Joint Thermocapillary and Thermogravitational Convection

Statement of the problem. Let us consider a similar problem in which the upper boundary of the channel is free and the surface tension j on it depends linearly on temperature. The balance of tangential stresses on the free surface will then involve the thermocapillary stresses. The corresponding boundary condition has the form 

The dimensionless equations and boundary conditions, as before, have the form (5.9.7), (5.9.8) except for the second boundary condition in (5.9.8), which must be replaced, according to (5.3.13), by 

Exact solution. The solution can be represented as the sum of three terms, each having a remarkably simple physical interpretation the Poiseuille motion due to the constant dimensionless pressure gradient along the layer, the thermo- 

Mass and Heat Transfer Under Complicating Factors 

The constant b can be determined from the zero-rate-of-flow condition  

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