External flows, 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. 

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 is classified according to the motivating flow. When the flow takes place because of density variations caused by temperature gradients, the motion is called natural convection. When it is caused by an external agency such as a pump or a fan the process is called forced convection. 

In forced convection, circulating currents are produced by an external agency such as an agitator in a reaction vessel or as a result of turbulent flow in a pipe. In general, the magnitude of the circulation in forced convection is greater, and higher rates of heat transfer are obtained than in natural convection. 

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. 

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. 

Movement of the Huid may be generated by means external to the heat transfer process, us by fans, blowers, or pumps. It may also be created by density differences connected with the heat transfer process itself. The first mode is culled timet cniireeiirtn the second one natural or free t ttttveclion. Convection heal transfer may also be classified as heat transfer in iltni /fnn. or in interna flow (over cylinders, spheres, air foils, and similar objects). In ilie case of external flow, the heal transfer process is essentially concentrated in a thin fluid layer surrounding the object (boundary layer . 

Here, L is the material thickness, T is the tlame temperature, v, is the velocity of the incoming oxidant flow if there is no external supply, v, is controlled by natural convection. A solid fuel which is heated throughout its depth prior to flame arrival is said to be thermally thin. If the thickness (L) of the material is more than that of the layer heated prior to flame arrival the material is said to be thermally thick. 

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. 

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. 

When a surface is subjected to external flow, the problem involves both natural and forced convection. The relative importance of each mode of heat transfer is determined by the value of the coefficient Gr /Ref Natural convection effects are negligible if GiJRel 1, free convection dominates and the forced convection effects are negligible if Gri/Re > 1, and both effects are significant atid must be considered if Grt/Re = 1. 

Studies on the effect of hydrodynamics on localized corrosion and electrochemical etching processes have been reviewed by West et al. Much of the work has been performed by Alkire and co-workers." They have used FIDAP, a commercial FEM code, to investigate the influence of fluid flow on geometries relevant to etching and to pitting corrosion. In most cases, Stokes flow was considered. The Stokes flow approximation is frequently valid inside the cavity because its characteristic dimension is small. However, the flow outside the cavity may not be in the Stokes flow regime. Since it is the external fluid motion that induces flow inside the cavity, under many (especially unsteady) situations, the use of the Stokes flow approximation may be problematic. Some of the work of Alkire and co-workers has been extended hy Shin and Economou, " who simulated the shape evolution of corrosion pits. Natural convection was also considered in their study. 

Another distinction among flows is whether the flow is forced by an external means such as a pump (termed forced convection) or whether the flow arises as a result of a density difference developed in the fluid circuit as a result of the heat transfer (termed natural convection or thermosiphon action). Some cases include both mechanisms. 

Vaporization processes may be divided into pool boiling, in which the hot surface is immersed in a pool of liquid and the vapor bubbles may flow freely away from the hot surface, driven by the difference in phase densities, and convective vaporization, where the liquid and vapor flow together along or away from the hot surface, driven either by natural convection of the two-phase mixture (termed thermosiphon action) or by an externally forced convection (e.g., by a circulating pump). 

Figure 15-17. Block diagram of the thermal flow in a lubricated gear and bearing system. Heat sources.—A oil film at tooth contact B churning of bulk oil C oil film in bearings and bulk churning D oil film at Seals E external sources. Heat transmission.—F m G c H c, m I c J f K m L f M f N m P f Q c, f, r R c S n, f, r T c. c = conduction f = forced convection m = mass transport n = natural convection r = radiation.

P. Cheng, Natural Convection Porous Medium External Flows, in Natural Convection Fundamentals and Applications, S. Kakac, W. Aung, and R. Viskanta eds., pp. 475-513, Hemisphere Publishing, Washington, DC, Springer-Verlag, Berlin, 1985. 

H. Auracher, Transition Boiling in Natural Convection Systems, in Pool and External Flow Boiling, V. K. Dhir and A. E. Bergles eds., pp. 219-236, ASME, New York, 1992. 

The design of natural convection evaporators is difficult because a complex interrelationship between the liquid circulation rate due to density differences and heat transfer coefficients exists. The circulation flow rate depends on the amount of evaporated liquid and is not controlled by an external device as in forced circula-... 

