Numerical Study of the Efficiency of Acoustic Streaming for Enhancing Heat Transfer between Two Parallel Beams

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.