Not much of institutions are available in Tamil Nadu except in Indian Institute of Technology Chennai. For admissions to Ph.D first you should have completed M.Tech from a reputed university with high credentials. You can try even in Anna University for your Ph.D programe. M.Phil in fluid dynamics is offered only in SKU University in Ananthapur in Andhra Pradesh.
Admissions to the both the programmes are through an entrance examination followed by an interview.