An axial convective flow in a rotating tube with a longitudinal temperature gradient

Group-theoretical Methods in Convection Theory

“…The presence of an interface is the cause for the appearance of the thermocapillary force, which drives the liquid to along the tube. If the tube rotates, the interaction of thermocapillary and centripetal forces leads to the formation of a complicated motion with several control parameters [31]. This motion is described in terms of elementary functions.…”

“…Both of them describe three dimensional flows in terms of solutions of two dimensional initial boundary value problems. Precise formulations of these problems for the system (42) and results concerning their solvability can be found in [31].…”

“…Unlike the typical situation in the inverse problems theory, our problem turns out to be correct. Algorithm for solving it is described in [31]. The second problem is to find the stationary rotationally symmetric solution of system (42) with a prescribed flux .…”

“…Then the initial boundary problem for the system (42) is simplified significantly and is reduced to the linear problems [31] that can be solved step by step. We mention here two of them.…”

Convection in Air water Layer with Side Heating

“…For a narrow gap, the cylindrical problem becomes close to that for a horizontal layer [6]. Birikh and Pukhnachev [14] generalized the solution [13] to describe a two-fluid thermal convection with the Marangoni effect taken into account. The numerical simulations of the air-water centrifugal convection in a cylindrical container [15] agree with the analytical solutions and help explain the emergence of new flow cells due to the Marangoni effect.…”