This study investigates the impact of various shapes of \(F{e}_{3}{O}_{4}\) and \(A{l}_{2}{O}_{3}\) nanometers immersed in water \(({H}_{2}O)\) base fluid over an unsteady vertically curved stretching surface. The article also covers the effects of velocity slip and variable magnetohydrodynamics (MHD). The mathematical model is based on fundamental principles, specifically the conservation of mass, momentum, and energy. We have transformed the modeled governing partial differential equations into highly nonlinear ordinary differential equations using suitable similarity conversions. The BVP4C program in MATLAB is used to generate numerical solutions for significant physical parameters, which can be visualized as graphs. The bar graphs are also drawn to analyze the impact of physical emerging parameters on skin friction coefficient and Nusselt Numbers. The result is also validated by comparing the present results with the available literature and found to be in good accord. It has been found that the addition of \(F{e}_{3}{O}_{4}\) and \(A{l}_{2}{o}_{3}\) nanoparticles improves the thermal conductivity of the base fluid \({H}_{2}O\) . This rise is more pronounced for platelet-shaped \(F{e}_{3}{O}_{4}\) nanoparticles. The shape and the size of the nanoparticles play a crucial role in the heat transfer mechanism. Furthermore, the brick-shaped \(A{l}_{2}{O}_{3}-{H}_{2}O\) nanofluid exhibits the lowest velocity, the greatest temperature, and the lowest skin friction coefficient.
