Coupling of Heat and Momentum Transfer Between Nanostructured Surfaces

Abstract

Heat transfer between nanostructured surfaces separated by a thin gas film is studied in the free-molecular flow and in the transition regime. Besides topographic features the surfaces are characterized by regions with different boundary conditions displaying either diffuse or specular reflection of the molecules. The thermal conductivity of the materials on both sides of the gas film is assumed to be very high such that isothermal conditions may be applied at both surfaces. We analyze the problem using a combination of analytical techniques in the free-molecular flow regime and Monte-Carlo simulations. Under certain conditions, when the surfaces are held at different temperatures heat transfer is accompanied by a transfer of momentum such that a force is created parallel to the surfaces. This force can be significant and vanishes in the classical regime when the continuum transport equations can be applied. It is only observed if the reflection symmetry in a direction parallel to the surfaces is broken. We derive an analytical expression for the thermally-induced force as a function of the geometric parameters characterizing the surface topography and compare the results to Monte-Carlo simulations. The latter provide numerical solutions of the Boltzmann equation both in the free-molecular flow and in the transition regime. The scenario studied points to a novel method for conversion of thermal into kinetic energy and may find applications in small-scale energy converters.