Origin data for Fig 1b.

The nonlinear effects of thermal radiation on the free convection flow of certain nanofluids along a heated wall are studied numerically using an original finite-difference method. Nanofluids are used to improve the performance of flat and curved integrated photovoltaic modules. The partial differential equations governing the flow are difficult to solve due to the strong non-linearity of the radiative term. In contrast to previous studies, the problem is solved directly without linearization by Rosseland’s nonlinear approximation. The proposed numerical method is validated with results from the literature. The effects of nonlinearity and various physical parameters such as time, volume fraction and radiation parameter on the velocity, temperature, Nusselt number and skin friction coefficient of the CuO-water nanofluid are analyzed and presented graphically. A comparative study between the solutions given by the linear and non-linear problems reveals that Rosseland’s linear approximation is no longer valid when the effect of thermal radiation is significant. On the other hand, the non-linear model better reflects the physical phenomena involved in the cooling process. Finally, a comparison of the performance of five nanofluids (CuO, Ag, Al2O3, Cu and TiO2 in water) shows that the Cu-water nanofluid performs best, with a high heat transfer rate and low shear stresses.

本研究采用原创有限差分法，针对热辐射对特定纳米流体沿受热壁面的自由对流流动的非线性效应开展数值研究。纳米流体（nanofluids）可用于提升平板型与曲面集成光伏组件的性能。由于辐射项存在强非线性特性，控制该流动的偏微分方程（partial differential equations）求解难度较大。与既往研究不同，本研究未借助罗斯兰非线性近似进行线性化处理，直接对该问题进行求解。本文所提出的数值方法已通过文献公开结果完成验证。针对氧化铜-水（CuO-water）纳米流体的速度、温度、努塞尔数（Nusselt number）与壁面摩擦系数（skin friction coefficient），本文分析了非线性效应以及时间、体积分数、辐射参数等各类物理参数的影响，并以图形形式进行展示。对比线性与非线性问题的求解结果可知，当热辐射效应较为显著时，罗斯兰线性近似不再适用。另一方面，非线性模型能够更精准地反映冷却过程中涉及的物理现象。最后，对五种水基纳米流体（分别为氧化铜CuO、银Ag、氧化铝Al₂O₃、铜Cu与二氧化钛TiO₂）的性能开展对比后发现，铜-水纳米流体表现最优，其传热速率更高且剪切应力更低。