The South-West Monsoon brings heavy rainfall to much of India from June to September.
The Arabian Sea branch of this monsoon hits the Western Ghats mountain range along the west coast of India.
As the moisture-laden winds rise over the mountains, they cool, condense, and cause heavy rainfall on the windward (western) side.
Tamil Nadu is located on the leeward (eastern) side of the Western Ghats.
By the time the winds cross the mountains and descend on the eastern side, they have lost most of their moisture. This dry region on the leeward side is known as a rain shadow area.
Therefore, Tamil Nadu receives very little rainfall from the South-West Monsoon because it lies in the rain shadow region of the Western Ghats. It gets most of its rainfall from the retreating North-East Monsoon later in the year.