Nanoparticles have the ability to augment heat transmission in the boundary layer flow zone. While dealing with momentum and thermal boundary layers, the Prandtl number is very important. Considering this, this article is the first to examine the consequence of an effective Prandtl number model on the nanoboundary layer, unsteady and laminar stagnation point flow of incompressible \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{\text{H}}_{2}\text{O}\) and \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{{\text{C}}_{2}\text{H}}_{6}\text{O}_{2}\) nanofluids across a spinning sphere with mass suction, MHD, viscous dissipation, heat absorption, and porous media. In MATHEMATICA, the shooting technique and the fourth-order Runge–Kutta (RK-IV) method are used to numerically solve the nonlinear governing equations of the boundary layer. For both the with and without effective Prandtl number scenarios, visualizations show the numerical findings for the velocity, temperature profile, skin friction coefficient, and decreased Nusselt number. It has been shown that the temperature of nanofluids increases with the rising volume fraction of \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}\) nanoparticles, both when the effective Prandtl number is present and when it is not. \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{\text{H}}_{2}\text{O}\) has a greater temperature profile than \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{{\text{C}}_{2}\text{H}}_{6}\text{O}_{2}\) . \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{{\text{C}}_{2}\text{H}}_{6}\text{O}_{2}\) has a greater heat transfer rate than \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{\text{H}}_{2}\text{O}\) . If there is no effective Prandtl number, the Nusselt number decreases by 2.76% when the \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{\text{H}}_{2}\text{O}\) nanofluid ( \(\phi\) ) rises from 0.01 to 0.04 and \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{{\text{C}}_{2}\text{H}}_{6}\text{O}_{2}\) decreases by 1.37%. The Nusselt number rises by 2.29% for \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{\text{H}}_{2}\text{O}\) and 6.37% for \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}/{{\text{C}}_{2}\text{H}}_{6}\text{O}_{2},\) when the effective Prandtl number is included, as \(\phi\) grows from 0.01 to 0.04. \(\gamma{\text{-Al}}_{2}{\text{O}}_{3}\) nanofluids may serve as a cooling medium in medical therapies like hyperthermia, which involves targeted heating to treat cancer, in order to safeguard adjacent healthy tissues. The study's findings on heat transmission qualities and the influence of magnetic fields may provide guidance for the improvement in hyperthermia equipment in terms of safety and effectiveness.
