4 natural convection

Heat transfer for natural convection systems may be represented by the following equations  

Coefficients of heat transfer by natural convection from bodies of various shapes, chiefly plates and cylinders, are correlated in terms of Grashof, Prandtl, and Nusselt numbers. Table 8.9 covers the 

Having learned the dimensionless numbers associated with forced convection we now proceed to those for natural convection. 

So far, we have learned that the correlation of forced convection, begins with 

Noting that Eq. (5.145) already involves p because of the inertial force, and now replacing V of this equation with gp AT, we have 

Consider first the II-theorem and, accordingly, express Eq. (5.156) in terms of the four fundamental units as 

At this stage the temperature dependence appears to be the simplest one. Elimination of [6 from Eq. (5.157) by combining cp, for example, with other temperature-dependent quantities yields 

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 convection along a vertical plate, Ra 109 indicates that turbulent flow is established and heat transfer by convection dominates. For smaller values of the Rayleigh number, Ra 104, the flow is laminar and conduction dominates. Thus, the Rayleigh number discriminates between conduction and convection [2]. 

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  

The Rayleigh criterion can also be written as a function of the Grashof criterion, which compares convective with conductive heat transfer and the Prandtl criterion, which compares the momentum diffusivity (kinematic viscosity) with the thermal diffusivity  

For natural convection along a vertical surface, the following correlations can be used [3]  

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Convection is the movement of a species due to external mechanical forces. This can be of two types natural convection, which arises from thennal gradients or density differences within the solution, and forced convection, which can take the fomi of gas bubbling, pumping or stirrmg. The fomier is undesirable and can occur m any solution... 

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. 

Wlien analysmg the data, it is important to consider a wide time range to ensure the reliability of the data, since at short times, <1 ms, it will be detemiined by tlie charging time of the double layer, and at longer times, >10 s, by the effects of natural convection. 

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. 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

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. 

Fig. 14. (a) Workpiece heated by natural convection (b) workpiece heated by forced convection (80). 

The buoyancy-driven natural convection along the freezing interface in horizontal operation tends to be fairly vigorous. However, it also leads to sprea ding of the zone at the top owing to convection transport of heat upward. 

Dehberate stirring can be imposed on conductors with a transverse rotating magnetic field or by passage of electric current axially with a transverse magnetic field. Conversely, a constant magnetic field with no current imposed greatly reduces natural convection. 

Convection is the transfer of heat from one point to another within a fluid, gas, or liquid by the mixing of one portion of the fluid with another. In natural convection, the motion of the flmd is entirely the result of differences in density resiilting from temperature differences in forced convection, the motion is produced by mechanical means. When the forced velocity is relatively low, it should be reahzed that Tree-convection factors, such as density and temperature difference, may have an important influence. 

Natural convection occurs when a solid surface is in contact with a fluid of different temperature from the surface. Density differences provide the body force required to move the flmd. Theoretical analyses of natural convection require the simultaneous solution of the coupled equations of motion and energy. Details of theoretical studies are available in several general references (Brown and Marco, Introduction to Heat Transfer, 3d ed., McGraw-HiU, New York, 1958 and Jakob, Heat Transfer, Wiley, New York, vol. 1, 1949 vol. 2, 1957) but have generally been applied successfully to the simple case of a vertical plate. Solution of the motion and energy equations gives temperature and velocity fields from which heat-transfer coefficients may be derived. The general type of equation obtained is the so-called Nusselt equation hL I L p gp At cjl... 

Nusselt Equation for Various Geometries Natural-convection coefficients for various bodies may be predicted from Eq. (5-32). The various numerical values of 7 andm have been determined experimen-... 

Metzner and Friend [Ind. Fng. Chem., 51, 879 (1959)] present relationships for turbulent heat transfer with nonnewtouiau fluids. Relationships for heat transfer by natural convection and through laminar boundaiy layers are available in Skelland s book (op. cit.). 

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. 

The lower Emit of applicability of the nucleate-boiling equations is from 0.1 to 0.2 of the maximum limit and depends upon the magnitude of natural-convection heat transfer for the liquid. The best method of determining the lower limit is to plot two curves one of h versus At for natural convection, the other ofh versus At for nucleate boiling. The intersection of these two cui ves may be considered the lower limit of apphcability of the equations. 

C. Laminar, local, flat plate, natural convection vertical plate... 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

H. Vertical tubes, laminar flow, forced and natural convection... 

Agrees with cylinder and oblate spheroid results, 15%. Assumes molecular (iffusion and natural convection are negligible. 

For subcooling, a liquid inventory may be maintained in the bottom end of the shell by means of a weir or a hquid-level-controUer. The subcoohng heat-transfer coefficient is given by the correlations for natural convection on a vertical surface [Eqs. (5-33 ), (5-33Z )], with the pool assumed to be well mixed (isothermal) at the subcooled condensate exit temperature. Pressure drop may be estimated by the shell-side procedure. 

Typical coil coefficients are listed in Table 11-2. More exact values can be calculated by using the methods for natural convection or forced convection given elsewhere in this section. 

Hot side Cold side Natural convection Forced convection Natural convection Forced convection... 

Free circulation of the coolant from the machine to the surrounding medium 0 Free convection No external power source is essential. Fleat dissipation is achieved through natural convection like a surface cooled motor... 

By forced convection The factors that can influence the temperature of the enclosure, installed outdoors are wind and snow, other than forced cooling. But their effect on actual cooling may be small. Sometimes this happens and sometimes not. It is better to ignore this effect when estimating various thermal effects. Natural convection and radiation will take account of this. 

We have estimated the likely heat that may be generated by a particular size of conductor and enclosure for a certain current rating and then have counterchecked whether the conductor and the enclosure so chosen can dissipate this heat by radiation and natural convection, and reach a state of thermal stability within permissible limits or we may have to increase the size of the conductor... 

Open Tube Sections (Air Cooled) Plain or finned tubes No shell required, only end heaters similar to water units. Condensing, high level heat transfer. Transfer coefficient is low, if natural convection circulation, but is improved with forced air flow across tubes. 0.8-1.8... 

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