Tubes noncircular

The Tube Wall Tubular heat exchangers are built using a number of circular (or noncircular) tubes thus, the heat-transfer rate across tubular walls, following Fourier s law of heat conduction, becomes... 

Noncircular tubes are often used in various compact heat exchangers and the Reynolds number in these tubes is of interest. For noncircular tubes such as square, rectangular, eUiptic, and triangular tubes, the so-called hydrauhc diameter, defined as... 

A snap can be characterized by the geometry of its spring component. The most common snaps are the cantilever type, the hollow-cylinder type (as in the lids of pill bottles) and the distortion type (Fig. 4-15). These snaps include those in any shape that is deformed or deflected to pass over interference. The shapes of the mating parts in a hollow cylinder snap is the same, but the shapes of the mating parts in a distortion snap are different, by definition. These classifications are rather nominal, because the cantilever category is used loosely to include any leaf-spring components, and the cylinder type is used also to include noncircular section tubes. 

All the relationships presented in Chapter 6 apply directly to circular pipe. However, many of these results can also, with appropriate modification, be applied to conduits with noncircular cross sections. It should be recalled that the derivation of the momentum equation for uniform flow in a tube [e.g., Eq. (5-44)] involved no assumption about the shape of the tube cross section. The result is that the friction loss is a function of a geometric parameter called the hydraulic diameter ... 

The circular tube expressions for/ and 7VRe can also be transformed into the equivalent expressions for a noncircular conduit by the substitution... 

In many processes (such as oil recovery, blood flow, underground water), one encounters liquid flow through thin (micrometer diameter), noncircular-shaped tubes, or pores. In the literature, one finds studies that address these latter systems. In another context of liquid drop formation, for example, in an inkjet nozzle, this technique falls under a class of scientifically challenging technology. The inkjet printer demands such quality that this branch of drop-on-demand technology is much in the realm of industrial research. All combustion engines are controlled by oil drop formation and evaporation characteristics. The important role of capillary forces is obvious in such systems. 

Perhaps the simplest classification of flow regimes is on the basis of the superficial Reynolds number of each phase. Such a Reynolds number is expressed on the basis of the tube diameter (or an apparent hydraulic radius for noncircular channels), the gas or liquid superficial mass-velocity, and the gas or liquid viscosity. At least four types of flow are then possible, namely liquid in apparent viscous or turbulent flow combined with gas in apparent viscous or turbulent flow. The critical Reynolds number would seem to be a rather uncertain quantity with this definition. In usage, a value of 2000 has been suggested (L6) and widely adopted for this purpose. Other workers (N4, S5) have found that superficial liquid Reynolds numbers of 8000 are required to give turbulent behavior in horizontal or vertical bubble, plug, slug or froth flow. Therefore, although this classification based on superficial Reynolds number is widely used... 

Inhibiting of Double-Base Catapult Propellants with Ethyl Cellosolve Gel Lacquers. Propellants for slotted tube catapults are designed to produce a const press system in the catapult tube. Catapult propellants usually have noncircular cross-sections and are completely externally inhibited... 

A significant heat-transfer enhancement can be obtained when a noncircular tube is used together with a non-Newtonian fluid. This heat-transfer enhancement is attributed to both the secondary flow at the comer of the noncircular tube (23,24) and to the temperature-dependent non-Newtonian viscosity (25). Using an aqueous solution of polyacrylamide the laminar heat transfer can be increased by about 300% in a rectangular duct over the value of... 

Granular PTFE resins are most frequently extruded as rods or tubes, but it is possible to produce extrudates of noncircular cross sections. 

There are many different shaped profiles. These profiles identify many varieties of shapes. Pipes and tubes could be included but the industry has had them classified as a separate category because they represent major and large markets on their own. Profiles normally identify shapes that are noncircular or are not symmetrical. However, there are exceptions where extruded products, such as capillary tubing and rod, are usually called profiles. They can be solid, hollow, or a combination of solid and hollow. Popular shapes include many hollow sections such as in window frame profiles, tapes, edgings, and gaskets as well as a combination of rods with different cross sections structural shapes in the form of Ts, Us, Is, Hs, squares, etc. The product shapes and sizes are as limitless as the number of applications. 

The situation is often encountered in which a fluid flows through a conduit having a noncircular cross section, such as an annulus. The heat-transfer coefficients for turbulent flow can be determined by using the same equations that apply to pipes and tubes if the pipe diameter D appearing in these equations is replaced by an equivalent diameter De. Best results are obtained if... 

Flow in Noncircular Ducts The length scale in the Nusselt and Reynolds numbers for noncircular ducts is the hydraulic diameter, D), = 4AJp, where A, is the cross-sectional area for flow and p is the wetted perimeter. Nusselt numbers for fully developed laminar flow in a variety of noncircular ducts are given by Mills (Heat Transfer, 2d ed., Prentice-Hall, 1999, p. 307). For turbulent flows, correlations for round tubes can be used with D replaced by l. ... 

Temperature Profile and the Nusselt Number 467 Constant Surface Heat Flux 467 Constant Surface femperaturc 468 I aminar Ftow in Noncircular Tubes 469 Developing laminar Flow in the Entrance Region 470... 

FIGURE 8-19 The relation for pressure loss (and head loss) is one of the most general relations in fluid mechanics, and it is valid for laminar or turbulent flows, circular or noncircular tubes, and pipes with smooth or rough surfaces. 

The head loss /i(, represents the additional height that the fluid needs to be raised by a pump in order to overcome the frictional losses in the pipe. The head loss is caused by viscosity, and it is directly related to the wall shear stress. Equation 8—45 is valid for both laminar and turbulent flows in both circular and noncircular tubes, but Eq. 8-46 is valid only for fully developed laminar flow in circular pipes. 

For fully developed turbulent flow, the inner and outer convection coefficients are approximately equal to each other, and the tube annulus can be treated as a noncircular duct with a hydrauLc diameter of - 77, . The Nusselt num-... 

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