In this study, the buoyancy-driven two-dimensional flow of a nanoliquid past a vertical plate subject to quadratic Rosseland thermal radiation and quadratic thermal convection (quadratic Boussinesq approximation) is investigated. The working liquid is ethylene glycol containing titania nanoparticles. The consequences of aggregation of nanoparticles are included using the modified Maxwell-Bruggeman and Krieger-Dougherty models for thermal conductivity and viscosity respectively. The analysis is performed under active and passive control of nanoparticles (NPs). To simulate the nanoliquid, the modified Buongiorno model is used which includes effective thermophysical properties and two significant slip mechanisms (nanoparticle random motion and thermophoresis). The phenomenon of physical flow is demonstrated with the help of a partial differential equation (PDE) system that uses conservation laws and the thermophysical properties of nanoparticles. Nonlinear PDEs related to the nanoliquid heat transport are transformed into ordinary two-point BVP (boundary value problem)and the obtained system has been solved numerically. It is found that the nanoparticle aggregation and quadratic thermal radiation aspects enhance the temperature field. Furthermore, the quadratic Boussinesq approximation aspect was found to hasten the heat transport rate at the plate.

在这项研究中，研究了受二次 Rosseland 热辐射和二次热对流（二次 Boussinesq 近似）影响的纳米液体通过垂直板的浮力驱动二维流动。工作液为含有二氧化钛纳米粒子的乙二醇。使用改进的 Maxwell-Bruggeman 和 Krieger-Dougherty 模型分别计算热导率和粘度，包括纳米颗粒聚集的后果。该分析是在纳米颗粒 (NP) 的主动和被动控制下进行的。为了模拟纳米液体，使用了改进的 Buongiorno 模型，该模型包括有效的热物理特性和两个重要的滑动机制（纳米粒子随机运动和热泳）。物理流动现象在偏微分方程 (PDE) 系统的帮助下得到证明，该系统使用守恒定律和纳米粒子的热物理特性。与纳米液体传热相关的非线性偏微分方程转化为普通的两点 BVP（边界值问题），得到的系统已被数值求解。发现纳米颗粒聚集和二次热辐射方面增强了温度场。此外，发现二次 Boussinesq 近似方面可以加快板的热传输速率。与纳米液体传热相关的非线性偏微分方程转化为普通的两点 BVP（边界值问题），得到的系统已被数值求解。发现纳米颗粒聚集和二次热辐射方面增强了温度场。此外，发现二次 Boussinesq 近似方面可以加快板的热传输速率。与纳米液体传热相关的非线性偏微分方程转化为普通的两点 BVP（边界值问题），得到的系统已被数值求解。发现纳米颗粒聚集和二次热辐射方面增强了温度场。此外，发现二次 Boussinesq 近似方面可以加快板的热传输速率。