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In recent times, ternary hybrid nanofluid has garnered attention from scientist and researchers due to its improved thermal efficiency. This study aims to delve into the examination of ternary hybrid nanofluid (Al₂O₃–Cu–TiO₂/water), particularly concerning axisymmetric flow over a nonlinearly permeable stretching/shrinking disk. In addition, the investigation of convective boundary conditions and thermal radiation effects is also considered within the context of the described flow problem.

Mathematical formulations representing this problem are reduced into a set of ordinary differential equations (ODEs) using similarity transformation. The MATLAB boundary value problem solver is then used to solve the obtained set of ODEs. The impact of considered physical parameters such as suction parameter, radiation parameter, nonlinear parameter, nanoparticle volumetric concentration and Biot number on the flow profiles as well as the physical quantities is illustrated in graphical form.

The findings revealed the thermal flux for the nonlinearly shrinking disk is approximately 1.33%, significantly higher when compared to the linearly shrinking disk. Moreover, the existence of dual solutions attributed to the nonlinear stretching/shrinking disk is unveiled, with the first solution being identified as the stable and reliable solution through temporal stability analysis.

Understanding ternary hybrid nanofluid behavior and flow has applications in engineering, energy systems and materials research. This study may help develop and optimize nanofluid systems like heat exchangers and cooling systems.

The study of flow dynamics across nonlinear stretching/shrinking disk gains less attention compared to linear stretching/shrinking geometries. Many natural and industrial processes involve nonlinear changes in boundary shapes or sizes. Understanding flow dynamics over nonlinear shrinking/stretching disks is therefore essential for applications in various fields such as materials processing, biomedical engineering and environmental sciences. Hence, this study highlights the axisymmetric flow over a nonlinear stretching/shrinking disk using ternary hybrid nanofluid composed of alumina (Al₂O₃), copper (Cu) and titania (TiO₂). Besides, this study tackles a complex problem involving multiple factors such as suction, radiation and convective boundary conditions. Analyzing such complex systems can provide valuable insights into real-world phenomena where multiple factors interact.

This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect.

The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid.

Dual solutions are discovered to occur for the case of shrinking disk (λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation.

Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.