What would happen if a transformer is connected to a DC supply?

The primary winding of a transformer is nothing but an inductor, so at DC, it will work as a node.
So there are possibility to blow up the primary winding and the DC source for flowing high amount of current.
Although, the secondary coil needs to see change in flux, there will no alternation so there will be no output. Hence, the transformer will not work.

When transformer is connected to dc supply, steady state current start flowing through the winding. in case of dc supply self inductance is zero hence large current flows through the primary winding which results transformer get damaged.

If DC supply is given to the primary of Transformer then DC current flows through primary winding which is constant (time invarient).For production of emf in any winding the current flowing through that must be sinusoidal since

e=L*(dI/dt).

So in the given case ie, for DC INPUT :
No emf produced in primary winding. So net voltage in the primary winding will be (Vin-0) more due to which primary winding draws more current which leads to burning of winding.