numerical simulation of melting heat transfer towards the stagnation point region over a permeable shrinking surface

The aim of deploying hybrid nanofluids is to optimize the heat transfer features of the model under consideration. hybrid nanofluids contain composite nanoparticles, which improve thermal conductivity. here, silver (ag) and graphene oxide (go) are used as nanoparticles with kerosene oil as a base fluid. the impact of ohmic heating, viscous dissipation, and thermal radiation are taken to model the problem of steady flow over a stretching/shrinking geometry. the governing equations are numerically solved by a built-in scheme, bvp4c in matlab. moreover, the existence of dual solutions is found for a given range of pertinent parameters. the impact of the melting heat transfer parameter is heeded on the coefficient of skin friction and nusselt number for both hybrid nanofluid and nanoparticles. a comparison is established with the pre-existing results, which is in good agreement. it is noted that the values of the coefficient of skin friction for the stable branch decrease for a particular range of shrinking parameter; however, for the lower branch opposite trend is observed. the magnetic force decreases the flow field and energy distribution for the upper branch; however, enhances for lower branch.