Why don't transformers work with a DC supply?

As an electrical engineer I think you should know that transformer cannot work on DC supply. This is because transformer need change in flux. Transformer work on the principle of mitual induction. For the induction, changing flux is mandatory. If we supply DC to the transformer, it will work not work at all because there is no any change in flux. Due to low resistance in primary side, heavy primary current will flow and transformer may burnt out so it is never preferred to connect a transformer with DC supply.

The basic reason is that you need a changing magnetic field in order to induce a voltage in a loop of wire.  So transformers work with AC since the magnetic field is oscillating at 60 Hertz.   If you plug the transformer into a DC circuit, the magnetic field is a constant, after a short initial spike.  No oscillating magnetic field, no output voltage.