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.

首次研究了混合纳米液体在经历二次热辐射的环空中的二次对流。考虑了抽吸/注入的影响以及环的均匀运动。非线性方程采用射击技术进行数值处理。通过使用响应面方法进行优化过程。对于有效参数的选定值（热辐射参数\（（5 \ le Rt \ le 15）\），温度比参数\（（1.1 \ le \ theta_ {w} \ le 5.1）\），观察到最大热传输和铜的纳米粒子体积分数\（（1 \％\ le \ phi _ {\ text {Cu}} \ le 3 \％））\）处于三个不同的级别（低（-1），中（0）和高（+1））。另外，针对摩擦系数和努塞尔数评估数据点的斜率。结果表明，二次热辐射对速度和温度分布的影响比线性热辐射更显着。此外，二次对流和二次热辐射的增加导致外环的内表面上的皮肤的摩擦系数的改善。此外，摩擦系数的灵敏度对于二次热辐射的出现是正的。