Hybridized ferrofluid flow with acute magnetic force over inclined shrinking/stretching surface: Slip conditions cases

This study examines how the inclination affects the heat transfer characteristics of an acute magnetic force under first-order slip conditions. A mixture of incompressible hybridized ferrofluids, specifically Cobalt ferrite $$( {{\mathrm{CoFe}}_2{{\mathrm{O}}}_4} )$$ and magnetite $$( {{\mathrm{Fe}}_3{{\mathrm{O}}}_4} )$$, are combined with water on an inclined plate. To control the flow, a force of transverse magnetic is applied at an angle $${\beta }^*$$. The system of PDEs is converted into a system of nonlinear ordinary differential equations (ODEs) through a similarity transformation. The bvp4c solver function in MATLAB software is then utilized to resolve these ODEs. Graphical representation illustrates impact of changing the angle of inclination $$\alpha $$, the acute angle $${\beta }^*$$, the mixed convection parameter $$\varepsilon $$, velocity slip parameter $${\delta }_v$$, thermal slip parameter $${\delta }_T$$, and other pertinent variables. Dual branches are found for different involved parameters, with 1st solution determined to be stable through stability analysis. The angle of inclination shown a positive correlation with the skin friction coefficient (SFC) in the boundary layer (BL) and the Nusselt number in the first solution. The augmentation of the volume fraction of Cobalt ferrite nanoparticles results in the enhancement of both Nusselt number and SFC. Simultaneously, it contributes to the postponement of BL separation at the bifurcation point. The incorporation of Cobalt ferrite nanoparticles into hybrid ferrofluids results in a superior heat transfer rate compared to that achieved with conventional ferrofluids. In the first solution, SFC is increased by the presence of a magnetic field, while in the second solution, it is decreased. The phenomenon of velocity slip exerts an influence on the velocity of fluid flow, resulting in a reduction in the thickness of the momentum BL within the stable solution. Dual solutions are observed for suction parameter $$S > 0$$ and shrinking parameter $$\lambda \in ( { - 1.3, - 1} )$$ only.