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Purpose Magnetohydrodynamics (MHD) in nanofluids is crucial in boundary layer flow as it enables the manipulation of fluid motion through magnetic fields, which leads to improved stability and efficiency. This study aims to introduce a model and solutions for the boundary layer flow of a ternary hybrid nanofluid past a permeable shrinking sheet, integrating both magnetohydrodynamic and slip effects. Design/methodology/approach The model is firstly expressed as partial differential equations and subsequently converted into ordinary differential equations (ODEs) through a similarity transformation technique. A finite difference scheme with the Lobatto IIIa formula in MATLAB is applied to numerically solve the ODEs, where the respective outcomes provide insights into the skin friction coefficient, Nusselt number, velocity profiles and temperature profiles. Findings The results highlight the significance of enhancing magnetohydrodynamic effects and first-order velocity slip to reduce skin friction, improve heat transfer, delay boundary layer separation, increase flow velocity and lower fluid temperature. In addition, the stable numerical solution is scrutinized using response surface methodology (RSM) to validate and optimize flow control. The RSM optimization confirms that higher suction, magnetohydrodynamic effects and first-order slip levels are essential for minimizing skin friction and maximizing heat transfer simultaneously. Originality/value The presented model together with the numerical and statistical results can be used as a guidance to control the flow and heat transfer that occur within a related practical application, especially in engineering and industrial activities such as cooling technologies, energy harvesting or fluid transport in nanotechnology, where precise control of heat transfer and fluid dynamics is essential for optimizing performance and reducing energy consumption.
Wahid et al. (Tue,) studied this question.