Effect of natural convection

Wlien analysmg the data, it is important to consider a wide time range to ensure the reliability of the data, since at short times, <1 ms, it will be detemiined by tlie charging time of the double layer, and at longer times, >10 s, by the effects of natural convection. 

For conditions in which only natural convection occurs, the velocity is dependent on the buoyancy effects alone, represented by the Grashof number, and the Reynolds group may be omitted. Again, when forced convection occurs the effects of natural convection are usually negligible and the Grashof number may be omitted. Thus ... 

Obtain by dimensional analysis a functional relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effects of natural convection can be neglected in comparison with those of forced convection. 

The density change on polymerization is typically about 20%, and this density gradient can cause significant secondary flows and natural convection effects. The experiments cited above for vinyl acetate polymerization were performed in a helical reactor. The centrifugal force in helical reactors induces secondary flows as well. The effects of helical flow have been analyzed, but were found to be less significant than the effects of natural convection [14]. 

The effect of natural convection can be illustrated by considering the following simplified model. The reaction rates and physical parameters are constant except for the density which is given as ... 

A. Mohoric, J. Stepisnik 2000, (Effect of natural convection in a horizontally oriented cylinder on NMR imaging of the distribution of diffiisivity), Phys. Rev. E 62, 6628. 

Experimental data on heat transfer from spheres to an air stream are shown in Fig. 5.20. Despite the large number of studies over the years, the amount of reliable data is limited. The data plotted correspond to a turbulence intensity less than 3%, negligible effect of natural convection (i.e., Gr/Re <0.1 see Chapter 10), rear support or freefloating, wind tunnel area blockage less than 10%, and either a guard heater on the support or a correction for conduction down the support. Only recently has the effect of support position and guard heating been appreciated a side support causes about a 10% increase in Nu... 

In Fig. 10.4 the sphere diameter, terminal velocity, and temperature difference each appear in only one dimensionless group. The effect of natural convection on is smaller at Pr = 10 because the region over which the buoyancy force acts is much thinner than for Pr = 1. As Pr oo the effect should disappear altogether. For Pr = 0, numerical solutions (W7) show effects about 50% larger than for Pr = 1. 

Positive deviations of it1/2 with increasing time can also be evidence for convection within an electrochemical cell. Convection can be caused by external vibrations or by density gradients created by the local concentration differences resulting from the electrochemical perturbation. While the influence of external vibrations can be largely eliminated by isolation of the cell with a damped table, the natural convection due to unequal densities of O and R is an unavoidable consequence of the experiment, the importance of which depends on the particular species involved. The effect of natural convection at planar electrodes is most serious when the surface is mounted vertically. It is therefore desirable to carry out electrochemical experiments at surfaces facing up or down whenever possible. 

Large t. The spherical term dominates, which represents a steady-state current. However, due to the effects of natural convection this steady state is never reached at conventionally-sized electrodes. The smaller the electrode radius, the faster the steady state is achieved. It is possible to achieve a steady state at microelectrodes. These are described further in Section 5.5. 

Discussion. The data and correlations at pressures of 10 atm to 200 atm are compared to literature values at low pressure (1 atm and 25 C) (20-22). Figure 4 shows that above the critical pressure mass transfer coefficients are less dependent on Re than below the critical pressure. At low pressure, the density gradient across the boundary layer is much smaller. Therefore, the effect of natural convection on mass transfer is very slight. Near the critical pressure, however, the effect of natural convection on mass transfer rates becomes important at low Reynolds number due to very large density gradients across the boundary layer. 

Heat transfer for laminar flow in tubes with a parabolic velocity profile. (Does not include effects of natural convection or viscosity gradients.)... 

EFF OF NATURAL CONVECTION IN LAMINAR-FLOW HEAT TRANSFER In laminar flow at low velocities, in large pipes, and at large temperature drops, natural convection may occur to such an extent that the usual equations for laminar-flow heat transfer must be modified. The effect of natural convection in tubes is found almost entirely in laminar flow, as the higher velocities characteristic of flow in the transition and turbulent regimes overcome the relatively gentle currents of natural convection. 

The effect of natural convection on the coefficient of heat transfer to fluids in laminar flow through horizontal tubes can be accounted for by multiplying the... 

Hence flow is laminar, and Eq. (12.25) applies. The results may later require correction for the effect of natural convection using Eq. (12.80). To use Eq. (12.25), the following quantities are needed ... 

Equations (2-34), (2-35), and (2-36) can be used only when the effects of natural convection are negligible, that is, when... 

Another aspect, usually overlooked, is the effect of natural convection inside the drop on the transfer coefficient. Transfer coefficients differing by about 25 % were found (W12) when drops were heated or cooled in the continuous phase (see Section 1V,B). 

It can be seen that at short times the spherical correction can be neglected. On the other hand, at large t values, a steady-state current will flow. The smaller the electrode radius, the faster the steady state is achieved. The steady state can easily be reached at microelectrodes however, at electrodes of ordinary size (To > 1 mm), steady-state current is seldom observed due to the effect of natural convection. 

The fluid properties are evaluated at the film temperature 7. A somewhat more accurate correlation is available for a Nr range 1-17 000 by others (S2), which takes into account the effects of natural convection at these lower Reynolds numbers. 

The zone close to the electrode surface where the concentrations of 0 and R are different from those in the bulk is known as the diffusion layer. In most experiments its thickness increases with time until it reaches a steady state value, approximately 10" cm thick, as natural convection stirring the bulk solution becomes important. It takes of the order of 10 s for this boundary layer to form. This also means that for the first 10 s of any experiment, the concentration changes close to the electrode are the result of only diffusion. Thereafter the effects of natural convection must be taken into account. 

---