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Seminars

Analysis Seminar

On thermal transpiration and thermomolecular pressure difference

2026/03/17 (Tue.) 10:00~13:00
  • Date : 2026/03/17 (Tue.) 10:00~13:00
  • Location : online
  • Speaker : Kai-Li Wang (National Taiwan University)
  • Organizer : Tai-Ping Liu (AS)
  • Abstract :
    In this article, we demonstrate the phenomenon of thermal transpiration in a bounded convex domain. We employ the stationary Boltzmann equation with a cutoff potential. For boundary condition, we partition the boundary into diffuse reflection and incoming regions. We establish the existence of solution in a weighted $L^∞$space. Furthermore, we consider a convex domain with diffuse reflection boundary condition in the middle and incoming boundary condition at the two ends. We first consider Maxwellians with the same pressure but different temperatures at the two ends. We prove that the total flux $U(x)$ is directed toward the hot end. Furthermore, we derive an estimate for the total flux:
    $U(x)≥C (1- \frac{1}{√T2})$ .
    In addition, we show that when the pressures and temperatures on the two ends satisfy the relation
    $\frac{P_1}{P_2} = √\frac{T_1}{T_2}$ ,
    the total flux of the solution is of order $O(\frac{1 }{κ})$. This result is consistent with Knudsen’s finding of thermomolecular pressure difference in 1909.

Click here to register: https://forms.gle/EhVyNa94MDEhQkqF9 (Deadline: 4pm, March 16)
本所保留開放連線之權限，報名並非確定可加入視訊討論。Registration does not guarantee participation.
請注意截止時間，逾時不受理報名。Please note the deadline; no applications will be accepted after the deadline.

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