Radiative influence on axisymmetric ternary hybrid nanofluid flow with convective boundary conditions over a nonlinearly permeable stretching/shrinking disk

Purpose 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. Design/methodology/approach 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. Findings 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. Practical implications 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. Originality/value 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.