Prediction of thermal conductivity of CuO-ZnO/(ethylene glycol-water) hybrid nanofluids based on radial basis neural network model
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摘要: 采用两步法制备CuO-ZnO质量分数为0~3 wt%的CuO-ZnO/(乙二醇(EG)-水)混合纳米流体。其中，纳米颗粒CuO和ZnO质量比为50∶50不变，基液混合比(EG与去离子水的质量比)变化范围为20∶80~80∶20，分析其导热系数随温度(25~60℃)及基液比的变化规律。然后，以质量分数、温度及基液混合比为自变量，导热系数为因变量，采用径向基神经网络(RBFNN)模型预测导热系数，并与反向传播神经网络(BPNN)模型和多元线性回归(MLR)模型的预测值对比。结果表明，CuO-ZnO/(EG-水)纳米流体导热系数随温度的升高呈非线性增大，当CuO-ZnO质量分数为3 wt%及基液混合比为20∶80时，其导热系数与纯基液相比增大了14.03%~23.47%；但随着基液中的EG含量增大，导热系数非线性下降。总之，CuO-ZnO/(EG-水)纳米流体的导热系数受粒子随机运动和温度变化呈非线性变化。采用RBFNN模型预测CuO-ZnO/(EG-水)纳米流体的导热系数，其结果与BPNN模型和MLR模型对比，RBFNN模型性能评价指标均方根误差(RMSE)、平均相对百分比误差(MRPE)及误差平方和(SSE)更接近于0，多元统计系数R2更接近于1，说明RBFNN模型预测导热系数的精度更高，能够较好地表征不同参数对导热系数的影响，为CuO-ZnO/(EG-水)纳米流体的热物理性能参数的预测提供了一种有效的数据驱动建模方法。Abstract: The CuO-ZnO/(ethylene glycol(EG)-water) nanofluid with CuO-ZnO mass fractions of 0–3 wt% were prepared by two-step method. First, the mixing mass ratio of nanoparticles CuO to ZnO was fixed at 50∶50, and the mass ratios of EG to deionized water varied from 20∶80 to 80∶20. Variations of thermal conductivity with temperature (25–60℃) and mixing mass ratios of base liquids were studied. Second, the radial basis function neural network (RBFNN) model was used to predict the thermal conductivity. In the model, the mass fraction, temperature and mixing mass ratios of base liquids were considered as independent variables while the thermal conductivity is the dependent variable. The predicted values were compared with the values predicted by back propagation neural network (BPNN) and multiple linear regression (MLR). The results show that the thermal conductivities of CuO-ZnO/(EG-water) nanofluid increase nonlinearly with the increase of temperature, while decrease with the increase of mixing mass ratios of base liquids. Compared with the thermal conductivity of the base fluid, it increases from 14.03% to 23.47% at the mass fraction of 3 wt% and the mixing mass ratio of base fluid of 20∶80. The thermal conductity of CuO-ZnO/(EG-water) changes nonlinear with random motion of nanoparticles and temperature. The results obtained by RBF model are more precise than that predited by BPNN model and MLR model. The model evaluated indexes of root mean square error (RMSE), mean relative percentage error (MRPE) and sum of squared error (SSE) are closer to 0 and duostatistical coefficient of multiple determination R2 is closer to 1 indicating that the RBFNN model can accurately predict the thermal conductivity. It can also be used to characterize the effect of various parameters on the thermal conductivity. The results offer an effective method to establish the data-driven model to accurately predict the thermal conductivity of CuO-ZnO/(EG-water) nanofluid.
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图 2 反向传播神经网络(BPNN)拓扑结构示意图
Figure 2. Schematic of back propagation neural network (BPNN) topology
w—Mass fraction; R—Mixing ratio; T—Temperature; knf—Thermal conductivity
图 3 径向基神经网络(RBFNN)模型的基本结构(a)和导热系数 (b)
Figure 3. Basic structure(a) and thermal conductivity(b) of radial basis function neural network (RBFNN) model
图 4 CuO-ZnO/(乙二醇(EG)-水)纳米流体导热系数随温度及混合比的变化
Figure 4. Thermal conductivity of CuO-ZnO/(ethylene glycol(EG)-water) nanofluids varied with temperature and mixing ratio
图 5 质量分数为1 wt%的CuO-ZnO/(EG-水)纳米流体有效导热系数与文献相关数据及经验公式对比
Figure 5. Comparison of effective thermal conductivity of CuO-ZnO/ (EG-water) nanofluids between present data and data in literature and empirical correlations at 1 wt% mass fraction of CuO-ZnO
kbf—Thermal conductivity of base liquids; knf—Thermal conductivity of hybrid nanofluids
图 6 CuO-ZnO/(EG-水)纳米流体的BPNN回归实验导热系数
Figure 6. BPNN regression of CuO-ZnO/(EG-water) nanofluids of experimental thermal conductivity
图 7 CuO-ZnO/(EG-水)纳米流体导热系数实验值与RBFNN预测值对比
Figure 7. Comparison of thermal conductivity of CuO-ZnO/(EG-water) nanofluids between experimental values and RBFNN predictive values
图 8 MLR、BPNN和RBFNN预测模型残差值对比
Figure 8. Comparison of residuals between prediction models of MLR, BPNN and RBFNN
图 9 CuO-ZnO/(EG-水)纳米流体导热系数的MLR、BPNN、RBFNN预测值与实验值对比
Figure 9. Comparison between MLR、BPNN and RBFNN predictions and experimental data of CuO-ZnO/(EG-water) nanofluids
表 1 隐含层节点数目选取结果评价指标对比
Table 1. Comparison of evaluation results of the number of hidden layer nodes
Number of neurons Transfer function Mean squared error/10–4 R2 [3] [logsig] 1.3662 0.99887 [4] [logsig] 2.1945 0.99863 [5] [logsig] 3.8805 0.99875 [6] [logsig] 3.7558 0.99881 [7] [logsig] 3.9099 0.99820 [8] [logsig] 0.4723 0.99944 [9] [logsig] 1.1441 0.99901 [10] [logsig] 3.6291 0.99926 [11] [logsig] 12.3670 0.99614 [12] [logsig] 2.3768 0.99836 Note: R2—Duostatistical coefficient of multiple determination. 
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表 2 RBFNN、BPNN及多元线性回归(MLR)预测模型CuO-ZnO/(EG-水)纳米流体导热系数性能评估
Table 2. Performance evaluation for CuO-ZnO/(EG-water) nanofluids by predictionmodel of RBFNN, BPNN and multiple linear regression (MLR)
Prediction model Root mean squared error $E_{\rm{RMSE}}$ Mean relative percentage error $E_{\rm{MRPE}}$/% Sum of squared error $S_{\rm{SE}}$ R2 RBFNN 0.0038 0.70 0.0003 0.9999 BPNN 0.0069 1.66 0.0011 0.9994 MLR 0.0109 2.03 0.0199 0.9876
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