Study of the thermo-magneto-hydrodynamic flow of micropolar-nanofluid in square enclosure using dynamic mode decomposition and proper orthogonal decomposition

In the present contribution, we analyze the non-stationary, incompressible, laminar, natural convection flow in a rectangular enclosure filled with a micropolar-nanofluid (Al₂O₃/water) in the presence of a magnetic field, using Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) method. DMD method utilizes numerically or experimentally obtained data (often generated by nonlinear dynamics) to compute the eigenvalues and the eigenmodes of an approximated linear model, and the growth/decay (damp) rates, frequencies and spatial structures for each mode. POD provides the energy content measure for different modes. DMD and POD method have been applied in the study, optimization and control of large-scale dynamical systems. They can be used supplementary to each other or separately for cross comparison. We propose an efficient way to (i) snapshots sampling (ii) select the optimal number for analysis and (iii) define the grid resolution (grid density) for obtaining a grid independent solution for the DMD analysis. We numerically solve the flow equations using a meshless point collocation method (MPCM), using the Moving Least Square (MLS) method to approximate the unknown field functions and their spatial derivatives. We demonstrate stability of the system using the Ritz and dynamic spectrum along with the phase portrait of time coefficients of the most dominant DMD modes. We estimate the energy contents of the captured modes for various Hartman (Ha) and Rayleigh (Ra) numbers, nanoparticles volume fractions (φ), magnetic field (ξ) and square enclosure angles (γ). The energy content of each mode for Al₂O₃/water nanofluid is associated with the corresponding eigenvalue and discloses its contribution to the total energy. The results show that the above mentioned parameters significantly affect the energy contents of the captured modes.