Sensitivity computation of nonlinear convective heat transfer in hybrid nanomaterial between two concentric cylinders with irregular heat sources

Heat exchangers, hot rolling, heat storage systems, and nuclear power plants utilize hybrid nanoliquid flow through an annulus for heat transport. The linear Boussinesq approximation is no longer suitable as these devices work at both moderate and extremely high temperatures. Hence, the salient features of quadratic convection on the hybrid nanoliquid flow in an inclined porous annulus are analyzed. The heat transport phenomenon is examined with an exponential space-related heat source (ESHS), the convective boundary conditions, and temperature-related heat source (THS). The significance of various shapes of nanoparticles (blades, spherical, platelets, bricks, and cylinders) on the heat and fluid flow characteristics has been explored. The complicated governing equations are solved numerically. Additionally, a statistical study (response surface methodology (RSM) and sensitivity analysis) is performed. The consequence of key parameters on the non-dimensional velocity, skin friction coefficient, temperature, and Nusselt number fields are presented through two-dimensional and surface plots. The irregular heat sources increase the magnitude of velocity and temperature fields. The quadratic and mixed convection mechanism favors the flow structure. The temperature and velocity fields are greater for platelet-shaped nanoparticles followed by cylinder, brick, and spherical-shaped nanoparticles. Further, the Nusselt number is more influenced by THS and less by the total nanoparticle volume fraction