rather like the equation for diffusion and flow in a straight tube, which, if to were the concentration of a solute, D( ) its spatially varying diffusion coefficient, and V(x) its spatially varying convective velocity, would be... 

The mass-transport parameters (diffusion coefficient, convective velocity, bioreaction rate constant) can vary as a function of the space coordinate ... 

In general case, as was mentioned, the diffusion coefficient and/or convective velocity can depend on the space coordinate, thus D=D(y), u(y), [or on the concentration, D = D(c) or both of them, D = D(c, y)]. In the boundary conditions the external mass-transfer resistance is also taken into account. 

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