Surface tension of fluids

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could not solve this exam problem completely please help:
Variations in surface tension can cause a flow in a liquid.One of the chief causes for variation of surface tension is temperature.Consider a thin film of liquid on a flat surface.The liquid film also has a free surface where the temperature varies with x.There is no variation in the z direction, the flow is 2 dimensional.Assume the flow to be incompressible and the temperature has no other effect but to change the surface tension.

a) Determine T(x) for fully developed flow?
b) What is the pressure gradient within the liquid film?
c) set up the governing equations.What are the boundary conditions?
d) Solve to get the velocity profile?
e) Obtain the non-dimensional parameters characterizing this flow?
 

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