The /th species mass flux, j, and the total heat flux, q, can be expressed in terms of transfer coefficients. This is useful in situations where the liquid or gas phase is not completely resolved, or when the flow conditions are not exactly known. Often, these transfer coefficients are determined experimentally for a particular flow situation. For instance, different expressions are used, depending on whether the transfer is due to pure conduction or whether it is dominated by ccaivection. Also, the type of convection plays a role, that is, if the convection is forced or non-forced. A forced convection has a non-zero relative velocity between droplet and environment, whereas for a non-forced convection, the relative drop-gas velocity is zero and only the Stefan flow dominates. Note that the natural convection due to gravity is taken to be zero since gravity is an external force, and external forces are neglected in this article. In addition, in forced convection, the nature of the flow, that is, whether the flow is laminar or turbulent, plays an important role. These issues will be discussed in more detail in the following subsections. 

Electrochemical systems where the mass transport of chemical species is due to diffusion and electromigration were studied in previous chapters. In the present chapter, we are going to consider the occurrence of the third mechanism of mass transfer in solution convection. Although the modelling of natural convection has experienced some progress in recent years [1], this is usually avoided in electrochemical measurements. On the other hand, convection applied by an external source forced convection) is employed in valuable and popular electrochemical methods in order to enhance the mass transport of species towards the electrode surface. Some of these hydrodynamic methods are based on electrodes that move with respect to the electroljAic solution, as with rotating electrodes [2], whereas in other hydrodynamic systems the electrolytic solution flows over a static electrode, as in waU-jet [3] and channel electrodes [4]. 

In the case of airlift reactors, the flow pattern may be similar to that in bubble columns or closer to that two-phase flow in pipes (when the internal circulation is good), in which case the use of suitable correlations developed for pipes may be justified [55]. Blakebrough et al. studied the heat transfer characteristics of systems with microorganisms in an external loop airlift reactor and reported an increase in the rate of heat transfer [56], In an analytical study, Kawase and Kumagai [57] invoked the similarity between gas sparged pneumatic bioreactors and turbulent natural convection to develop a semi-theoretical framework for the prediction of Nusselt number in bubble columns and airlift reactors the predictions were in fair agreement with the limited experimental results [7,58] for polymer solutions and particulate slurries. 

Sodium coolant has very good thermal conductivity. In the event of failure of the main sodium pumps, heat can be transferred to the vessel boundary by conduction and natural convection without large increases in temperature. Provided the reactor is small enough, decay heat can then be transferred through the vessel wall to a natural convection air flow. Alternatively a small additional heat exchanger in the sodium pool can be used to take heat to an external heat sink by natural convection. Thus the sodium and the small size permit a passive decay heat removal system. 

The heat transfer to air depends on the temperature difference, the surface of the resistor, and the speed and direction of the air flow. Air flow along the resistor may be due to external causes but it can also be caused by natural convection. The air that is heated by the resistor becomes lighter than the surrounding air and, therefore, it tends to rise. The actual formulas for the transfer of heat to air are complicated as they depend strongly on the geometry of the resistor and its surroundings. 

The protected loss of heat sink (PLOHS) event was simulated to predict the heat removal capability of the RVACS. PLOHS was assumed to be initiated by a loss of the external alternate current (AC) power, resulting in a total loss of AC power, because the 4S-LMR has no emergency AC power on-site. The steam/water system cannot remove the decay heat in this event. The primary coolant flow shifts to natural convection mode. The design heat removal capabilities of the PRACS and the RVACS are 2.5 MW(th) and 1 MW(th), respectively. 

The solution of the heat transfer equations is largely controlled by the boundary conditions used to specify the problem. In solidification problems, these boundary conditions depend on the nature of the contact between the freezing material and its container as well as the heat transferred by the container to the external cooling media. The latter problem has been well documented in the heat transfer literature over the years where correlations for convective heat transfer to flowing streams of coolant, natural convection and so on abound. The boundary conditions between the freezing material and mold however, are less well documented. 

The complex set of physical phenomena that occur in a gravity environment when a geometrically distinct heat sink and heat source are connected by a fluid flow path can be identified as natural circulation (NC). No external sources of mechanical energy for the fluid motion are involved when NC is established. In a number of publications, including textbooks, the term natural convection is used as a synonym of NC. Within the present context, natural convection is used to identify the phenomena that occur when a heat source is put in contact with a fluid. Therefore, natural convection characterizes a heat transfer regime that constitutes a subset of NC phenomena. 

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