Generation of Shock Wave by Temperature Change at Wall

Introduction

In principle, temporal change in wall temperature can cause a thermo-acoustic effect of generating a sound wave from its surface into a gas medium (Rayleigh [1]). It is difficult to apply a fluid dynamics approach to visualize this effect mainly because of the boundary-value fitting at the wall surface (Sugimoto et al. [4]). There should be a time-dependent heat flow from inside the solid to the outside fluid, which is not easy to incorporate into the boundary conditions for the fluid dynamic system. We utilized instead the molecular kinetic approach represented by the Boltzmann equation and actually observed a sound wave advancing from a wall surface of changing temperature by employing the condition of diffuse reflection at the boundary. This condition seems to effectively represent the heat flow in the interaction between the fluid and the solid (Sakaguchi et al. [2]). Here, we extend the above approach for generating a shock wave from a solid wall surface whose temperature changes rapidly with time.