Experimental investigation and artificial intelligent estimation of thermal conductivity of nanofluids with different nanoparticles shapes

Determining and modelling the effective thermal conductivity of nanofluids is always a concern of investigators. The effect of nanoparticles' shape on the effective thermal conductivity of nanofluids has not been accurately correlated with other influencing factors such as temperature and nanoparticle concentration. The main purpose of this study is to reveal the effects of influencing factors on the effective thermal conductivity of nanofluids by experimental investigation and artificial intelligence (AI). We prepared the TiO₂/water nanofluids with four shapes of TiO₂ nanoparticles (spherical, ellipsoidal, clubbed, and sheet) and measured the effective thermal conductivities of the samples with nanoparticles concentrations from 0.5 to 4.0 vol% as a function of temperature from 20 to 60 °C. Besides, 389 experimental datasets collected from literature and 80 datasets from our experiment were used to determine the optimum structure of AI-based models. Temperature, concentrations, shape factor, and thermal conductivity of nanoparticles were selected as independent variables, and the relative thermal conductivity of nanofluids was selected as the dependent variable. Six AI-based models were examined, including four artificial neural networks of multi-layer perceptron, cascade feedforward, radial basis function, and generalized regression neural network, adaptive neuro-fuzzy inference systems, and least-squares support vector machines, and the estimating performances were compared. The experimental results showed that increasing temperature and nanoparticles concentrations led to a remarkable improvement in the relative thermal conductivity of nanofluids, attributed to the intensified Brownian motion of nanoparticles with the high temperature and the effective collision of nanoparticles with the high concentrations. Besides, nanoparticles with a large aspect ratio provided the fast pathway with seldom crossing an interparticle boundary or junction point for effective heat transfer in the nanofluids, resulting in higher relative thermal conductivity of nanofluids. Statistical analyses confirmed that the cascade feed-forward neural network with ten hidden neurons and the Levenberg–Marquardt training algorithms was the optimized AI-based model for estimating the relative thermal conductivity of nanofluids. This model estimated allover experimental data by MSE = 0.0039, RMSE = 0.0622, AARD% = 2.66%, and R² = 0.9908.