Stability of thermal transpiration flows in rectangular enclosures – Axisymmetric disturbances

Occurrence of instabilities for thermal transpiration flow of rarefied gases has been discussed in two-dimensions. Only axisymmetric disturbances have been considered due to symmetry of the basic flow. Effect of four second-order slip models (Cercignani, Deissler, Schamberg, and Beskok) and a first-order slip model (Maxwell) on the limits of the proposed instability have been examined. We have found that Beskok model is always stable to axisymmetric disturbances and Maxwell model is more stable compared with the other second order models. Variation of critical Reynolds number for different rarefaction levels (Knudsen numbers) has also been studied. Increase in Knudsen number leads to monotonic decrease in critical Re numbers.