Free convective transfer

Another case of free convection with some complications, but amenable to solution, is that due to combined temperature and concentration differences. De Leeuw den Bouter et al. (DIO) experimented with such combined free convective transfer, assuming complete analogy of heat and mass transfer if the Grashof number employed is of the form... 

On the outside, we have free convection transfer to a horizontal tube. In the laminar flow case we have... 

As an example, absorption of gas in liquid film fiow at high pressures may even increase the liquid density and thus make infiuence on mass transport [43]. Nevertheless, free convective heat and mass transfer in liquids are of minor importance because the driving density differences decrease at high pressures. Thus, common correlations are applicable for free convective transfer in liquids. 

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. 

As an example, for free convective heat transfer from a vertical wall. 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

The convective heat transfer for the panel is free convection from a heated surface faced down. It can be calculated from Incropera and DeWitt ... 

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

The solar radiation absorbed on external building surfaces increases the wall surface temperature, thus leading to a change in the heat conducted through the component. In low-wind conditions, free convective flows drift up the warm external wall surface. This changes the convective heat transfer and leads to increased temperatures of supply air for natural ventilation. 

Convection is heat transfer between portions of a fluid existing under a thermal gradient. The rate of convection heat transfer is often slow for natural or free convection to rapid for forced convection when artificial means are used to mix or agitate the fluid. The basic equation for designing heat exchangers is... 

This design is not well adapted to free-convection heat transfer outside a tube or coil therefore, for this discussion only agitation is considered using a submerged helical coil, Oldshue and Kern . 

Wiebelt,J. A.,J. B. Henderson, andj. D. Parker, Free Convection Heat Transfer from the Outside of Radial Fin Tubes, Heat Trans. Eng.,Y. 4, April une (1980) p. 53. 

FI. Farber, E. A., Free convection heat transfer from electrically heated wires, J. Appl. Phys. 22, 1437 (1951). 

Kato H NtSHtWAKi, N. and Hirata, M. Im. Jl. Heat Mass Transfer 11 (1968) 1117. On the turbulent heat transfer by free convection from a vertical plate. 

Garner, F.H. andKEEY, R.B. Chem. Eng. Sci. 9 (1959) 218. Mass transfer from single solid spheres — H. Transfer in free convection. 

Heat transfer coefficient a (for free convection) for heating from a wall a = 3-6 W/m2 K (surface vertical), for floor heating a = 6-10 W/m2 K (surface horizontal) and no heating from ceilings, as the temperature gradient would suppress convection ... 

Cheng, L. Y., andP. R.Tichler, 1991, CHF for Free Convection Boiling in Their Rectangular Channels, ANS Proc. Natl. Heat Transfer Conf., Minneapolis, MN, pp. 83-90. (2)... 

Kutateladze, S. S., V. N. Moskvicheva, G. I. Bobrovich, N. N. Mamontova, and B. P. Avksentyuk, 1973, Some Peculiarities of Heat Transfer Crisis in Alkali Metals Boiling under Free Convection, Int. 

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. 

In binary solutions, for example, CuS04 in H20, the limiting current exceeds that due to convective diffusion alone by a factor of about two. The excess mass transfer is caused by migration of the reacting ion in the electric field. In both forced and free convection it is important to know the ion flux contributed by migration, which can never be suppressed completely. 

The diffusivities thus obtained are necessarily effective diffusivities since (1) they reflect a migration contribution that is not always negligible and (2) they contain the effect of variable properties in the diffusion layer that are neglected in the well-known solutions to constant-property equations. It has been shown, however, that the limiting current at a rotating disk in the laminar range is still proportional to the square root of the rotation rate if the variation of physical properties in the diffusion layer is accounted for (D3e, H8). Similar invariant relationships hold for the laminar diffusion layer at a flat plate in forced convection (D4), in which case the mass-transfer rate is proportional to the square root of velocity, and in free convection at a vertical plate (Dl), where it is proportional to the three-fourths power of plate height. 

The effective diffusivities determined from limiting-current measurements appear at first applicable only to the particular flow cell in which they were measured. However, it can be argued plausibly that, for example, rotating-disk effective diffusivities are also applicable to laminar forced-convection mass transfer in general, provided the same bulk electrolyte composition is used (H8). Furthermore, the effective diffusivities characteristic for laminar free convection at vertical or inclined electrodes are presumably not significantly different from the forced-convection diffusivities. 

Of course, in free-convection mass transfer the transition time is dependent on the density difference generated at the electrode. The dimensionless time variable of the transient process is... 

Table IV includes theoretical transition times (C2, R14, SI7c) in laminar flow between parallel plates, following a concentration step at the wall (Leveque mass transfer). Clearly, in laminar flow (Re 100 or lower), transition times are comparable to those in laminar free convection. Here, however, the dependence on concentration (through the diffusivity) is weak. The dimensionless time variable in unsteady-state mass transfer of the Leveque type is...

Unsteady-state mass transfer caused by excessively fast current or potential ramps. This is especially likely to occur in measurements involving laminar flow past elongated surfaces and in free-convection studies, in which the establishment of secondary flow patterns may require long times. A compromise between the time sufficient to reach steady-state transport and the time necessary to avoid bulk depletion and surface roughening (in metal deposition) is required, and is found most reliably by preliminary experimentation. 

In free-convection mass transfer at electrodes, as well as in forced convection, the concentration (diffusion) boundary layer (5d extends only over a very small part of the hydrodynamic boundary layer <5h. In laminar free convection, the ratio of the thicknesses is... 

Free convection flow around horizontal cylinders and spheres is laminar for moderate values of GrSc (see Table VII, Part C) mass-transfer rates obey correlations of the same type as that for a vertical plate electrode, Eq. (29a) ... 

Marchiano and Arvia (M3) also measured mass transfer by thermal and diffusional free convection at a vertical plate. They derived on theoretical grounds a combined Grashof number as follows ... 

The Grashof number given by Eq. (40) appears to have a weaker theoretical basis than that given by Eq. (37), since it is based on an analysis that approximates the profile of the vertical velocity component in free convection, for example, by a quadratic function of the distance to the electrode. The choice of an appropriate Grashof number, as well as the experimental conditions in the work of de Leeuw den Bouter et al. (DIO) and Marchiano and Arvia (M3), has been reviewed critically by Wragg and Nasiruddin (W10). They measured mass transfer by combined thermal and diffusional, turbulent, free convection at a horizontal plate [see Eq. (31) in Table VII], and correlated their results satisfactorily with the Grashof number of Eq. (37). 

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