Evaluation and intelligent forecasting of energy and exergy efficiencies of a nanofluid-based filled-type U-pipe solar ETC using three machine learning approaches

The thermodynamic modeling of a filled layer U-type was conducted considering the six water-based and Engine Oil (EO)-based nanofluids (NFs). The results demonstrated that Fe2O3/EO NF is efficient from the exergy efficiency point of view. While MWCNT/water NF outperforms from the energy efficiency aspect. Moreover, the outcome indicated that when (Tin−Tamb)/It increased above 0.04 (K m2/W), Ltube has no considerable effect on the exergy efficiency. Still, the length impact is noticeable regarding outlet temperature and energy efficiency. Furthermore, the advantage of the filled-type over the conventional ETSC is more prominent at low m˙ (e.g. 4.0 kg/h). So that ηex in the filled type with Fe2O3/EO is improved by 2.29 % and 3.70 %, respectively, for (Tin−Tamb)/It of 0 and 0.04. Moreover, the increase in m˙ of the water/based and oil-based NFs, respectively, between 6 and 10 kg/h and 8–20 kg/h is suggested from the energy efficiency aspect. The results of machine learning modeling revealed that three models namely group method for data handling (GMDH), response surface method (RSM), and modified response surface model (MRSM) are capable of estimating ηen and ηex. While MRSM outperforms the two other models in terms of (R2 | ηen = 0.9986 and RMSE| ηen = 0.7849; R2 |ηex = 0.9988 and RMSE| ηex= 0.1513).