Question

what happens to heat energy which is supplied to solid once it start melting?

Answer 1

The Heat energy supplied to solid  is used to increase the kinetic enrgy of the object's atoms and thus change it into the higher form of state of matter - liquid. And thus it consumes the heat energy suppliedhile melting into the liquid form...

Answer 2

Heat energy supplied to a solid increases if the current temperature is less than its melting point. When the temperature reaches the melting point, the solid, absorbs energy and increases its internal energy. That  breaks the close bonds between the molecules and makes them more mobile. The liquid starts melting. At the same temperature, the solid absorbs an energy called the latent heat of fusion to change its state to liquid. After the solid melts, its temperature increases further if more heat is supplied.