Hello!Richa
Here are list of some best private engg college in Chennai:
Amrita school of engg.
PSG College of Techology
SRM Institute of science and technology
VIT Vellore.
For more visit below mention link:
https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/colleges/ranking/top-private-engineering-colleges-in-tamil-nadu&ved=2ahUKEwi_rZne56vhAhXKVisKHTDiA0kQFjAAegQIAxAB&usg=AOvVaw1GtUVMWTyzdVJc9nRjRlkF.
GOod luck!