O. Oehlsen, S.I. Cervantes-Ramírez, P. Cervantes-Avilés, I.A. Medina-Velo, Approaches on ferrofluid synthesis and applications: current status and future perspectives, ACS omega, 7(4) (2022) 3134-3150.
 R.E. Rosensweig, Ferrohydrodynamics, Courier Corporation, 2013.
 H. Aminfar, M. Mohammadpourfard, Y.N. Kahnamouei, A 3D numerical simulation of mixed convection of a magnetic nanofluid in the presence of non-uniform magnetic field in a vertical tube using two phase mixture model, Journal of Magnetism and Magnetic Materials, 323(15) (2011) 1963-1972.
 H. Aminfar, M. Mohammadpourfard, S.A. Zonouzi, Numerical study of the ferrofluid flow and heat transfer through a rectangular duct in the presence of a non-uniform transverse magnetic field, Journal of Magnetism and Magnetic materials, 327 (2013) 31-42.
 M. Sheikholeslami, M. Seyednezhad, Nanofluid heat transfer in a permeable enclosure in presence of variable magnetic field by means of CVFEM, International Journal of Heat and Mass Transfer, 114 (2017) 1169-1180.
 M. Mohammadpourfard, H. Aminfar, S. Ahangar Zonouzi, Numerical investigation of the magnetic field effects on the entropy generation and heat transfer in a nanofluid filled cavity with natural convection, Heat Transfer—Asian Research, 46(5) (2017) 409-433.
 G. Ashwinkumar, C. Sulochana, S. Samrat, Effect of the aligned magnetic field on the boundary layer analysis of magnetic-nanofluid over a semi-infinite vertical plate with ferrous nanoparticles, Multidiscipline Modeling in Materials and Structures, 14(3) (2018) 497-515.
 M.B. Gerdroodbary, M. Sheikholeslami, S.V. Mousavi, A. Anazadehsayed, R. Moradi, The influence of non-uniform magnetic field on heat transfer intensification of ferrofluid inside a T-junction, Chemical Engineering and Processing-Process Intensification, 123 (2018) 58-66.
 A. Khosravi, M. Malekan, M.E. Assad, Numerical analysis of magnetic field effects on the heat transfer enhancement in ferrofluids for a parabolic trough solar collector, Renewable Energy, 134 (2019) 54-63.
 P.S. Szabo, W.-G. Früh, The transition from natural convection to thermomagnetic convection of a magnetic fluid in a non-uniform magnetic field, Journal of Magnetism and Magnetic Materials, 447 (2018) 116-123.
 T. Javed, M.A. Siddiqui, Effect of MHD on heat transfer through ferrofluid inside a square cavity containing obstacle/heat source, International Journal of Thermal Sciences, 125 (2018) 419-427.
 W. Wrobel, E. Fornalik-Wajs, J. Szmyd, Experimental and numerical analysis of thermo-magnetic convection in a vertical annular enclosure, International Journal of Heat and Fluid Flow, 31(6) (2010) 1019-1031.
 M. Lee, Y.-J. Kim, Effect of non-uniform magnetic fields on the characteristics of ferrofluid flow in a square enclosure, Journal of Magnetism and Magnetic Materials, 506 (2020) 166697.
 S.Y. Motlagh, E. Golab, A.N. Sadr, Two-phase modeling of the free convection of nanofluid inside the inclined porous semi-annulus enclosure, International Journal of Mechanical Sciences, 164 (2019) 105183.
 H. Soltanipour, A. Gharegöz, M.B. Oskooee, Numerical study of magnetic field effect on the ferrofluid forced convection and entropy generation in a curved pipe, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 42(3) (2020) 135.
 S. Banik, A.S. Mirja, N. Biswas, R. Ganguly, Entropy analysis during heat dissipation via thermomagnetic convection in a ferrofluid-filled enclosure, International Communications in Heat and Mass Transfer, 138 (2022) 106323.
