Thermocapillary instability of a liquid layer on interior surface of a rotating cylinder

Stability problem of a liquid, situated on the inner surface of a cylinder, which rotates about its axis with a constant angular velocity, is considered. The flow is assumed to be non-isothermal, and thermocapillary instability is investigated. The temperature at the free boundary satisfies the condition of the third kind with a given Biot number. It is supposed that the free boundary is undeformable. The exact solution of Navier-Stokes and heat conduction equations is obtained. Neutral disturbances of this solution are considered, where Marangoni number is taken as the spectral number. Asymptotics of critical values of Marangoni number for long and short waves are found analytically. Neutral curves are constructed numerically for various values of independent dimensionless parameters. The dependences of critical Marangoni number on Reynolds number, Biot number and the aspect ratio are investigated.