In this study, a numerical examination of the significance of rotation and changeable gravitational field on the start of nanofluid convective movement in an anisotropic porous medium layer is shown. A model that accounts for the impact of Brownian diffusion and thermophoresis is used for nanofluid, while Darcy’s law is taken for the porous medium. The porous layer is subjected to uniform rotation and changeable downward gravitational field which fluctuates with the height from the layer by linearly or parabolic. The higher-order Galerkin technique is applied to obtain the numerical solutions. The outcomes demonstrate that the rotation parameter TD, the thermal anisotropy parameterh and the gravity variation parameter λ slow the beginning of convective motion, whereas the mechanical anisotropy parameter ξ, the nanoparticle Rayleigh-Darcy number Rnp, the modified diffusivity ratio NAnf and the modified nanofluid Lewis number Lenf quick the start of convective motion. For instance, by rising the gravity variation parameterfrom zero to 1.4, the critical nanofluid thermal Rayleigh-Darcy number Rnf,c and the critical wave numberboost maximum around 133% and 7%, respectively for linear variation of the gravity field, while it were 47% and 2.8% for parabolic variation of the gravity field. It is also observed that the system is more unstable for the parabolic variation of the gravity field.
 B.A. Suleimanov, F. Ismailov, E. Veliyev, Nanofluid for enhanced oil recovery, Journal of Petroleum Science and Engineering, 78(2), 2011, 431-437.
 A. Kasaeian, R. Daneshazarian, O. Mahian, L. Kolsi, A.J. Chamkha, S. Wongwises, I. Pop, Nanofluid flow and heat transfer in porous media: a review of the latest developments, International Journal of Heat and Mass Transfer, 107, 2017, 778-791.
 R.A. Mahdi, H. Mohammed, K. Munisamy, N. Saeid, Review of convection heat transfer and fluid flow in porous media with nanofluid, Renewable and Sustainable Energy Reviews, 41, 2015, 715-734.
 A.I. Alsabery, A.J. Chamkha, H. Saleh, I. Hashim, Natural Convection Flow of a Nanofluid in an Inclined Square Enclosure Partially Filled With a Porous Medium, Scientific Reports, 7, 2017, 2357.
 W.C. Tan, L.H. Saw, H.S. Thiam, J. Xuan, Z. Cai, M.C. Yew, Overview of porous media/metal foam application in fuel cells and solar power systems, Renewable and Sustainable Energy Reviews, 96, 2018, 181-197.
 A. Asadi, A guideline towards easing the decision-making process in selecting an effective nanofluid as a heat transfer fluid, Energy Conversion, and Management, 175, 2018, 1-10.
 A. Asadi, F. Pourfattah, I.M. Szilágyi, M. Afrand, G. Zyla, H.S. Ahn, S. Wongwises, H.M. Nguyen, A. Arabkoohsar, O. Mahian, Effect of Sonication Characteristics on stability, thermophysical properties, and Heat Transfer of nanofluids: A Comprehensive Review, Ultrasonics Sonochemistry, 58, 2019, 104701.
 A. Asadi, I.M. Alarifi, V. Ali, H.M. Nguyen, An experimental investigation on the effects of ultrasonication time on stability and thermal conductivity of MWCNT-water nanofluid: Finding the optimum ultrasonication time, Ultrasonics Sonochemistry, 58, 2019, 104639.
 D.A. Nield, A.V. Kuznetsov, Thermal instability in a porous medium layer saturated by a nanofluid, International Journal of Heat and Mass Transfer, 52, 2009, 5796-5801.
 R. Chand, G.C. Rana, On the onset of thermal convection in rotating nanofluid layer saturating a Darcy–Brinkman porous medium, International Journal of Heat and Mass Transfer, 55, 2012, 5417-5424.
 J. Sharma, U. Gupta, Double-Diffusive Nanofluid Convection in Porous Medium with Rotation: Darcy-Brinkman Model, Procedia Engineering, 127, 2015,783-790.
 D. Yadav, R. Bhargava, G.S. Agrawal, Boundary and internal heat source effects on the onset of Darcy–Brinkman convection in a porous layer saturated by nanofluid, International Journal of Thermal Sciences, 60, 2012, 244-254.
 D. Yadav, J. Lee, H.H. Cho, Brinkman convection induced by purely internal heating in a rotating porous medium layer saturated by a nanofluid, Powder Technology, 286, 2015, 592-601.
 D. Yadav, Electrohydrodynamic Instability in a Heat Generating Porous Layer Saturated by a Dielectric Nanofluid, J. Appl. Fluid Mech., 10, 2017, 763-776.
 D. Yadav, The onset of longitudinal convective rolls in a porous medium saturated by a nanofluid with non-uniform internal heating and chemical reaction, Journal of Thermal Analysis and Calorimetry, 135, 2019, 1107-1117.
 D.A. Nield, A.V. Kuznetsov, Onset of convection with internal heating in a porous medium saturated by a nanofluid, Transport in Porous Media, 99, 2013, 73-83.
