A Transformer cannot be operated on the DC source or never connected to DC supply. If a rated dc voltage is applied to the primary of the transformer, the flux produced in the transformer core will not vary but remain constant in magnitude. So therefore no emf is induced in the secondary winding except during the moment of switching on the dc supply. As no induced emf is produced current cannot be delivered from the secondary side to the load.
Also the flux flowing through the iron core from primary winding to secondary winding not only links the secondary winding but also primary winding. Due to this flux linkage self induced emf is produced in the primary winding. This self induced emf in the primary winding will oppose the applied voltage and hence it acts as back emf. This back emf limits the primary current flowing through the primary winding in normal operating condition (similar like dc machine armature current).
When a dc supply is provided to the transformer primary no self induced emf will be generated (no back emf). Therefore heavy current will flow in the transformer primary winding which may result in burning down the transformer primary winding.