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

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.