In the realm of fluid mechanics, the flow of a hybrid nanofluid under an exponentially stretching/shrinking surface has been extensively investigated by researchers due to its capability in altering the flow and heat transfer characteristics. Considering the above-mentioned setup with the addition of porous media, this study investigates the flow and heat transfer characteristics of Cu–TiO2/water hybrid nanofluid in the presence of magnetohydrodynamics, heat source, and slip conditions. The complex governing equations, originally in PDEs were transformed into ODEs using a similarity transformation, and the numerical result was obtained using the MATLAB bvp4c function. The Cu–Al2O3/water was found to be conducting scarcely higher rate of heat transfer compared to Cu–TiO2/water. The Cu–TiO2/water hybrid nanofluid boosted heat transfer by 4.04% when compared to water, whereas Cu/water nanofluid enhanced heat transfer by 2.13%. Dual solutions were found, and the stability analysis proved that the upper branch solution is stable. Moreover, the additional MHD and permeability parameter accelerates the skin friction, whereas copper nanoparticle volume fraction expands the heat transfer rate of Cu–TiO2/water hybrid nanofluid.
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