Analytical (perturbation) solution to the problem of free‐molecule gas flows in two‐body systems: Results for flows over two unequal‐size cylinders

In this study, the grand (translational) friction tensor for free‐molecule (large Knudsen number) flows over two, unequal‐size cylinders is obtained analytically considering both ‘‘shielding’’ effects and multiple collisions off cylinder surfaces, as well as including both diffuse and specular molecule‐surface boundary conditions. A perturbation solution is used where the leading‐order term accounts for molecular collisions from the free‐streaming gas including all shielding effects. The first‐order correction term is also obtained here and accounts for collisions by molecules reflected off neighboring surfaces from the free‐stream gas. It is shown that the grand friction tensor is symmetric under the conditions of small ratios of the free‐stream gas velocity to the thermal gas velocity, the same type of molecular reflection boundary condition on both cylinders, and constant temperature. It is also shown that the two‐term expansion formula is accurate under isothermal conditions in the so‐called ‘‘far‐fie...