Is there a way to find my iPhone when battery is dead

No. The phone needs to powered on with an internet connection.

The only way to locate an iPhone with a dead battery is retrace your steps and look for the phone with your eyes. Ask at shops, restaurants, lost & found, etc.

only by looking the old fashion way,

electronic devices require power to have any sort of functionality

Same issue I had, is there any solution to track the phone if it is out of charge.

Ok thanks