Could you perhaps provide us with a bit more information to enable the community the ability to assist you.
- What motherboard are you using for your configuration? Please list your complete specifications for transparency purposes to assist us while troubleshooting.
- Although you stated that the installation was performed correctly, have you attempted to re-seat the heat sink and reapply the thermal compound once more to ensure it wasn't user installation error?
- Have you tested the heat sink fan for issues when not installed after the issue occurred? If so, were you able to replicate the overtly loud ambient sound out of the encasement?
- Please describe the instance with more detail in regards to your sound issues (Example: Maximum fan rpm operation, Motor malfunction "rattle" etc.)
Once I receive all of the information requested above, I'll have a clearer perspective on your current situation.
In a country with a very hot climate like India, you would be well advised to get a capable aftermarket closed loop liquid cooler.