Thermocapillarity in a liquid film on an unsteady stretching surface. (English) Zbl 1048.76502

Summary: The influence of thermocapillarity on the flow and heat transfer in a thin liquid film on a horizontal stretching sheet is analysed. The time-dependent governing boundary layer equations for momentum and thermal energy are reduced to a set of coupled ordinary differential equations by means of an exact similarity transformation. The resulting three-parameter problem is solved numerically for some representative values of an unsteadiness parameter S and a thermocapillarity number \(M\) for Prandtl numbers from 0.001 to 100. The thermocapillary surface forces drag the liquid film in the same direction as the stretching sheet and a local velocity minimum occurs inside the film. The surface velocity, the film thickness, and the Nusselt number at the sheet increase with \(M\) for \(Pr \lesssim 10\). For higher Prandtl numbers, the thermal boundary layer is confined to the lower part of the liquid film and the temperature at the free surface remains equal to the slit temperature and the thermocapillary forces vanish.


76A20 Thin fluid films
76D45 Capillarity (surface tension) for incompressible viscous fluids
80A20 Heat and mass transfer, heat flow (MSC2010)
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