Boundary effects in the rayleigh line for a fluid out of thermal-equilibrium

We analyze the effect of boundary conditions in the Rayleigh spectrum of a fluid under a temperature gradient. A specific wave vector geometry prevents coupling between temperature and velocity fluctuations and could make boundary effects observable. These effects are introduced by means of dimensionless numbers, which combine both the nature of the contact surfaces and the size of the system. We then show that the height of the peak as well as the total intensity under the Rayleigh line are modified by the presence of the walls.