Optimization and sensitivity analysis of heat transport of hybrid nanoliquid in an annulus with quadratic Boussinesq approximation and quadratic thermal radiation

The quadratic convective flow of hybrid nanoliquid in an annulus subjected to quadratic thermal radiation is studied for the first time. The impact of suction/injection and the uniform movement of the rings are considered. Nonlinear equations are handled numerically by adopting the shooting technique. An optimization procedure is performed by using response surface methodology. The maximum heat transport is observed for chosen values of effective parameters (thermal radiation parameter $$ (5 \le Rt \le 15) $$, temperature ratio parameter $$ (1.1 \le \theta_{w} \le 5.1) $$ and nanoparticle volume fraction of copper $$ (1\% \le \phi_{\text{Cu}} \le 3\% )) $$ at three different levels (low(− 1), middle(0) and high(+ 1)). In addition, a slope of the data point is evaluated for the friction coefficient and the Nusselt number. The results showed that the impact of quadratic thermal radiation on velocity and temperature distributions is more significant than linear thermal radiation. Further, an increase in quadratic convection and quadratic thermal radiation leads to an improvement in the friction coefficient of the skin on the inner surface of the outer annulus. Furthermore, the sensitivity of the friction coefficient is positive for the appearance of quadratic thermal radiation.