Numerical study of second-grade fuzzy hybrid nanofluid flow over the exponentially permeable stretching/shrinking surface

The study of hybrid nanoliquids can aid in developing numerous advanced features that facilitate heat transmission, such as pharmaceutical processes, hybrid-powered engines, microelectronics, engine cooling, and domestic refrigerators. In the current study, a mathematical model is designed to elaborate the physical inception of an unsteady second-grade hybrid nanofluid with Al2O3-Cu/SA, a combination concentrated over the permeable exponentially heated stretching/shrinking sheet under hydromagnetic, heat source/sink, and viscous dissipation implications. The set of similarity transforms is used to convert underlying partial differential equations into the system of ordinary differential equations. The well-known homotopy analysis method is applied to tackle the formulated differential system in the MATHEMATICA program, which can obtain non-uniqueness outcomes. The imprecision of nanofluid and hybrid nanofluid volume fractions was modeled as a triangular fuzzy number [0%, 5%, 10%] for comparison. The double parametric approach was applied to deal with the fuzziness of the associated fuzzy parameters. The nonlinear ordinary differential equations are converted into fuzzy differential equations, and the homotopy analysis method is used for the fuzzy solution. In terms of code validity, our results are matched to previous findings. The features of several parameters against the velocity, surface-friction coefficient, heat transfer, and Nusselt number are described via graphs. Furthermore, the nanoparticle volume fraction magnifies the fluid temperature and retards the flow profile throughout the domain, according to our findings. Thermal profiles increase with progress in the heat source, nanoparticles volumetric fractions, viscous dissipation, and nonlinear thermal radiation. The percentage increase in the drag force and heat transfer rate are 15.18 and 5.54 when the magnetic parameter takes input in the range 0.1 <= M <= 0.3 and nanoparticle volume fraction inputs 0.01 <= phi 1 <= 0.15. From our observation, the hybrid nanofluid displays the maximum heat transfer compared to nanofluids. This important contribution will support industrial growth, particularly in the processing and manufacturing sectors.