THERMOACOUSTIC STREAMING EFFECTS FROM A SPHERE SUBJECT TO TIME-PERIODIC TEMPERATURE DISTURBANCES
The thermal analysis of the effect of the steady streaming motion induced by a solid sphere in an acoustic field is carried out by the singular perturbation method. For sufficiently large frequencies, a thin Stokes layer region on the surface of the sphere constitutes the inner solution for the flow field which is then matched with a suitable outer solution. The temperature field in the fluid is induced by a thermal oscillation on the sphere boundary while the ambient is held at a constant, temperature. The interaction of the thermal oscillations and the acoustic field results in a nonzero time averaged steady convective transport of heat in the fluid. This is the principal effect being investigated in this study, with attention restricted to gases with Pr ≈ 1. As in the case of the velocity field, a singular perturbation procedure is employed for determining the temperature distribution in the fluid. For large streaming Reynolds numbers, Rs being considered, the matching of the inner Stokes layer with the outer field is through a thicker outer boundary layer. While the inner solution can be found analytically, the outer solution requires numerical work. The final results show that although there is no net exchange of heat between the sphere and the fluid, there is, however, a steady flow of heat, into and out of, each hemisphere of the physical domain. This flow causes an equal heating and cooling of the fluid in each hemisphere, while within the solid sphere it is indicative of a steady temperature gradient across its poles.