On general expressions of temporal means of mass flux, shear stress and heat flux due to thermoacoustic waves

Abstract

IntroductionPerformance of thermoacoustic heat engines is determined crucially by various nonlinear phenomena. Among them, steady streaming of mass and energy impacts on it significantly. To aim at making its quantitative description, nonlinear theory of thermoacoustic waves in a channel and a tube has been developed by the author and a nonlinear diffusion-wave equation has been derived for a case that a diffusion layer is thick enough compared with a span length [1]. Within the same framework, this paper derives general expressions of temporal means of mass flux, shear stress and heat flux on a wall by assuming time-periodic wave. It is shown that the mean pressure is set down and that all mean values are expressed in terms of the mean pressure and its spatial gradients.