Natural convection buoyancy force

We introduce the buoyancy factor as the relative influence of the natural convection over forced convection... 

Natural convection and forced convection, depending respectively on the magnitude of buoyancy and the power of the pump or fan, may be laminar or turbulent. As we know from fluid mechanics, the streamlines of a laminar flow behave in an orderly manner, while the streamlines of a turbulent flow fluctuate irregularly about a mean flow. In this chapter, we shall deal with laminar convection. Turbulent convection will be left to Chapter 6. 

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 ... 

Dimensional analysis shows that, in the treatment of natural convection, the dimensionless Grashof number, which represents the ratio of buoyancy to viscous forces, is often important. The definition of the Grashof number, Gr, is... 

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. 

The relationships developed from field measurements have been made dimensionless with the assumptions that v = 1.33 x 10 m /s and AijO = 2.6 x 10 m /s to facilitate comparisons between relations and avoid dimensional problems. They are given in Table 9.2. The early measurements were to investigate the loss of water from the reservoirs of the Colorado River in the United States, and the later measurements were designed to investigate heat loss from heated water bodies. A revelation occurred in 1969, when Shulyakovskyi brought in buoyancy forces as related to natural convection to explain the heat loss from heated water at low wind velocities. This was picked up by Ryan and Harleman (1973), who realized that natural convection could explain the need for a constant term in front of the relationship for gas film coefficient, as had been found by Brady et al. (1969), Kohler (1954), Rymsha and Dochenko (1958), and Shulyakovskyi (1969). Finally, Adams et al. (1990) rectified... 

When a liquid warms up, its density decreases, which results in buoyancy and an ascendant flow is induced. Thus, a reactive liquid will flow upwards in the center of a container and flow downwards at the walls, where it cools this flow is called natural convection. Thus, at the wall, heat exchange may occur to a certain degree. This situation may correspond to a stirred tank reactor after loss of agitation. The exact mathematical description requires the simultaneous solution of heat and impulse transfer equations. Nevertheless, it is possible to use a simplified approach based on physical similitude. The mode of heat transfer within a fluid can be characterized by a dimensionless criterion, the Rayleigh number (Ra). As the Reynolds number does for forced convection, the Rayleigh number characterizes the flow regime in natural convection ... 

For natural convection, a correlation was established between the Nusselt criterion, which compares convective and conductive resistances to heat transfer and the Rayleigh criterion, which compares buoyancy forces with viscous friction ... 

Natural Convection, where the flow is induced by buoyancy forces, which result from the thermal expansion of hotter fluids that rise relative to cooler, denser fluids. 

Gr Grashof Pp2f]gAT buoyancy x inertial forces Natural convection... 

Free or natural convection occurs when fluid motion is generated predominantly by body forces caused by density variations, under the earth s gravitational field. In the absence of the gravitational field, body forces may be caused by surface tension. The subject material here is focussed on heat transfer with motion produced by buoyancy forces. 

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. 

Available analyses of turbulent natural convection mostly rely in some way on the assumption that the turbulence structure is similar to that which exists in turbulent forced convection, see [96] to [105]. In fact, the buoyancy forces influence the turbulence and the direct use of empirical information obtained from studies of forced convection to the analysis of natural convection is not always appropriate. This will be discussed further in Chapter 9. Here, however, a discussion of one of the earliest analyses of turbulent natural convective boundary layer flow on a flat plate will be presented. This analysis involves assumptions that are typical of those used in the majority of available analyses of turbulent natural convection. 

The buoyancy forces that arise as the result of the temperature differences and which cause the fluid flow in free convection also exist when there is a forced flow. The effects of these buoyancy forces are, however, usually negligible when there is a forced flow. In some cases, however, these buoyancy forces do have a significant influence on the flow and consequently on the heat transfer rate. In such cases, the flow about the body is a combination or mixture of forced and free convection as indicated in Fig. 9.1 and such flows are referred to as combined or mixed forced and free (or natural) convection. 

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. 

A number of practical situations involve convection heat transfer which is neither forced nor free in nature. The circumstances arise when a fluid is forced over a heated surface at a rather low velocity. Coupled with the forced-flow velocity is a convective velocity which is generated by the buoyancy forces resulting from a reduction in fluid density near the heated surface. 

Convection is called forced convection if Ihe fluid is forced to flow over the surface by external means such as a fan, pump, or the wind. In contrast, convection is called natural (or free) convection if the fluid motion is caused by buoyancy forces that are induced by density differences due to the variation of temperature in the fluid (Fig. 1 33). For example, in the absence of a fan, heat transfer from the surface of the hot block in Fig. 1-32 is by natural convection since any motion in the air in this case is due to the rise of Ihe warmer (and thus lighter) air near the surface and the fall of the cooler (and thus heavier) air to fill its place. Heat transfer between the block and the surrounding air is by conduction if the temperature difference between Ihe air and the block is not large enough to overcome the resistance of air to movement and thus to initiate natural convection currents. 

