Natural Convection Flows

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 can be seen from Figs. 7.58 and 7.59, the amount of air in the convection flows increases with height, due to entrainment of the surrounding air. The amount of air transported in a natural convection flow depends on the temperature and the geometry of the surface or source and the temperature of the surrounding air. Because the driving force in convection flows... 

Natural convection flows in nonconfined and nonstratified environments (Section 7.5.2)... 

Natural convection depends strongly on cell geometry. No convection can arise in capillaries or in the thin liquid layers found in narrow gaps between electrodes. The rates of natural convective flows and the associated diffusion-layer thicknesses depend on numerous factors and cannot be calculated in a general form. Very rough estimates show that the diffusion-layer thickness under a variety of conditions may be between 100 and 500 pm. 

The interaction of forced and natural convective flow between cathodes and anodes may produce unusual circulation patterns whose description via deterministic flow equations may prove to be rather unwieldy, if possible at all. The Markovian approach would approximate the true flow pattern by subdividing the flow volume into several zones, and characterize flow in terms of transition probabilities from one zone to others. Under steady operating conditions, they are independent of stage n, and the evolution pattern is determined by the initial probability distribution. In a similar fashion, the travel of solid pieces of impurity in the cell can be monitored, provided that the size, shape and density of the solids allow the pieces to be swept freely by electrolyte flow. 

The details of natural convective flows over surfaces other than flat plates have only recently been studied experimentally (A7, Jl, P3, SI2). We consider a heated sphere in an infinite, stagnant medium. Flow is directed toward the surface over the bottom hemisphere and away from the surface over the top hemisphere with a stagnation point at each pole (P3, S12). The lower pole is considered the forward stagnation point. 

Natural convection is the flow induced by the unequal pull of gravity on fluid elements of different densities. For example, if we inject a globule (or layer) of dense aqueous solution marked with a dye into a beaker of water, the dense globule will be observed to sink under the influence of gravity, as illustrated in Figure 4.8. That sinking motion is actually a form of bulk displacement or flow, specifically natural convective flow. 

In some cases, natural convective flow plays an integral role in separations. For example, thermogravitational (TG) columns rely on a combination of thermal convective flow and relative (selective) displacement by thermal diffusion. 

We note here that natural convective flow is countercurrent the vacation of space by any descending volume elements of fluid is immediately compensated by an ascending volume. 

The reduction of the thickness of the flow channel, as discussed earlier, is equivalent to introducing more surface area per unit volume of medium. High surface areas inhibit all flow, including natural convective flow. One can increase relative surface areas by going to thinner tubes or channels, or by using a fine granular or porous support medium. Both approaches are used in electrophoresis as discussed in a subsequent chapter. 

As explained in Chapter 1, natural or free convective heat transfer is heat transfer between a surface and a fluid moving over it with the fluid motion caused entirely by the buoyancy forces that arise due to the density changes that result from the temperature variations in the flow, [1] to [5]. Natural convective flows, like all viscous flows, can be either laminar or turbulent as indicated in Fig. 8.1. However, because of the low velocities that usually exist in natural convective flows, laminar natural convective flows occur more frequently in practice than laminar forced convective flows. In this chapter attention will therefore be initially focused on laminar natural convective flows. 

It should be noted that, in contrast to forced convective flows, in natural convective flows, due to the temperature-dependent buoyancy forces in the momentum equations, the velocity and temperature fields are interrelated even though the fluid properties are assumed to be constant except for the density change with temperature. 

BOUNDARY LAYER EQUATIONS FOR NATURAL CONVECTIVE FLOWS... 

As previously discussed, there are two limiting cases for natural convective flow through a vertical channel. One of these occurs when /W is large and the Rayleigh number is low. Under these circumstances all the fluid will be heated to very near the wall temperature within a relatively short distance up the channel and a type of fully developed flow will exist in which the velocity profile is not changing with Z and in which the dimensionless cross-stream velocity component, V, is essentially zero, i.e., in this limiting solution ... 

Eqs. (8.120) and (8.121) represent the limiting boundary layer solution for natural convective flow through a vertical plane duct. For the particular case of Pr = 0.7, the similarity solution for natural convective boundary layer flow on a vertical plate... 

The analysis of natural convective flow through a vertical plane duct that was described above is easily, extended to deal with other geometrical situations, such as natural convective flow through a vertical pipe, and to deal with other thermal boundary conditions at the wall. 

Heat transfer by natural convection across an enclosed space, called an enclosure or, sometimes, a cavity, occurs in many real situations, see [34] to [67]. For example, the heat transfet between the panes of glass in a double pane window, the heat transfer between the collector plate and the glass cover in a solar collector and in many electronic and electrical systems basically involves natural convective flow across an enclosure. 

In the discussions of natural convective flows presented so far in this chapter it has been assumed that the flow is laminar. Turbulent flow can, however, as discussed before, occur in natural convective flows, see [84] to [95], this being illustrated... 

Transition to turbulence in the natural convective flow over a vertical plate. 

This analysis is based on the use of the momentum and energy integral equations which for natural convective flow over a vertical plate are ... 

Turbulent natural convective flows can also be analyzed by numerically solving the governing equations together with some form of turbulence model. This is... 

Some of the more commonly used methods of obtaining solutions to problems involving natural convective flow have been discussed in this chapter. Attention has been given to laminar natural convective flows over the outside of bodies, to laminar natural convection through vertical open-ended channels, to laminar natural convection in a rectangular enclosure, and to turbulent natural convective boundary layer flow. Solutions to the boundary layer forms of the governing equations and to the full governing equations have been discussed. 

Consider the natural convective flow of air at 10°C though a plane vertical channel with isothermal walls whose temperature is 40°C and whose height is 10 cm. Determine how the mean heat transfer rate from the heated walls varies with the gap between the walls. 

Oosthuizen, P.H. and Paul, J.T., Natural Convective Flow in a Cavity with Conducting Top and Bottom Walls , Proc. 9th International Heat Trans. Conf., Vol. 2, Hemisphere Publisher, New York, pp. 263-268, 1990. 

Gebhart, B., Natural Convection Flows and Stability , in Advances tn Heat Transfer, Academic Press. New York. 1973. 

Godaux, R. and Gebhart, B., An Experimental Study of the Transition of Natural Convection Flow Adjacent to a Vertical Surface , Int. J. Heat Mass Transfer, Vol. 17, pp. 93-107, 1974. 

Natural convective flows in porous media occur in a number of important practical situations, e.g., in air-saturated fibrous insulation material surrounding a heated body and about pipes buried in water-saturated soils. To illustrate how such flows can be analyzed, e.g., see [20] to [22], attention will be given in this section to flow over the outer surface of a body in a porous medium, the flow being caused purely by the buoyancy forces resulting from the temperature differences in the flow. The simplest such situation is two-dimensional flow over an isothermal vertical flat surface imbedded in a porous medium, this situation being shown schematically in Fig. 10.25. 

Natural convective flow over a vertical plate. 

The above equations apply to forced convection. Their extension and the extension of the rest of the equations given in this section to natural convective flows is straight-forward and will not be discussed here. 

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