Parametric Dynamic Mode Decomposition with multi-linear interpolation for prediction of thermal fields of Al2O3-water nanofluid flows at unseen parameters

TL;DR

This work develops a non-intrusive, data-driven framework that combines Dynamic Mode Decomposition (DMD) with parametric interpolation to predict thermal fields of $Al_2O_3$-water nanofluids in laminar, incompressible flows at unseen Reynolds numbers and nanoparticle concentrations. By constructing a DMD operator from quasi-steady snapshots and applying either linear interpolation in one parameter ($Re$) or bi-linear interpolation across two parameters ($Re$, $ε$), the authors demonstrate highly accurate temperature fields and heat-transfer metrics compared with CFD: maximum field errors as low as $2.7\times 10^{-2}\%$ and Nu errors below approximately $6\%$ in tested regimes. The 1D LI approach achieves near-CFD accuracy for $Re>100$ and successfully interpolates to $Re$ values outside the training set, while the 2D BLI approach reveals regime-dependent performance, with $A_1$ excelling for $Re\ge 278$ and $0.5\%\le ε\le 1.5\%$, and $A_2$ performing better at lower $Re$. The results indicate that parametric DMD with interpolation can provide rapid, accurate predictions for nanofluid thermal fields, enabling fast design and optimization of nanofluid cooling systems in laminar regimes, with future extensions to more parameters and interpolation strategies.

Abstract

The study proposes a data-driven model which combines the Dynamic Mode Decomposition with multi-linear interpolation to predict the thermal fields of nanofluid flows at unseen Reynolds numbers (Re) and particle volume concentrations ($ε$). The flow, considered for the study, is laminar and incompressible. The study employs an in-house Fortran-based solver to predict the thermal fields of Al$_2$O$_3$-water nanofluid flow through a two-dimensional rectangular channel, with the bottom wall subjected to a uniform heat flux. The performance of two models operating in one- and two-dimensional parametric spaces are investigated. Initially, a DMD with linear interpolation (DMD-LI) based solver is used for prediction of temperature of the nanofluid at any Re $>$ 100. The DMD-LI based model, predicts temperature fields with a maximum percentage difference of just 0.0273\%, in comparison with the CFD-based solver at Re =960, and $ε$ = 1.0\%. The corresponding difference in the average Nusselt numbers is only 0.39\%. Following that a DMD with bi-linear interpolation (DMD-BLI) based solver is used for prediction of temperature of the nanofluid at any Re $>$ 100 and $ε$ $>$ 0.5\%. The performance of two different ways of stacking the data are also examined. When compared to the CFD-based model, the DMD-BLI-based model predicts the temperature fields with a maximum percentage difference of 0.21 \%, at Re = 800 and $ε$ = 1.35\%. And the corresponding percentage difference in the average Nusselt number prediction is only 6.08\%. All the results are reported in detail. Along side the important conclusions, the future scope of the study is also listed.

Figures (19)

• Figure 1: A comparison between (a). the outlet temperature profiles, (b). the outlet velocity profiles and (c) Average Nusselt number of pure water flow through a two dimensional channel at a Reynolds number of 1000 obtained using different grid sizes.
• Figure 2: A comparison between (a). the velocity profiles and (b). the temperature profiles of 1% -Al$_2$O$_3$ -water nanofluid obtained using the current solver and that reported by Kalteh et al. Kalteh2012
• Figure 3: A schematic representation of data instances in the dataset used for obtaining the DMD model in one dimensional parametric space. The stacking of the data instances to obtain the DMD operator is also shown.
• Figure 4: Eigen Values of the DMD operator [A].
• Figure 5: A comparison between the temperature fields predicted using (a). CFD based homogeneous modeling of nanofluid flows, (b). DMD based prediction of the temperature fields at Re = 1000 and (c) the percentage difference between the CFD and DMD based predictions of the temperature fields.