 K. Ayoubi Ayoubloo, S. Yazdani, M. Sheremet, O. Younis, M. Ghalambaz, Ferro-hydrodynamic induced convection flow and heat transfer of nanofluids in a corrugated wall enclosure, Journal of Taibah University for Science, 17(1) (2023) 2215675.
 B. Iftikhar, M.A. Siddiqui, T. Javed, Computational analysis of heat transfer via heatlines for MHD natural convection ferrofluid flow inside the U-shaped cavity, The European Physical Journal Plus, 138(2) (2023) 164.
 L. Shi, W. Tao, N. Zheng, T. Zhou, Z. Sun, Numerical study of convective heat transfer and particle distribution subject to magneto-static field in a square cavity, International Journal of Thermal Sciences, 185 (2023) 108081.
 D.D. Dixit, A. Pattamatta, Effect of uniform external magnetic-field on natural convection heat transfer in a cubical cavity filled with magnetic nano-dispersion, International Journal of Heat and Mass Transfer, 146 (2020) 118828.
 M. Goodarzi, M. Safaei, K. Vafai, G. Ahmadi, M. Dahari, S. Kazi, N. Jomhari, Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model, International Journal of Thermal Sciences, 75 (2014) 204-220.
 H. Abdi, S.Y. Motlagh, H. Soltanipour, Study of magnetic nanofluid flow in a square cavity under the magnetic field of a wire carrying the electric current in turbulence regime, Results in Physics, 18 (2020) 103224.
 H. Sajjadi, M. Beigzadeh Abbassi, G.R. Kefayati, Lattice Boltzmann simulation of turbulent natural convection in a square cavity using Cu/water nanofluid, Journal of Mechanical Science and Technology, 27 (2013) 2341-2349.
 A.K. Kareem, S. Gao, A comparison study of mixed convection heat transfer of turbulent nanofluid flow in a three-dimensional lid-driven enclosure with a clockwise versus an anticlockwise rotating cylinder, International Communications in Heat and Mass Transfer, 90 (2018) 44-55.
 Y. Cao, Y. Bai, J. Du, S. Rashidi, A computational fluid dynamics investigation on the effect of the angular velocities of hot and cold turbulator cylinders on the heat transfer characteristics of nanofluid flows within a porous cavity, Journal of Energy Resources Technology, 142(11) (2020) 112104.
 H. Ghodsinezhad, M. Sharifpur, J.P. Meyer, Experimental investigation on cavity flow natural convection of Al2O3–water nanofluids, International Communications in Heat and Mass Transfer, 76 (2016) 316-324.
 A.P. Patel, D. Bhatnagar, R.S. Kumar, S. Prabhu, Numerical study on turbulent natural convection and radiation heat transfer of nanofluids in a differentially heated square enclosure, Journal of Thermal Analysis and Calorimetry, (2020) 1-10.
 R. Harish, R. Sivakumar, Turbulent thermal convection of nanofluids in cubical enclosure using two-phase mixture model, International Journal of Mechanical Sciences, 190 (2021) 106033.
 R. Harish, R. Sivakumar, Effects of nanoparticle dispersion on turbulent mixed convection flows in cubical enclosure considering Brownian motion and thermophoresis, Powder Technology, 378 (2021) 303-316.
 E. Mignot, W. Brevis, Coherent turbulent structures within open-channel lateral cavities, Journal of Hydraulic Engineering, 146(2) (2020) 04019066.
 G. Janiga, Large-eddy simulation and 3D proper orthogonal decomposition of the hydrodynamics in a stirred tank, Chemical Engineering Science, 201 (2019) 132-144.
 P.S. Mahapatra, S. Chatterjee, A. Mukhopadhyay, N.K. Manna, K. Ghosh, Proper orthogonal decomposition of thermally-induced flow structure in an enclosure with alternately active localized heat sources, International Journal of Heat and Mass Transfer, 94 (2016) 373-379.
 B. Podvin, A. Sergent, Proper orthogonal decomposition investigation of turbulent Rayleigh-Bénard convection in a rectangular cavity, Physics of Fluids, 24(10) (2012).
