As you said have completed PG and want to do phd from IIT Chennai, so here I am telling related info :

IIT Chennai offered PhD program in following departments
Aerospace Engineering,
Applied Mechanics,
Biotechnology,
Chemical Engineering,
Chemistry,
Civil Engineering,
Computer Science & Engineering,
Electrical Engineering,
Engineering Design,
Humanities & Social Sciences,
Management Studies,
Mathematics,
Mechanical Engineering,
Metallurgical & Materials Engineering,
Ocean Engineering and Physics

Key dates for admission
Registration of Application Forms will be Open on: 28th February 2016

Last Date for Registration of Application through Online: 24th March 2016

Interview and or Test (on or before): 25th April 2016 to 16th May 2016

Selected Candidates List Display in the Research Website: 03rd June 2016

Selected Candidates to Join on 17th July 2016

Admission eligibility
Students must have master’s degree with a good academic record in related subjects and of exceptional merit are eligible, for the relevant Engineering disciplines and with a valid GATE score or UGC-JRF/NET/CSIR-JRF/NBHM/INSPIRE or equivalent qualification are also apply

Apply process

Students seeking admission to IIT Madras in PhD /MS Programmes can apply online from the official website. Before applying for PhD Programmes, Students must ensure their eligibility criteria

Application Fee
Application Fee Rs.200/- payable online (Rs.100/- only for SC/ST/Physically Challenged & Women Candidates) (non-refundable)

Online Mode of Fee Payment enabled (Net-banking, Credit Card and Debit Card)

Address
Indian Institute of Technology (IIT) Madras
IIT P.O., Chennai-600036, Main Gate,
Opposite to C.L.R.I and beside the Adyar Cancer Institute,
on Sardar Patel Road, Adyar, Chennai-600036,