Reduced order modelling of natural convection of nanofluids in horizontal annular pipes based on deep learning

Natural convection of nanofluids in annular pipes has been investigated in many studies due to its high occur-rence in heat transfer systems. Solving natural convection problems numerically itself requires numerical dis-cretization and iteration of differential equations, and introduction of nanofluids makes the solution process more complicated. In this paper, we propose and investigate a deep learning-based reduced-order model (ROM) for fast prediction of natural convection of nanofluids in annulus pipes. We construct the model using U-net structure of deep convolutional neural network and an end-to-end supervised learning method. The geometry presented by the Nearest Wall Signed Distance Function (NWSDF) is combined with numerical results to train the network model by minimizing model prediction error. The trained network model works as a ROM, which es-tablishes the accurate mapping between the problem geometry, boundary conditions and the steady-state natural convection field. To validate the feasibility, stability and accuracy of the network model, current work studies the natural convection of nanofluids in single inner-ring annulus and multi-inner-ring annulus with different posi-tions and diameters. The results show that the network model enables accurate predictions for natural convection of nanofluid with arbitrary inner-ring geometry, where an average accuracy of 99.9% for temperature field and 99% for velocity field are achieved; and the prediction speed of the proposed network model is more than three orders of magnitude faster than numerical solver. Furthermore, we also investigate and confirm the approach of setting the thermal boundary conditions in the neural network model, which will greatly enhance the applica-bility of the network model. The accurate and extremely fast prediction ability of the proposed network model proves that it can serve as a fast geometry optimization tool for design of heat exchangers or solar energy col-lectors of nanofluid in the future.