Natural convection example

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. 

The heat pipe has properties of iaterest to equipmeat desigaers. Oae is the teadeacy to assume a aeady isothermal coaditioa while carrying useful quantities of thermal power. A typical heat pipe may require as Htfle as one thousandth the temperature differential needed by a copper rod to transfer a given amount of power between two poiats. Eor example, whea a heat pipe and a copper rod of the same diameter and length are heated to the same iaput temperature (ca 750°C) and allowed to dissipate the power ia the air by radiatioa and natural convection, the temperature differential along the rod is 27°C and the power flow is 75 W. The heat pipe temperature differential was less than 1°C the power was 300 W. That is, the ratio of effective thermal conductance is ca 1200 1. 

For example, vaporization may occur as a result of heat absorbed, by radiation and convection, at the surface of a pool of hquid or as a result of heat absorbed by natural convect ion from a hot wall beneath the disengaging surface, in which case the vaporization takes place when the superheated liquid reaches the pool surface. Vaporization also occurs from falling films (the reverse or condensation) or from the flashing of hquids superheated by forced convec tion under pressure. 

Natural convection is self-induced and is created by the density differences, which are temperature related the boiling of water in a kettle is an example of free convection. Forced convection is caused by an external force being applied by mechanical means such as a fan or pump the cooling of a warm bottle in cool flowing water is an example of forced convection. 

Convection. Heat transfer by convection arises from the mixing of elements of fluid. If this mixing occurs as a result of density differences as, for example, when a pool of liquid is heated from below, the process is known as natural convection. If the mixing results from eddy movement in the fluid, for example when a fluid flows through a pipe heated on the outside, it is called forced convection. It is important to note that convection requires mixing of fluid elements, and is not governed by temperature difference alone as is the case in conduction and radiation. 

M at 25°C [114]. Equation (51) or (52) enables the diffusivity of a solute to be measured. For example, from the slope of the line in Fig. 17 under sink conditions, D is calculated to be 6.1 X 10-6 cm2/sec for 2-naphthoic acid. At low rotational speeds, the dissolved solute may not be uniformly distributed throughout the volume of the dissolution medium, and/or natural convection may become significant. The former effect may complicate the analytical procedure, while the latter effect will cause positive deviations of J values from Eqs. (51) and (52). At high rotational speeds, turbulence may disturb the flow pattern in Fig. 16, causing other deviations [101,104],... 

Example 6.2 Estimate the mass flux evaporated for methanol in dry air at 25 °C and 1 atm. Assume natural convection conditions apply at the liquid-vapor surface with h = 8 W/m2 K. 

Example 6.3 Consider Example 6.2 for a shallow pool of methanol with its bottom surface maintained at 25 °C. Assume that natural convection occurs in the liquid with an effective convective heat transfer coefficient in the liquid taken as 10 W/m2 K. Find the surface temperature, surface vapor mass fraction and the evaporation flux for this pool. 

Since accidental fire spread mostly occurs under natural convection conditions within buildings and enclosures, some examples of configurations leading to opposed or wind-aided types of spread are illustrated in Figure 8.3. Flame spread calculations are difficult... 

Figure 8.3 Examples of surface flame spread under natural convective conditions...

The experimental setup, described in Example 8.1, for calculating the bias in a dynamic environment will be used here to discuss the parameter estimation methodology. In this case both the surface heat transfer coefficient (h) and the thermal conductivity (A) of the body in the condition of natural convection in air are considered (Bortolotto et al., 1985). 

When a fluid is heated, the hot less-dense fluid rises and is replaced by cold material, thus setting up a natural convection current. When the fluid is agitated by some external means, then forced convection takes place. It is normally considered that there is a stationary film of fluid adjacent to the wall and that heat transfer takes place through this film by conduction. Because the thermal conductivity of most liquids is low, the main resistance to the flow of heat is in the film. Conduction through this film is given by the usual relation (74), but the value of h is not simply a property of the fluid but depends on many factors such as the geometry of the system and the flow dynamics for example, with tubes there are significant differences between the inside and outside film coefficients. 

This burner, a butane lighter, a candle, a burning log, and a match (after ignition) are aU examples of diffusion flames where one generally provides the fuel and relies on natural convection of air to provide the oxidant... 