Convection is classified as natural (or free) and forced convection, depend ing on how the fluid motion is initiated. In forced convection, the fluid is forced to flow over a surface or in a pipe by external means such as a pump or a fan. In natural convection, any fluid motion is caused by natural means such as the buoyancy effect, which manifests itself as the rise of warmer fluid and the fall of the cooler fluid. Convection is also classified a.s external and internal, depending on whether the fluid is forced to flow over a surface or in a pipe. 

In Chapters 7 and 8, we considered heat transfer by forced convection, where a fluid was forced to move over a surface or in a tube by external means such as a pump or a fan. In this chapter, we consider natural convection, where any fluid motion occurs by natural means such as buoyancy. The fluid motion in forced convection is quite noiicenhle, since a fan or a pump can transfer enough momentum to the fluid to move it in a certain direction. Tlie fluid motion in natural convection, however, is often not noticeable because of the low velocities involved. 

The magnitude of the natural convection heal transfer between a surface and a fluid is directly related to the flow rate of the fluid. The higher the flow rate, tbe higher the heat transfer rate. In fact, it is the very high flow rales that increase the heat transfer coefficient by orders of magnitude when forced convection is used. In natural convection, no blowers are used, and therefore the flow rale cannot be controlled externally. The flow rale in this case is established by the dynamic balance of buoyancy and friction. 

As we have discussed earlier, the buoyancy force is caused by the density difference between the healed (or cooled) fluid adjacent to the surface and tiie fluid surrounding it, and is proportional to this density difference and the volume occupied by the warmer fluid. It is also well knowu ll at whenever Iwc bodies in contact (.solid--solid, solid-fluid, or fluid-fluid) move relative to cacf other, a friction force develops at the contact surface in the direction opposite ic that of the motion. This opposing force slows down the fluid and thus reduce the flow rate of the fluid. Under steady conditions, the airflow rate driven b buoyancy is established at the point where these two effects balance each othet The friction force increases as more and more solid surfaces are introduced, se tiously disrupting the fluid flow and heat transfer. For that reason, heat sink with closely spaced fins are not suitable for natural convection cooling. 

In this section we derive the equation of motion that governs the natural convection flow in laminar boundary layer. The conservation of mass and energy equations derived in Chapter 6 for forced convection are also applicable for natural convection, but tlie momentum equation needs to be modified to incorporate buoyancy. 

Consider a vertical hot flat plate immersed in a quiescent fluid body. We assume the natural convection flow to be steady, laminar, and two-dimensional, and the fluid to be Newtonian with constant properties, including density, with one exception the density difference p — is to be considered since it is this density difference between the inside and the outside of the boundary layer that gives rise to buoyancy force and sustains flow. (This is known as the Boussines.q approximation.) We take the upward direction along the plate to be X, and the direction normal to surface to be y, as shown in Fig. 9-6. Therefore, gravelly acts in the —.t-direclion. Noting that the flow is steady and two-dimensional, the.t- andy-compoijents of velocity within boundary layer are II - u(x, y) and v — t/(.Y, y), respectively. 

Natural convection can enhance or inhibit heat transfer, depending on the relative directions of buoyancy-induced motion and the forced convection motion. 

So far we presented some general discussions on boiling. Now we turn our attention to the physical mechanisms involved in pool boiling, that is, the boiling of stationary fluids. In pool boiling, the fluid is not forced to flow by a mover such as a pump, and any motion of the Iluid is due to natural convection currents and Ihe motion of the bubbles under the influence of buoyancy. 

Heat is transferred from or to a region by the motion of fluids and the phenomenon of convection. In natural convection, the movement is caused by buoyancy forces induced by variations in the density of the fluid these variations are caused by differences in temperature. In forced convection, movement is created by an external agency such as a pump. 

We have already noted that the general class of flows driven by buoyancy forces that are created because the density is nonuniform is known as natural convection. If we examine the Boussinesq approximation of the Navier-Stokes equations, (12-170), we can see that there are actually two types of natural convection problems. In the first, we assume that a fluid of ambient temperature 71, is heated at a bounding surface to a higher temperature I. This will produce a nonuniform temperature distribution in the contiguous fluid, and thus a nonuniform density distribution too. Let us suppose that the heated surface is everywhere horizontal. Then there is a steady-state solution of (12-170) with u = 0, and the body-force terms balanced by a modification to the hydrostatic pressure distribution, such that... 

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