My application would be for CPUs. You would pulsate heat towards the heatsink using a tone generate on the underside of the socket.
A. I really don't have a strong mathematical grasp of the physics. B. I imagine the frequency of the waves might damage the silicone lattice. C. Other issues I don't have the knowledge to even consider.
This is just an idea that came to as I was walking home from work. I'm sure it's absolute hogwash.
In other words, the more materials you could test at different temperatures, with different types of vibration going through them, the more you'd gain an understanding of the phenomena... perhaps there's a new theory or discovery in there... I can see the research paper or theory: "Heat dissipation via pulsation in different materials at different frequencies".
Of course, you might fail... but you'd (have to!) learn a lot of things from diverse areas of physics (and probably math too) in the process!
That would be a win, no matter what.