Analytical Solution of Thermocapillary Flow in Cylindrical Annuli with Curved Free Surface

In this paper we consider thermocapillary flow with interface deformation in cylindrical annuli subjected to lateral temperature gradient. Based on the assumption that Reynolds, Marangoni and capillary numbers are very small, we expanded the governing equations in terms of a small parameter, and the zeroth-order one is the Stokes problem, which can be analytically solved by use of separation of variables formulation. Solutions are obtained for the zeroth-order fluid and thermal fields as well as the first-order interfacial shapes. Streamlines, temperature distributions and interface shapes are presented and the influence of aspect ratios is investigated.