Effect of temperature gradient on pressure profile in thermal transpiration flow

In relatively high Knudsen number flows, namely in the slip and transitional flow regimes, a temperature gradient induces a flow known as thermal transpiration, directed from the cold side to the hot side. This phenomenon has been studied for a long time, experimentally and numerically, mainly using the system consisting of two reservoirs at different temperatures connected by a channel. However, the pressure profile along the channel has never been obtained experimentally. From reported numerical simulations, it was indicated that the pressure profile exists even if the pressures in the two reservoirs are the same, and that its shape is sensitive to the temperature profile. In this study, mid-channel pressure was measured experimentally and compared with the numerical results under identical conditions, to clarify the effect from the temperature profile on the pressure profile. The effect of varying rarefaction was also investigated. The result showed that the pressure profile was convex for a linear temperature profile and concave for an exponential temperature profile. Furthermore, the relationship between the pressure profile and the curvature of the temperature profile was systematically investigated, showing that an almost constant pressure profile was realized under a slightly curved temperature distribution. These findings demonstrate that the internal pressure profile in the thermal transpiration appeared to be highly sensitive to the curvature of the temperature profile.