In chemistry we use ultrasonication for cleaning vessels ,synthesis of chemical compounds (sonochemistry) etc.I know that during ultrasonication high temperature and pressure is formed "locally".But I want to know whether there is any equations which relates between ultrasonication and temperature .
The temperature is highly nonlinear with sound pressure and dependent on external pressure, tensile strength of liquid etc. Cavitation, http://en.wikipedia.org/wiki/Cavitation, can produce local shock waves and temperatures of thousands of K, causing sonoluminescence. See also http://www.scs.illinois.edu/suslick/sonochembrittanica.html.
Because of that nonlinearity and all the dependencies, I do not know if any equation for calculating the peak temperatures exists, and there is still research going on to see how much of sonoluminescence is due to black-body radiation, the recombination of radicals etc.
BTW, you can view a mantis shrimp with a sonoluminescent punch at https://www.youtube.com/watch?v=sNzI8K-lCqo and https://www.youtube.com/watch?v=ti2Uoc1RXuQ, and another species at https://www.youtube.com/watch?v=QXK2G2AzMTU.