Natural convection defined

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

The secondary flows from natural convection can become larger than the primary flow, so it seems likely that the secondary flows might become turbulent or nonsteady. Shown in Tables 1 and 2 are the dimensionless groups at the inlet and outlet, based on cup-average quantities, as well as the Reynolds numbers for the primary and secondary flows (Reynolds numbers defined in terms of the respective total mass flowrate, the viscosity and the ratio of tube perimeter to tube area). 

Natural antioxidants, 12 60-61 Natural attenuation, defined, 3 759t Natural boric acid, 4 133t Natural cements, 5 502 Natural colors, 12 51 Natural color system (NCS), 7 309 Natural convection, 13 245 Natural defenses, against silver, 22 655, 681... 

Consideration of the available data for spheres indicates that forced flow correlations are accurate to about 10% for Gq/Re < 0.2. The analogous limit for natural convection is not so well defined, being about 10 at Pr = 0.7 and increasing with Pr. Additional studies of mixed convection are needed to elucidate the physical phenomena and provide correlations. Simultaneous mass... 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

The studied BCAP0350 DLC has a D-cell battery shape factor which is defined in the standard with a 33 mm outside diameter and a 61.5mm length. The total external surface is about 80cm2. The production of losses inside the DLC is assumed to be uniform in the volume. In the case of a 30 A charge/discharge current the dissipated power is equal to 2.88 W. The measurements have been performed at room temperature 7 = 20°C which was constant during the experiment. The DLC is only cooled with a slowly moving airflow due to the natural convection. 

It can be seen that the expression for the average Nusselt number for Pr 1 is closer in form to the case where Pr — oo, than the case where Pr —> 0. The reason for this is that in natural convection, the driving force is caused by the temperature gradients, and thus defined by the thermal boundary layer. When Pr 1 and when Pr — co, the thermal boundary layer is thicker than the velocity boundary layer. Hence, the behavior of the Nusselt number would be similar in form for both cases. When Pr — 0, the behavior of the kinematic viscosity relative to the thermal diffusivity is going to be different from that of the other two cases. In addition, the right-hand side of the expression for Pr — 0 is independent of o, as one would expect for this case where the effects of the kinematic viscosity are very small or negligible. 

The correlations for the Nussell number Nu = hL /k in natural convection are expressed in terms of the Rayleigh number defined as... 

Experimental systems used for electrochemical measurements should be selected to take maximum advantage of well-imderstood phenomena such as mass transfer so as to focus attention on the less-understood phenomena such as electrode kinetics. For example, the study of electrochemical reactions in stagnant environments should be avoided because concentration and temperature gradients give rise to natural convection, which has an effect on mass transfer that is difficult to characterize. It is better to engage in such experimental investigations in systems for which mass transfer is well defined. To simplify interpretation of the impedance data, the electrode should be uniformly accessible to mass transfer. 

Let the medium between the flat surfaces of two bodies (now a fluid because of practical reasons) flow with a mean velocity V (Fig. 1.13). This flow results from either an imposed pressure drop or an induced buoyancy, respectively called forced and natural convection. Lettheinlettemperatureofthefluidbe72. (Note that the fluid temperature need not be Tz- Selection of Tz for this temperature eliminates temperature gradient near plate 2 and simplifies the following development.) The convection heat transfer from plate 1 is defined as the conduction in the fluid next to plate 1 (in view of the fact... 

The heat transfer coefficient defined by Eq. 1.12 is sensitive to the geometry, to the physical properties of the fluid, and to the fluid velocity. However, there are some special situations in which h can depend on the temperature difference NT = T - Tf. For example, if the surface is hot enough to boil a liquid surrounding it, h will typically vary as AT2 or in the case of natural convection, h varies as some weak power of AT— typically as AT1 4 or AT1 3. It is important to note that Eq. 1.12 as a definition of h is valid in these cases too, although its usefulness may well be reduced. 

As mentioned before, there is a subset of flow problems, called natural convection, where the flow pattern is due to buoyant forces caused by temperature differences. Such buoyant forces are proportional to the coefficient of thermal expansion (1, defined as ... 

The above equation of motion is used for setting up problems in natural convection when the ambient temperature T may be defined. 

Equations are presented in this section for evaluating the heat transfer by natural convection from the external surfaces of bodies of various shapes. The correlation equations are of the form described in the section on the heat transfer correlation method, and the orientation of the surface is given by the surface angle defined in Fig. 4.4. Supporting experimental evidence for each such equation set is outlined after each equation tabulation. The correlations are in terms of Nu, Ra, and Pr, parameters that involve physical properties, a length scale, and a reference temperature difference. Rules for the evaluation of property values are provided in the nomenclature, and the relevant length scale and reference temperature difference are provided in a separate definition sketch for each problem. 

