Cavities natural convection

FIGURE 4.20 Various configurations in which open cavity natural convection occurs. 

Equation (2-113) means that any cylindrical cavity for any liquid-solid combination under a given pressure has a minimum heat flux below which boiling will not be stable, and a transition between natural convection and stable nucleate boiling (bumping) is always observed. 

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. 

Ayyaswamy, P.S. and Catton, I., The Boundary-Layer Regime Ifor Natural Convection in a Differentially Heated, Tilted Rectangular Cavity , J. Heat Transfer, Vol. 95, pp. 543-545,1973. 

Kimura, S. and Bejan, A., The Boundary Layer Natural Convection Regime in a Rectangular Cavity with Uniform Heat Flux From the Side , J. Heat Transfer, Vol. 106, pp. 98-103, 198 . 

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. 

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. 

Three examples of shallow-cavity flows that we consider in this section are sketched in Fig. 6-7. At the top is the case in which all four boundaries are solid walls, the fluid is assumed to be isothermal, and the motion is driven by tangential motion of the lower horizontal boundary. In the middle, a generalization of this problem is sketched in which the fluid is still assumed to be isothermal and driven by motion of the lower horizontal boundary, but the upper boundary is an interface with air that can deform in response to the flow within the cavity. Finally, the lower sketch shows the case in which fluid in the shallow cavity is assumed to have an imposed horizontal temperature gradient, produced by holding the end walls at different, constant temperatures, and the motion is then driven by Marangoni stresses on the upper interface. In the latter case, there will also be density gradients that can produce motion that is due to natural convection, but this contribution is neglected here (however, see Problem 6-13.)... 

V. S. Arpaci, Two thermal microscales for natural convection and heat transfer correlations," Significant Questions in Buoyancy Affected Enclosure or Cavity Flows, ASME HTD-60,117,1986b. 

P. S. Ayyaswamy and I. Catton, The boundary layer regime for natural convection in a differentially heated, tilted rectangular cavity, J. Heat Transfer, 95,543-545,1973. 

The first section presents some fundamental ideas that are frequently referred to in the remainder of the chapter. The next three sections deal with the major topics in natural convection. The first of these addresses problems of heat exchange between a body and an extensive quiescent ambient fluid, such as that depicted in Fig. 4.1a. Open cavity problems, such as natural convection in fin arrays or through cooling slots (Fig. 4.1fe), are considered next. The last major section deals with natural convection in enclosures, such as in the annulus between cylinders (Fig. 4.1c). The remaining sections present results for special topics including transient convection, natural convection with internal heat generation, mixed convection, and natural convection in porous media. 

Enclosure problems (Fig. 4.1c) arise when a solid surface completely envelops a cavity containing a fluid and, possibly, interior solids. This section is concerned with heat transfer by natural convection within such enclosures. Problems without interior solids include the heat transfer between the various surfaces of a rectangular cavity or a cylindrical cavity. These problems, along with problems with interior solids including heat transfer between concentric or eccentric cylinders and spheres and enclosures with partitions, are discussed in the following sections. Property values (including P) in this section are to be taken at Tm = (Th+ TC)I2. 

The problem of natural convection in a cavity without interior solids is exemplified by the two situations sketched in Fig. 4.25. In both situations, the fluid-filled cavity is bounded by two isothermal parallel plates that are inclined at angle 0 from horizontal, spaced at distance L, and held at different temperatures. The temperature Th is assumed to be larger than Tc, so cavities with 0 = 0° are described as horizontal with heating from below, those with 0 = 90° are described as vertical with heating from the side, and those with 0 = 180° are described as horizontal with heating from above. 

A. Bejan and C. L. Tien, Laminar Natural Convection Heat Transfer in a Horizontal Cavity with Different End Temperatures, /. Heat Transfer (100) 641-647,1978. 

R. F. Bergholz, Natural Convection of a Heat Generating Fluid in a Closed Cavity, J. Heat Transfer (102) 242-247,1980. 

G. de Vahl Davis, Natural Convection of Air in a Square Cavity A Bench Mark Numerical Solution, Int. J. Numerical Methods Fluids (3) 249-264,1983. 

S. M. ElSherbiny, G. D. Raithby, and K. G. T. Hollands, Heat Transfer by Natural Convection Across Vertical and Inclined Cavities, J. Heat Transfer (104) 96-102,1982. 

N. Seki, S. Fukusako, and H. Inaba, Heat Transfer of Natural Convection in a Rectangular Cavity With Vertical Walls of Different Temperatures, Bull. JSME (21/152) 246-253,1978. 

In all accidents and accident combinations, a maximum fuel element temperature of approx. 1600°C is not exceeded even without active removal of the decay heat from the core. Decay heat removal can be effected solely by heat conduction, heat radiation, and natural convection to the cavity coolers positioned outside the reactor pressure vessel. 

Figure 4.2 Typical air flow patterns in insulated cavities (a) air rotation by natural convection, (b) air infiltration by natural or forced (wind) convection, (c) windwashing around corner, (d) diffuse air leakage, (e) air leakage through gaps and (f) mixed pattern (after Ojanen and Kohonen [29]).

Concrete canister (or Silo). A massive container comprising one or more individual storage cavities. It is usually circular in cross-section, with its long axis vertical. An inner sealed liner and the massive concrete of the canister body provide the necessary containment and shielding of the radioactive material inside the container. Heat removal is accomplished by radiant emission, conduction and convection within the body of the canister, and by natural convection on its exterior surface. Canisters may be located in enclosed or non-enclosed areas. 

Prasad, V, Kulacki, FA, 1984b. Natural convection in a rectangular porous cavity with constant heat flux on one vertical wall. ASME J. Heat Transf. 106, 152-157. 

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