Researchers have expressed a strong interest in using Melting Heat Transfer and nanofluids to improve electronics cooling and energy storage efficiency. This chapter investigates the effects of magnetohydrodynamics, thermal radiation, and the dynamics of stretching and shrinking on the heat transfer characteristics of a copper–water nanofluid over a stretching/shrinking sheet, including melting effects. The governing equations are transformed to nonlinear ordinary differential equations and numerically solved using the Keller Box technique. This chapter discusses the relationship between melting, stretching, and shrinking characteristics, as well as their influence on heat transmission rates. In addition, we give a detailed study of the effects of all of the aforementioned driving characteristics. The findings are presented as graphical and tabular data and compared to current literature.