When both bottom and top surfaces are maintained at constant temperatures and there is internal generation, there is a superposition of the horizontal layer problem discussed in the section on natural convection within enclosures and the internal generation problem previously described. These are characterized by the external Rayleigh number defined in the section on natural convection within enclosures and the internal Rayleigh number defined in Fig. 4.40a. The dependence of the layer stability on these parameters has been discussed by Ning et al. [208]. The heat transfer at the top and bottom surfaces has been estimated for these conditions by Baker et al. [13], Suo-Anttila and Catton [276], and Cheung [51],... 

On the basis of data available up to 1964, Metais and Eckert [190] established the forced convection boundary of the mixed convection regime, and their results are presented in Fig. 4.50. The line was drawn where natural convection was thought to alter the heat transfer from that for pure forced convection by 10 percent. Figure 4.49 defines the nomenclature for this problem. 

At the turn of the century, Henri Benard, a young French physicist, published the first truly systematic study of natural convection in a horizontal fluid layer (B4, B5, B6). In a horizontal liquid layer heated from below B6nard, sought to measure and to define the most stable steady-state convection currents prevailing under given conditions. He utilized liquid layers only a few millimeters in thickness, initially in an apparatus giving a free upper surface, and of considerable horizontal extent (about 20 cm) so that edge effects could not influence the form of the convection pattern. For these studies. 

A surface heat transfer coefficient h can be defined as the quantity of heat flowing per unit time normal to the surface across unit area of the interface with unit temperature difference across the interface. When there is no resistance to heat flow across the interface, h is infinite. The heat transfer coefficient can be compared with the conductivity the conductivity relates the heat flux to the temperature gradient the surface heat transfer coefficient relates the heat flux to a temperature difference across an unknowm distance. Some theoretical work has been done on this subject [8], but since it is rarely possible to achieve in practice the boundary conditions assumed in the mathematical formulation, it is better to regard it as an empirical factor to be determined experimentally. Some typical values are given in Table 2. Cuthbert [9] has suggested that values greater than about 6000 W/m K can be regarded as infinite. The spread of values in the Table is caused by mold pressure and by different fluid velocities. Heat loss by natural convection also depends on whether the sample is vertical or horizontal. Hall et al. [10] have discussed the effect of a finite heat transfer coefficient on thermal conductivity measurement. 

Mass transfer coefficient (fe) A measure of the solute s mobility due to forced or natural convection in the system. Analogous to a heat transfer coefficient, it is measured as the ratio of the mass flux to the driving force. In membrane processes the driving force is the difference in solute concentration at the membrane surface and at some arbitrarily defined point in the bulk fluid. When lasing the film theory to model mass transfer, k is also defined as D/S, where D is solute diffusivity and d is the thickness of the concentration boundary layer. 

It is worthwhile to note that Equations (A.22) and (A. 23) have genuine steady state solutions without the need to introduce a boundary layer. This is because the chemical reaction (A. 19) causes the formation of a steady state kinetic layer. Only within this boundary layer is R present in solution, and the concentration of 0 perturbed from its initial concentration. The thickness of the kinetic layer depends on k the larger k the thinner the layer. Certainly for high values of k, the kinetic layer will lie well within the normal steady state diffusion layer defined by natural convection. The time required to reach the steady state (form the kinetic layer) also depends inversely on k. 

Recall that 6 = /i Dt is the electric double-layer defined in Chapter 3. Experimentally, 0.3 mm < 6 < 0.5 mm for most practical electrochemicd cells under diffusion and natural convection [2]. The latter topic will be dealt with in a later section. In this section, 6 is due to diffusion and migration and its value is normally 6 < 1 mm. 

Despite the fact that the Nernst model is rather rough, it has been used in electrochemical kinetics up till now due to its simplicity and obviousness. It has been established by means of different methods that similar structures actually form in the conditions of natural convection. Their thickness makes up 0.01-0.03 cm however, it is rather difficult to strictly define because it depends on various factors, including the current density i. The empirical regularity const has been established experimentally under the steady-state conditions [1]. It should be mentioned that varies with the potential sweep rate v when a linear variation... 

That is, 843 W of heat removed for just 15 W of electrical power. Is that efficient It may be. But it is not, if more of that heat could be removed by natural convection and radiation, and we are using a larger fan than is necessary. The point is that the efficiency of the heat removal system depends more on the design of the airflow path, and how much temperature the air can pick up as it goes through, than on the performance of the motor. Rather than the efficiency of such a cooling system, it is more useful to define effectiveness as... 

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