Thermodynamic aspects of thermoacoustic theory

Abstract

The study of thermoacoustic phenomena has a long history, and a fluid mechanics description of them has been developed in this century. Thermodynamic aspects of the thermoacoustic theory are discussed in this paper. Work flux, heat flux and energy conversion are introduced. Two thermodynamic media (a solid and an oscillating fluid) are regarded as catalysts for the heat flow and energy conversion. Three basic equations of fluid mechanics in Lagrange's frame are linearized in terms of three oscillating variables, namely pressure, entropy and displacement or velocity of the fluid element. The energy conversion is shown to consist of viscous dissipation of kinetic energy and the trajectory area in the temperature-entropy space. The entropy oscillation is discussed using the general equation of heat transport and the second law of thermodynamics. Finally the heat flux and energy conversion are expressed in terms of oscillating pressure and displacement or velocity. Transverse inhomogeneity of oscillating entropy or temperature, including phase lag, results in standing components of energy conversion W stand and heat flux Q stand, in addition to the pressure induced dissipation W P and displacement enhanced heat conduction Q D .