This paper aims to investigate the solutions for the axisymmetric flow and heat transfer coming from a permeable disk in hybrid nanofluids. The nanofluids are under the influence of thermal radiation and contain magnetohydrodynamics and melting phenomena. For this, the momentum and temperature mathematical model is developed to investigate the axisymmetric flow of two-dimensional hybrid nanofluids, containing nanoparticles and a base fluid. Using appropriate similarity variables, nonlinear partial differential equations have been transformed into ordinary differential equations. These are further solved using the function bvp4c, which is built into MATLAB software. The physical behavior of parameters is discussed for the values on the basis of visuals and tables. The analysis further shows an increase in the local Nusselt number and skin frictional coefficient due to nonlinear thermal radiation and magnetic parameters. The results may be promising for the applications of hybrid nanofluids in heat transfer and cooling systems of all modern industries. The authors have confidence in their study due to the novelty of the results and underline the numerous practical utilities of hybrid nanofluids.