This study examined the flow and heat transfer over a stretching sheet subject to effective viscosity and thermal conductivity models suggested by Roscoe, Brinkman viscosity, Maxwell thermal conductivity, and the Koo-Kleinstreuer & Li models. The electro-periodic magnetohydrodynamics (MHD), and melting heat transmission are all important foundational concepts for the modern industrial sector and energy storage. Therefore, the objective of this research is to explore the effective momentum and energy transfer Powell-Eyring-Casson nanofluids consisting of \(\:A{l}_{2}{O}_{3}-{H}_{2}O\) past a melting stretching sheet. The flow model investigate the comparative study of three well-known models and their impact on momentum and energy transfer rate which is not been explored in the literature. To analyze the proposed mathematical model, a combination of statistical quadratic regression with sensitivity analysis and computational Bvp4c scheme is used. The findings suggest that maximum average shear stress and Nusselt number are observed in the Koo & Kleinstreuer model. The average Nusselt number enhances approximately by 12% to further 23% at increased viscoelastic effects when the magnetic effects are present. With additional load of nanoparticles, the skin friction and Nusselt number expand progressively. The thermal transfer process contributes significantly due to frictional and melting heating effects. The magnetic effects enhance the mechanism of heat transfer. Furthermore, the MHD control the flow regime and elevated skin friction. The heat transfer process contributes significantly due to frictional and melting heating effects. The sensitivity analysis reveals that the Nusselt number is sensitive against melting heat.