 S.Y. Motlagh, S. Taghizadeh, POD analysis of low Reynolds turbulent porous channel flow, International Journal of Heat and Fluid Flow, 61 (2016) 665-676.
 E. Tzirtzilakis, M. Xenos, Biomagnetic fluid flow in a driven cavity, Meccanica, 48 (2013) 187-200.
 R.E. Rosensweig, Heating magnetic fluid with alternating magnetic field, Journal of magnetism and magnetic materials, 252 (2002) 370-374.
 J. Buongiorno, Convective Transport in Nanofluids, Journal of Heat Transfer, 128(3) (2005) 240-250.
 M.I. Shliomis, Convective Instability of Magnetized Ferrofluids: Influence of Magnetophoresis and Soret Effect, in: W. Köhler, S. Wiegand (Eds.) Thermal Nonequilibrium Phenomena in Fluid Mixtures, Springer Berlin Heidelberg, Berlin, Heidelberg, 2002, pp. 355-371.
 M.I. Shliomis, B.L. Smorodin, Convective instability of magnetized ferrofluids, Journal of Magnetism and Magnetic Materials, 252 (2002) 197-202.
 J. Smagorinsky, General circulation experiments with the primitive equations: I. The basic experiment, Monthly weather review, 91(3) (1963) 99-164.
 S.Y. Motlagh, H. Soltanipour, Natural convection of Al2O3-water nanofluid in an inclined cavity using Buongiorno's two-phase model, International Journal of Thermal Sciences, 111 (2017) 310-320.
 H. Soltanipour, Two-phase simulation of magnetic field effect on the ferrofluid forced convection in a pipe considering Brownian diffusion, thermophoresis, and magnetophoresis, The European Physical Journal Plus, 135(9) (2020) 1-23.
 B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Experimental Heat Transfer an International Journal, 11(2) (1998) 151-170.
 Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, International Journal of heat and Mass transfer, 43(19) (2000) 3701-3707.
 J.C. Maxwell, A treatise on electricity and magnetism, Clarendon press, 1873.
 H. Weller, C. Greenshields, C. de Rouvray, The OpenFOAM Foundation Ltd, OpenFOAM. https://openfoam
. org, (2016).
 J. Jeong, F. Hussain, On the identification of a vortex, Journal of fluid mechanics, 285 (1995) 69-94.
 M. Farge, G. Pellegrino, K. Schneider, Coherent vortex extraction in 3D turbulent flows using orthogonal wavelets, Physical Review Letters, 87(5) (2001) 054501.
 J.L. Lumley, The structure of inhomogeneous turbulent flows, Atmospheric turbulence and radio wave propagation, (1967) 166-178.
 C. Ho, W. Liu, Y. Chang, C. Lin, Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: An experimental study, International Journal of Thermal Sciences, 49(8) (2010) 1345-1353.
 G.A. Sheikhzadeh, M. Dastmalchi, H. Khorasanizadeh, Effects of nanoparticles transport mechanisms on Al2O3–water nanofluid natural convection in a square enclosure, International Journal of Thermal Sciences, 66 (2013) 51-62.
 K.W. Song, T. Tagawa, Thermomagnetic convection of oxygen in a square enclosure under non-uniform magnetic field, International Journal of Thermal Sciences, 125 (2018) 52-65.
 F. Ampofo, T. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, International Journal of Heat and Mass Transfer, 46(19) (2003) 3551-3572.
 R. Kumar, A. Dewan, A study of LES–SGS closure models applied to a square buoyant cavity, International Journal of Heat and Mass Transfer, 98 (2016) 164-175.
 R. Puragliesi, E. Leriche, Proper orthogonal decomposition of a fully confined cubical differentially heated cavity flow at Rayleigh number Ra= 109, Computers & fluids, 61 (2012) 14-20.
 L.-H. Feng, J.-J. Wang, C. Pan, Proper orthogonal decomposition analysis of vortex dynamics of a circular cylinder under synthetic jet control, Physics of Fluids, 23(1) (2011).