Group analysis of equations of an unsteady Marangoni boundary layer
Abstract
An analysis is made of the group properties of a boundary value problem for a set of equations of a two-dimensional unsteady boundary layer. The solution to this problem describes the flow in a Marangoni boundary layer arising near the free surface of a nonuniformly heated fluid due to the thermocapillary effect. A steady solution is obtained which corresponds to the generalized solution of a degenerate parabolic equation, to which is reduced the steady analog of the above-mentioned set of equations on the plane of Mises variables.
- Publication:
-
Akademiia Nauk SSSR Doklady
- Pub Date:
- 1984
- Bibcode:
- 1984DoSSR.279.1061P
- Keywords:
-
- Boundary Layer Equations;
- Group Theory;
- Marangoni Convection;
- Two Dimensional Boundary Layer;
- Boundary Layer Stability;
- Boundary Value Problems;
- Lie Groups;
- Unsteady Flow;
- Fluid Mechanics and Heat Transfer