Abstract
In this paper, the efficiency of acoustic streaming for enhancing heat transfer in a channel composed by two parallel beams is studied. A rectangular heat source isattached to the upper beam. The lower beam, kept at a constantand uniform temperature, vibrates and scatters standing acousticwaves into the gap, which induces acoustic streaming in the gapdue to the non-zero mean of the acoustic field. By utilizing theperturbation method, the compressible Navier–Stokes equationsare decomposed into the first-order acoustic equations and thesecond-order streaming equations. Only the steady state energyequation associated with the streaming field is of interestbecause the acoustic field is adiabatic. These governingequations are discretized by the finite-difference method on auniform mesh and solved numerically. Nonreflective boundaryconditions are imposed at the open ends. SIMPLER algorithm isutilized to solve the streaming equation. The cooling effect isinvestigated by comparing the average temperature of the heatedregion of the upper beam with and without the acoustic streamingin the gap. Analysis of the steaming flow field reveals a systemof steady vortices in the gap that are responsible for heattransfer enhancement. Acoustic streaming generated by vibrationof the lower beam with the angular frequency of 1000 rad/s andthe amplitude of 100 microns reduces the temperature of theupper beam by 1% for the constant heat flux case and by 0.5%for the case of a heat source with a constant rate of internalheat generation. A more significant cooling effect is expectedif the intensity of the acoustic field is increased.
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References
Vainshtein, P., Rayleigh streaming at large Reynolds number and its effect on shear flow. J. Fluid Mech. 285 (1995) 249–264.
Lord Raleigh, On the circulations of air observed in Kundt's tubes and on some allied acoustical problems. Philos. Trans. Roy. Soc. London A175 (1884) 1–71.
Westerwelt, P.J., The theory of steady rotational flow generated by sound field. J Acoust. Soc. Amer. 25 (1953) 60–67.
Nyborg, W.L., Acoustic streaming due to attenuated plane wave. J. Acoust. Soc. Amer. 25 (1953) 68–75.
Nyborg, W.L., Acoustic streaming near a boundary. J. Acoust. Soc. Amer. 30 (1958) 329–339.
Schlichting, H., Boundary-Layer Theory. McCraw-Hill, New York (1955).
Lighthill, J., Acoustic streaming, J. Sound Vibration 61 (1978) 391–418.
Stuart, J.T., Double boundary layers in oscillating viscous flow. J. Fluid Mech. 24 (1966) 673–687.
Davidson, B.J. and Riley, N., Jets induced by oscillating motion. J. Fluid Mech. 53 (1972) 287–303.
Duck, P.W. and Smith, F.T., Steady streaming induced between oscillating cylinders. J. Fluid Mech. 91 (1979) 93–110.
Kim, S.K. and Troesch, A.W., Streaming flow generated by high-frequency small-amplitude oscillations of arbitrary shaped cylinders. Phys. Fluids A 1 (1989) 975–985.
Wang, C.Y., Acoustic streaming on a sphere near an unsteady source. J. Acoust. Soc. Amer. 71 (1982) 580–584.
Amin, N. and Riley, N., Streaming from a sphere due to pulsating source. J. Fluid Mech. 210 (1990) 459–473.
Lee, C.P. and Wang, T.G., Near-boundary streaming around a small sphere due to two orthogonal standing waves. J. Acoust. Soc. Amer. 85 (1989) 1081–1088.
Vainshtein, P., Fichman, M. and Pnueli, D., Secondary streaming in a narrow cell caused by a vibrating wall. J. Sound Vibration 180 (1995) 529–537.
Matta, L.M., Zhu, C., Jagoda, J.I. and Zinn, B.T., Mixing by resonant acoustic driving in a closed chamber. J. Propulsion Power 12 (1996) 366–370.
Stansell, P. and Greated, C.A., Lattice gas automation simulation of acoustic streaming in a twodimensional pipe. Phys. Fluids 9 (1997) 3288–3299.
Richardson, P.D., Heat transfer from a circular cylinder by acoustic streaming. J. Fluid Mech. 30 (1967) 337–355.
Davidson, B.J., Heat transfer from a vibrating circular cylinder. Internat. J. Heat Mass Transfer 16 (1973) 1703–1727.
Gopinath, A. and Mills, A.F., Convective heat transfer from a sphere due to acoustic streaming. ASME, J. Heat Transfer 115 (1993) 332–341.
Gopinath, A. and Mills, A.F., Convective heat transfer due to acoustic streaming across the ends of a Kundt tube. ASME, J. Heat Transfer 116 (1994) 47–53.
Vainshtein, P., Fichman, M. and Gutfinder, C., Acoustic enhancement of heat transfer between two parallel beams. Internat. J. Heat Mass Transfer 38 (1995) 1893–1899.
Mozurkewich, G., Heat transfer from a cylinder in an acoustic standing wave. J. Acoust. Soc. Amer. 98 (1995) 2209–2216.
Secomb, T.W., Flow in a channel with pulsating walls. J. Fluid Mech. 88 (1978) 273–288.
Hall, P., Unsteady viscous flow in a pipe of slowly varying cross-section. J. Fluid Mech. 64 (1974) 209–226.
Hydon, P.E. and Pedley, T.J., Axial dispersion in a channel with oscillating walls. J. FluidMech. 249 (1993) 535–555.
Dragon, C.A. and Grotberg, J.B., Oscillatory flow and mass transport in a flexible tube. J. Fluid Mech. 231 (1991) 135–155.
Broday, D. and Kimmel, E., On the axial dispersion induced by vibrations of a flexible tube. Internat. J. Engrg. Sci. 37 (1999) 863–881.
Bradley, C.E., Acoustic streaming field structure: The influence of radiator. J. Acoust. Soc. Amer. 100 (1996) 1399–1408.
Nyborg, W.L., Acoustic streaming. In: Mason, W.P. (ed.), Physical Acoustics, Vol. 2(B). Academic, New York (1965) pp. 65–331.
Ro, P.I. and Loh, B.G., Feasibility of using flexural waves as a cooling mechanism. IEEE Trans. Ind. Electr. 48 (2001) 143–149.
Loh, B.G., Hyun S., Ro, P.I. and Kleinstreuer, C., Acoustic streaming induced by ultrasonic flexural vibrations and associated enhancement of convective heat transfer. J. Acoust. Soc. Amer. 111 (2002) 875–883.
Zhao, X., Zhu, Z. and Du G., A note about acoustic streaming: Comparison of C.E. Bradley's and W.L. Nyborg's theories. J. Acoust. Soc. Amer. 104 (1998) 1116–1117.
Temkin, S., Elements of Acoustics. Wiley, New York (1981) pp. 382–393.
Givoli, D., Non-reflecting boundary conditions. J. Comput. Phys. 94 (1991) 1–29.
Patanker, S.V., Numerical Heat Transfer and Fluid Flow. Hemisphere, New York (1980).
Bejan, A., Convective Heat Transfer. John Wiley & Sons, New York (1995) pp. 112–117.
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Wan, Q., Kuznetsov, A. Numerical Study of the Efficiency of Acoustic Streaming for Enhancing Heat Transfer between Two Parallel Beams. Flow, Turbulence and Combustion 70, 89–114 (2003). https://doi.org/10.1023/B:APPL.0000004916.01838.63
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DOI: https://doi.org/10.1023/B:APPL.0000004916.01838.63