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Abstract : This article emphasizes the heat transfer of thermally stratified nanofluid towards a melting stretching surface with first and second-order velocity slips for the first time. The model used for the nanofluid incorporates the effect of volume fraction parameter. The boundary layer equations governed by a nanofluid, which are partial differential equations of motion and energy, are converted to a set of non-linear ordinary differential equations using a set of non-dimensional transformations. Then the reduced equations are solved numerically using Shooting method along with Runge-Kutta fourth order technique. The interesting features of the results for alumina-water and copper-water nanofluids includes (i) the velocity and temperature reduces but, skin friction and Nusselt number enhances with increase of Melting parameter in the presence and/or absence of stratification, (ii) it can be noticed that for both types of thermally stratified nanofluids, the skin friction enhances and Nusselt number reduces with increase of solid volume fraction parameter , and (iii) the skin friction and heat transfer rate are more with existence of second order velocity slip and are less in the absence of the second order velocity slip for both types of thermally stratified nanofluids.