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Researchers are using different types of nanomaterials for the enhancement of the thermal performance of regular fluids such as water, kerosene oil, etc. However, these days, the researchers are more interested in hybrid nanomaterials. The purpose of this communication is to examine the stability analysis of Cu–Al₂O₃/water hybrid nanofluid over a non-linear shrinking sheet. The hybrid nanomaterials are composed of Cu and Al₂O₃. These hybridized nanomaterials are then dissolved in water taken as base fluid to form Cu–Al₂O₃//water hybrid nanofluid. Mathematical analysis and modeling have been attended in the presence of viscous dissipation and suction/injection effects. The governing equations of mathematical models are transformed into self-similar solutions in the form of ODEs by using similarity transformation. Solutions of the non-linear ODEs are created by employing of three-stage Lobatto IIIa …