What happens if a DC supply is applied on the primary winding of a transformer?

If DC is applied to the transformer winding then high current flows as there is no back emf produced to limit the current and hence the winding burns out. 

Where as when AC current flows in to primary winding it induces an alternating flux which also links with the secondary winding, and so secondary current flow in secondary winding due to primary current. Again the secondary current also induces an emf (Back emf) in secondary winding which opposes the induced emf of primary winding and thus controls the primary current.