Thermal edge animation in a two-dimensional micro-cavity: Effect of nonuniform boundary smoothness in the entire range of gas rarefaction rates

We study the steady gas flow generated in a micro-cavity through the coupling between all-imposed temperature differences and non-uniformity in surface smoothness. A two-dimensional square cavity is considered, where the boundary–gas interaction is modeled via the microscopic Maxwell condition. The upper cavity wall is diffuse reflecting and maintained at a uniform temperature. Its facing bottom surface is divided between fully specular and fully diffuse sections, where the latter is fixed at a temperature different from the upper wall. The side surfaces are fully specular, making the cavity enclosure equivalent to an infinite channel configuration with periodic diffuse-specular distribution of its bottom boundary. The problem is solved in the entire range of gas rarefaction rates, combining an analytical solution in the free-molecular limit with direct simulation Monte Carlo calculations at arbitrary Knudsen numbers. A pure conduction description is provided in the limit of vanishing rarefaction. The results indicate that, while the gas is stationary at free-molecular and continuum conditions, circular gas flow is generated in the near-free-molecular, intermediate and near-continuum regimes. The flow is induced by a thermal-edge-like effect, applied at the attachment between the specular and diffuse wall parts, where the non-uniformity in wall smoothness couples sharp temperature gradients. The forces on the cavity walls are calculated, suggesting the shear loading on the specular-diffuse surface as an indicator for the intensity of the thermal-edge effect in the cavity.