Waviness

The factor in wavy brackets is obviously an exact differential because the coefficient of d9 is a fiinction only of 9 and the coefficient of dVis a fiinction only of V. (The cross-derivatives vanish.) Manifestly then... 

Figure B2.3.8. Energy-level sehemes deseribing various optieal methods for state-seleetively deteeting ehemieal reaetion produets left-hand side, laser-indueed fluoreseenee (LIF) eentre, resonanee-enlianeed multiphoton ionization (REMPI) and right-hand side, eoherent anti-Stokes Raman speetroseopy (CARS). The ionization oontinuiim is denoted by a shaded area. The dashed lines indieate virtual eleetronie states. Straight arrows indieate eoherent radiation, while a wavy arrow denotes spontaneous emission.

Figure B3.3.11. The classical ring polymer isomorphism, forA = 2 atoms, using/ = 5 beads. The wavy lines represent quantum spring bonds between different imaginary-time representations of the same atom. The dashed lines represent real pair-potential interactions, each diminished by a factor P, between the atoms, linking corresponding imaginary times.

Fig. 1. Pumping methods for lasers where is the pump light frequency and is the laser frequency, wavy lines represent radiationless transitions, and the dashed line collisions (a) optical pumping in three-level systems (b) optical pumping in four-level systems (c) pumping by electron impact and...

Foi cladding 3.2-mm metal to 12.7-imn AlSl 1008 Carbon Steel. Wavy unless otherwise noted. MLW = melted layer and waves. Not detectable. 

The clad plate is x-rayed perpendicular from the steel side and the film contacts the aluminum. Radiography reveals the wavy interface of explosion-welded, aluminum-clad steel as uniformly spaced, light and dark lines with a frequency of one to three lines per centimeter. The waves characterize a strong and ductile transition joint and represent the acceptable condition. The clad is interpreted to be nonbonded when the x-ray shows complete loss of the wavy interface (see X-ray technology). 

Flow Regimes in Multiphase Reactors. Reactant contacting, product separations, rates of mass and heat transport, and ultimately reaction conversion and product yields are strong functions of the gas and Hquid flow patterns within the reactors. The nomenclature of commonly observed flow patterns or flow regimes reflects observed flow characteristics, ie, armular, bubbly, plug, slug, spray, stratified, and wavy. 

The production of hydroxide ions creates a localized high pH at the cathode, approximately 1—2 pH units above bulk water pH. Dissolved oxygen reaches the surface by diffusion, as indicated by the wavy lines in Figure 8. The oxygen reduction reaction controls the rate of corrosion in cooling systems the rate of oxygen diffusion is usually the limiting factor. 

Lockhart and Martinelh (ibid.) correlated pressure drop data from pipes 25 mm (1 in) in diameter or less within about 50 percent. In general, the predictions are high for stratified, wavy, ana slug flows and low for annular flow The correlation can be applied to pipe diameters up to about 0.1 m (4 in) with about the same accuracy. 

Ripple flow has an upward-moving wavy layer of liquid on the pipe wall it may be thought of as a transition region to annular, annular mist, or film flow, in which gas flows in the core of the pipe while an anniilus of hquid flows up the pipe wall. Some of the liquid is entrained as droplets in the gas core. Mist flow occurs when all the liquid is carried as fine drops in the gas phase this pattern occurs at high gas velocities, typically 20 to 30 m/s (66 to 98 ft/s). 

Demonstrations (a) Balloons and safety pin (see Chapter 13, p. 121). Afterwards, put fractured edges of balloon rubber on overhead to show that wavy fracture path closely parallels that seen when metals have undergone fast fracture, (b) for Sellotape (see Chapter 13, p. 122). 

Warping, difficulty of moulding to close tolerances and wavy or fibre-patterned surfaces or faults arising from the high shrinkage during cure. 

Starting with a ceramic and depositing an aluminum oxide coating. The aluminum oxide makes the ceramic, which is fairly smooth, have a number of bumps. On those bumps a noble metal catalyst, such as platinum, palladium, or rubidium, is deposited. The active site, wherever the noble metal is deposited, is where the conversion will actually take place. An alternate to the ceramic substrate is a metallic substrate. In this process, the aluminum oxide is deposited on the metallic substrate to give the wavy contour. The precious metal is then deposited onto the aluminum oxide. Both forms of catalyst are called monoliths. 

Stratified (S) - Liquid flows at the bottom of the pipe with gas at the top. The stratified pattern is subdivided into stratified smooth (SS) where the liquid surface is smooth, and stratified wavy (SW) where the interface is wavy. 

The plates can be straight or wavy. Wavy plates, due to their greater surface area, enhance the heat transfer between air and the plates but are unsuitable in dusty environments. 

Next consider the wavy plate with herringbone waves. This arrangement with the relevant geometrical parameters is shown in Fig. 9.13. 

We see that the wavy profile of the fin plate increases the heat transfer coefficient greatly. 

Kim, N.-H, Yun, f.-H., and Webb, R. L. Heat transfer and friction correlations for wavy plate fin-and-tube heat exchangers. Journal of Heat Transfer 119 (1997) August, pp. 560-567,... 

A plate buckles when the in-plane compressive load gets so large that the originally flat equilibrium state is no longer stable, and the plate deflects into a nonflat (wavy) configuration. The load at which the departure from the flat state takes place is called the buckling load. The flat equilibrium state has only in-plane forces and undergoes only ex-... 

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