The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

/pdf/heat-and-mass-transfer-1yaijfx8vp.pdf

Heat and Mass Transfer

Thermoacoustic engines (TAEs) can be used to pump heat using a sound wave or pump a sound wave using a temperature gradient. The basic arrangement is a gas-filled acoustic resonator with appropriately positioned thermoacoustic elements. Two types of thermoacoustic elements are used in these engines: (1) heat exchangers used to communicate heat between the gas and external heat reservoirs; and (2) the TAE, also known as a stack. The TAEs are sections of porous media that support the temperature gradient, transport heat on the acoustic wave between the exchangers, and produce or absorb acoustic power. Previous results have been developed for TAEs with circular or parallel slit pore geometries. The theory is extended for gas-filled TAEs to include pores of arbitrary cross-sectional geometry. An approximate analysis of energy flow and acoustical measurements of a thermoacoustic prime mover are given. >

http://ieeexplore.ieee.org/iel2/886/6033/00234265.pdf

Thermoacoustic engines

Electrical and mechanical power, together with other forms of useful work, are generated worldwide at a rate of about 1012 watts, mostly using heat engines. The efficiency of such engines is limited by the laws of thermodynamics and by practical considerations such as the cost of building and operating them. Engines with high efficiency help to conserve fossil fuels and other natural resources, reducing global-warming emissions and pollutants. In practice, the highest efficiencies are obtained only in the most expensive, sophisticated engines, such as the turbines in central utility electrical plants. Here we demonstrate an inexpensive thermoacoustic engine that employs the inherently efficient Stirling cycle1. The design is based on a simple acoustic apparatus with no moving parts. Our first small laboratory prototype, constructed using inexpensive hardware (steel pipes), achieves an efficiency of 0.30, which exceeds the values of 0.10–0.25 attained in other heat engines5,6 with no moving parts. Moreover, the efficiency of our prototype is comparable to that of the common internal combustion engine2 (0.25–0.40) and piston-driven Stirling engines3,4 (0.20–0.38).

A thermoacoustic Stirling heat engine

We found that very thin carbon nanotube films, once fed by sound frequency electric currents, could emit loud sounds. This phenomenon could be attributed to a thermoacoustic effect. The ultra small heat capacity per unit area of carbon nanotube thin films leads to a wide frequency response range and a high sound pressure level. On the basis of this finding, we made practical carbon nanotube thin film loudspeakers, which possess the merits of nanometer thickness and are transparent, flexible, stretchable, and magnet-free. Such a single-element thin film loudspeaker can be tailored into any shape and size, freestanding or on any insulating surfaces, which could open up new applications of and approaches to manufacturing loudspeakers and other acoustic devices.

Flexible, stretchable, transparent carbon nanotube thin film loudspeakers.

Experimental measurements and flow visualiza- tion of synthetic jets and continuous jets with matched Reynolds numbers are described. Although they have the same profile shape, synthetic jets are wider and slower than matched continuous jets. The synthetic jets are ex- amined at higher Reynolds numbers than previously studied and over a large range of dimensionless stroke lengths. Nomenclature b cross-stream location where velocity is 0.5Ucl h slot width f driving frequency L0 stroke length = R T=2 0 u0 t ðÞ dt Q volume flux Q0 U0h for synthetic jet, and Q0 = Uaveh for con- tinuous jet Reh Reynolds number of continuous jet=Uaveh/m ReU0 Reynolds number of synthetic jet=U0h/m t time (with zero at start of blowing stroke) T driving period=1/f u measured instantaneous velocity U time-averaged velocity Uave time-averaged slot velocity for continuous jet Ucl time-averaged centerline velocity u0(t) centerline or cross-stream-averaged velocity at x=0 for synthetic jet umax maximum of u0(t) U0 L0f x streamwise coordinate y cross-stream coordinate m kinematic viscosity

A comparison between synthetic jets and continuous jets

Measurements and analysis of a 13‐cm‐diam thermoacoustic engine are presented. At its most powerful operating point, using 13.8‐bar helium, the engine delivered 630 W to an external acoustic load, converting heat to delivered acoustic power with an efficiency of 9%. At low acoustic amplitudes, where (linear) thermoacoustic theory is expected to apply, measurements of temperature difference and frequency agree with the predictions of theory to within 4%, over conditions spanning factors of 4 in mean pressure, 10 in pressure amplitude, 6 in frequency, and 3 in gas sound speeds. But measurements of the square of pressure amplitude versus heater power differ from the predictions of theory by 20%, twice the estimated uncertainty in the results. At higher pressure amplitudes (up to 16% of the mean pressure), even more significant deviation from existing thermoacoustic theory is observed. Several causes of this amplitude‐dependent deviation are identified, including resonance‐enhanced harmonic content in the acoustic wave, and a new, first‐order temperature defect in thermoacoustic heat exchangers. These causes explain some, but not all, of the amplitude‐dependent deviation of the high‐amplitude measurements from existing (linear) theory.

Analysis and performance of a large thermoacoustic engine

The Los Alamos thermoacoustics code, available at www.lanl.gov/thermoacoustics/, has undergone extensive revision this year. New calculation features have been added to the original Fortran computational core, and a Python‐based graphical user interface wrapped around that core provides improved usability. A plotter routinely displays thermoacoustic wave properties as a function of x or tracks results when a user‐specified input variable, such as frequency or amplitude, is varied. The Windows‐like user interface provides mouse‐based control, scrolling, and simultaneous displays of plots and of several categories of numerical values, in which color indicates important features. Thermoacoustic phenomena can be calculated with superimposed steady flow, and time‐averaged pressure gradients are calculated. In thermoacoustic systems with toroidal topology, this allows modeling of steady flow caused by gas diodes (with or without time‐averaged heat transfer) and Gedeon streaming. Thermoacoustic mixture separation is included, also with superimposed steady flow. The volume integral of the complex gas momentum is available, so vibrations of thermoacoustic systems can be analyzed.

Design environment for low-amplitude thermoacoustic energy conversion (DeltaEC)

We ordinarily think of a sound wave in a gas as consisting of coupled pressure and displacement oscillations. However, temperature oscillations always accompany the pressure changes. The combination of all these oscillations, and their interaction with solid boundaries, produces a rich variety of “thermoacoustic” effects. Although these effects as they occur in everyday life are too small to be noticed, one can harness extremely loud sound waves in acoustically sealed chambers to produce powerful heat engines, heat pumps and refrigerators. Whereas typical engines and refrigerators have crankshaft‐coupled pistons or rotating turbines, thermoacoustic engines and refrigerators have at most a single flexing moving part (as in a loudspeaker) with no sliding seals. Thermoacoustic devices may be of practical use where simplicity, reliability or low cost is more important than the highest efficiency (although one cannot say much more about their cost‐competitiveness at this early stage).

/pdf/thermoacoustic-engines-and-refrigerators-4n45plu6kz.pdf

Gregory W. Swift

Papers

A thermoacoustic Stirling heat engine

A comparison between synthetic jets and continuous jets

Analysis and performance of a large thermoacoustic engine

Design environment for low-amplitude thermoacoustic energy conversion (DeltaEC)

Thermoacoustic Engines and Refrigerators