Thermal stress vs. thermal transpiration: A competition in thermally driven cavity flows

The velocity dependent Maxwell (VDM) model for the boundary condition of a rarefied gas, recently presented by Struchtrup [“Maxwell boundary condition and velocity dependent accommodation coefficient,” Phys. Fluids 25, 112001 (2013)], provides the opportunity to control the strength of the thermal transpiration force at a wall with temperature gradient. Molecular simulations of a heated cavity with varying parameters show intricate flow patterns for weak, or inverted transpiration force. Microscopic and macroscopic transport equations for rarefied gases are solved to study the flow patterns and identify the main driving forces for the flow. It turns out that the patterns arise from a competition between thermal transpiration force at the boundary and thermal stresses in the bulk.