Thermal and velocity slip impacts on MHD tetra-hybrid nanofluids flow over a porous stretching surface

Abstract Tetra-hybrid nanofluids with Al 2 O 3 , Cu, SiO 2 and TiO 2 offer better control over heat transfer rate. These nanofluids are useful for thermal applications in engineering, biomedical material science and the energy sector. Different nanoparticle shapes also influence the heat transfer performance of tetra-hybrid nanofluids and allow the fluid to be tailored for specific industrial needs. This study examines the flow aspects of a radiative magnetohydrodynamics tetra-hybrid nanofluid flowing past a stretching surface in a porous medium. The flow system is further interpreted under the influence of first- order velocity and thermal slip conditions. Initially formulated flow governing equations are highly nonlinear partial differential equations that are changed into a set of linear ordinary differential equations adopting relevant similarity transformations. The subsequent equations are then dealt with using both numerical and analytical approaches. Specifically, we employ the MATLAB-based bvp4c solver for the numerical solution and the optimal auxiliary functions method for the analytical treatment. The responses of key governing flow parameters on velocity, temperature, skin friction, and Nusselt number are examined and presented through both graphs and tabulated data. Raising the porosity parameter from $$Ps=0.1$$ to $$Ps=0.4$$ results in a noticeable decline in momentum profiles, dropping from $$f'\left( {\eta =0.6} \right)=0.49860$$ to $$f'\left( {\eta =0.6} \right)=0.33058$$ . Enhancing the nanoparticle volume fraction $$\left( {0.00 \leqslant \phi \leqslant 0.05} \right)$$ elevates the temperature distribution from $$\theta \left( {\eta =2} \right)=0.06349$$ to $$\theta \left( {\eta =1} \right)=0.21466$$ . The trend of decreasing skin friction with enhancing inputs of nanoparticle shape factor and magnetic parameter remains consistent in both no-slip and slip conditions. Slip effects significantly impact the heat transfer rate compared to the no-slip condition under the impact of Eckert number and nanoparticle shape factors.