In electrochemical reactors, the externally imposed velocity is often low. Therefore, natural convection can exert a substantial influence. As an example, let us consider a vertical parallel plate reactor in which the electrodes are separated by a distance d and let us assume that the electrodes are sufficiently distant from the reactor inlet for the forced laminar flow to be fully developed. Since the reaction occurs only at the electrodes, the concentration profile begins to develop at the leading edges of the electrodes. The thickness of the concentration boundary layer along the length of the electrode is assumed to be much smaller than the distance d between the plates, a condition that is usually satisfied in practice. 

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. 

This example is motivated by a natural-convection problem (Fig. 3.13) where the body-force term is caused by slight density variations (often caused by temperature variations). Using the so-called Boussinesq approximation, the flow may be considered incompressible, but with the buoyant forces depending on slight density variations. 

The boundary conditions for the stream-function-vorticity system requires specifying the stream function on all the boundaries. This is usually straightforward for known inflow and outflow conditions and solid walls. The vorticity boundary conditions comes from evaluating Eq. 3.281 on the boundary. Along the boundary, which usually corresponds with one of the coordinate directions, one of the terms in Eq. 3.281 (i.e., the one in which the derivatives align with the boundary) can be evaluated explicitly since the stream function is already specified. Thus the boundary conditions becomes a relationship between the boundary vorticity and a boundary-normal second derivative of stream function. For example, consider the natural convection in a long horizontal tube. Here, since there is no inflow or outflow, the stream function is simply zero all around the tube wall. Thus the vorticity boundary conditions are... 

The usual specific flow-rates for extraction are very small. In terms of space velocities, these are about 5 to 15 kg/h per litre of extractor volume, with superficial velocities in the range of 0.5 to 10 mm/s. With these small velocities, natural convection mass transfer is the favoured mechanism of transport. Gas densities are in the range of 500 to 800 kg/m3, and viscosities are about 5 x 10 7 kg/(m s), thus giving kinematic viscosities of about 10 9 m2/s, which is a very small value for a fluid. For example, the kinematic viscosity of water is 10"7 m2/s and that of ambient air is 2 x 10 5 m2/s. This makes free convection a principal mechanism for mass-transfer in high pressure gases. 

By introduction of a typical value for D0, 10 r> cm2 s 1, it is seen that the value of 8 after, for example, 5 seconds amounts to 0.1 mm. At times larger than 10-20 seconds, natural convection begins to interfere and the assumption of linear diffusion as the only means of mass transport is no longer strictly valid. At times larger than approximately 1 minute, the deviations from pure diffusion are so serious and unpredictable that the current observed experimentally cannot be related to a practical theoretical model. 

The third step checks if natural convection is sufficient to maintain heat losses, to provide a sufficient cooling capacity. The additional data required in this step comprises the variation of density as a function of temperature (P), the viscosity, and the thermal conductivity. This again is only meaningful as long as the reacting mass has a low viscosity allowing for buoyancy. If this data set is not sufficient or the natural convection cannot be established, for example, as for solids, the system must be considered as purely conductive. 

The first example illustrates the behavior of a binary mixture in an open-batch distillery with a stagnant sweep gas. Figure 4.14 shows the historical set-up from 1977 [19, 23-29]. The still was heated by a Bunsen burner, while the condenser was installed in the form of a watchglass cooled by evaporation of water due to natural convection. 

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. 

The density differences leading to natural convection most often have a thermal origin. The lofting of warm air masses at the earth s surface and their replacement by cooler and denser masses from above is an example of convective flow (thermal convection) that profoundly affects our atmosphere. Likewise, heated fluid elements in a separation chamber will rise convectively while cooler elements descend. The resulting transport of solute can profoundly affect separations. 

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. 

Physical situations that involve radiation with convection are fairly common. Examples include solar radiation interacting with the earth s environment to produce complex natural convection, water environmental studies for predicting natural convection patterns in lakes, seas and oceans, and heat transfer along copper tubes in the furnace of a boiler. 

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. 

The stabilizing effect of cocurrcnt cooling has hardly been exploited up to now in industrial reactors. This may be due to the fear that, at the required low flow velocity (in the example of Fig. 20B, , = 0.01 m/s). heat transfer will be inadequate and natural convection will occur in the cooling jacket. However, , describes the mean coolant velocity parallel to the tube axis. With a cross-cocurrcnt flow of the coolant, the actual flow velocity may in fact be substantially larger, de-... 

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