The sensitivity of the heat transport rate in the thermo-solutal Marangoni convection of \({\mathrm{Al}}_{2}{\mathrm{O}}_{3}-{\mathrm{H}}_{2}\mathrm{O}\) nanoliquid at 300 K is analyzed. The nanoliquid is modeled using the modified Buongiorno model which incorporates the Brownian motion, effective nanoliquid properties, and thermophoresis effects. The thermophysical models proposed by Khanafer and Vafai are chosen in this analysis as these correlations are in good agreement with the experimental values. External constraining factors like thermal radiation and variable magnetic field are also considered. The basic equations are solved using apposite transformation variables and Finite Difference Method (FDM). The impacts of the effectual parameters on all the profiles are analyzed. Furthermore, the heat transport is analyzed by executing a Response Surface Methodology (RSM) model with the Brownian motion parameter (\(0.1\le \mathrm{Nb}\le 0.5\)), thermophoretic parameter (\(0.1\le \mathrm{Nt}\le 0.5\)), and nanoparticle volume fraction (\(1\%\le \varphi \le 3\%\)). The modified Buongiorno model yields lower temperature and concentration profiles when compared to the conventional Buongiorno model. The heat transfer rate is the most sensitive to the Brownian motion parameter than thermophoresis and nanoparticle (NP) volume fraction parameters. The results of this study would be instrumental in improving the efficiency of the welding process, crystal growth, and coating technologies.

\（{\ mathrm {Al}} _ {2} {\ mathrm {O}} _ {3}-{\ mathrm {H}} _ {2}的Marangoni热对流中传热速率的敏感性} \ mathrm {O} \）分析了300 K下的纳米液体。使用改良的Buongiorno模型对纳米液体进行建模，该模型结合了布朗运动，有效的纳米液体性质和热泳效应。在分析中选择了Khanafer和Vafai提出的热物理模型，因为这些相关性与实验值非常吻合。还考虑了外部约束因素，例如热辐射和可变磁场。基本方程使用适当的变换变量和有限差分法（FDM）求解。分析了有效参数对所有配置文件的影响。此外，通过执行具有布朗运动参数（\（0.1 \ le \ mathrm {Nb} \ le 0.5 \）的响应表面方法（RSM）模型来分析热传递），热泳参数（\（0.1 \ le \ mathrm {Nt} \ le 0.5 \））和纳米粒子体积分数（\（1 \％\ le \ varphi \ le 3 \％\））。与传统的Buongiorno模型相比，修改后的Buongiorno模型产生的温度和浓度曲线较低。与热泳和纳米颗粒（NP）体积分数参数相比，传热速率对布朗运动参数最敏感。这项研究的结果将有助于提高焊接工艺，晶体生长和涂层技术的效率。