 A. Mahajan, M.K. Sharma, The onset of penetrative convection stimulated by internal heating in a magnetic nanofluid saturating a rotating porous medium, Canadian Journal of Physics, 96, 2017, 898-911.
 F. Selimefendigil, H.F. Öztop, Conjugate mixed convection of nanofluid in a cubic enclosure separated with a conductive plate and having an inner rotating cylinder, International Journal of Heat and Mass Transfer, 139, 2019, 1000-1017.
 M. Hadavand, S. Yousefzadeh, O.A. Akbari, F. Pourfattah, H.M. Nguyen, A. Asadi, A numerical investigation on the effects of mixed convection of Ag-water nanofluid inside a sim-circular lid-driven cavity on the temperature of an electronic silicon chip, Applied Thermal Engineering, 162, 2019, 114298.
 D. Yadav, Impact of chemical reaction on the convective heat transport in nanofluid occupying in porous enclosures: A realistic approach, International Journal of Mechanical Sciences, 157-158, 2019, 357-373.
 P. Akbarzadeh, The onset of MHD nanofluid convection between a porous layer in the presence of purely internal heat source and chemical reaction, Journal of Thermal Analysis and Calorimetry, 131, 2018, 2657-2672.
 P. Akbarzadeh, O. Mahian, The onset of nanofluid natural convection inside a porous layer with rough boundaries, Journal of Molecular Liquids, 272, 2018, 344-352.
 D. Yadav, G.S. Agrawal, R. Bhargava, Thermal instability of rotating nanofluid layer, International Journal of Engineering Science, 49, 2011, 1171-1184.
 D. Yadav, R. Bhargava, G.S. Agrawal, Numerical solution of a thermal instability problem in a rotating nanofluid layer, International Journal of Heat and Mass Transfer, 63, 2013, 313-322.
 D. Yadav, G.S. Agrawal, R. Bhargava, Onset of double-diffusive nanofluid convection in a layer of saturated porous medium with thermal conductivity and viscosity variation, Journal of Porous Media, 16, 2013, 105-121.
 D. Yadav, R. Bhargava, G.S. Agrawal, Thermal instability in a nanofluid layer with a vertical magnetic field, Journal of Engineering Mathematics, 80, 2013, 147-164.
 D. Yadav, R. Bhargava, G.S. Agrawal, G.S. Hwang, J. Lee, M.C. Kim, Magneto‐convection in a rotating layer of nanofluid, Asia‐Pacific Journal of Chemical Engineering, 9, 2014, 663-677.
 D. Yadav, Numerical solution of the onset of natural convection in a rotating nanofluid layer induced by purely internal heating, International Journal of Applied and Computational Mathematics, 3, 2017, 3663-3681.
 D. Yadav, R.A. Mohamed, J. Lee, H.H. Cho, Thermal convection in a Kuvshiniski viscoelastic nanofluid saturated porous layer, Ain Shams Engineering Journal, 8, 2017, 613-621.
 D. Yadav, A. Wakif, Z. Boulahia, R. Sehaqui, Numerical Examination of the Thermo-Electro-Hydrodynamic Convection in a Horizontal Dielectric Nanofluid Layer Using the Power Series Method, Journal of Nanofluids, 8, 2019, 1-15.
 D. Yadav, The effect of pulsating throughflow on the onset of magneto convection in a layer of nanofluid confined within a Hele-Shaw cell, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 233, 2019, 1074–1085.
 R. Chand, D. Yadav, G.C. Rana, Electrothermo convection in a horizontal layer of rotating nanofluid, International Journal of Nanoparticles, 8, 2015, 241-261.
 R. Chand, G.C. Rana, D. Yadav, Electrothermo convection in a porous medium saturated by nanofluid, J. Appl. Fluid Mech., 9, 2016, 1081-1088.
 R. Chand, G.C. Rana, D. Yadav, Thermal Instability in a Layer of Couple Stress Nanofluid Saturated Porous Medium, Journal of Theoretical and Applied Mechanics, 47, 2017, 69-84.
 R. Chand, D. Yadav, G.C. Rana, Thermal instability of couple-stress nanofluid with vertical rotation in a porous medium, Journal of Porous Media, 20, 2017, 635-648.
 M. Sheikholeslami, D.D. Ganji, Heated permeable stretching surface in a porous medium using Nanofluids, Journal of Applied Fluid Mechanics, 7, 2014, 535-542.
 F. Selimefendigil, H.F. Öztop, Effects of nanoparticle shape on slot-jet impingement cooling of a corrugated surface with nanofluids, Journal of Thermal Science and Engineering Applications, 9, 2017, 021016.
 F. Selimefendigil, H.F. Öztop, Forced convection in a branching channel with partly elastic walls and inner L-shaped conductive obstacle under the influence of magnetic field, International Journal of Heat and Mass Transfer, 144, 2019, 118598.
 F. Selimefendigil, H.F. Öztop, MHD Pulsating forced convection of nanofluid over parallel plates with blocks in a channel, International Journal of Mechanical Sciences, 157-158, 2019, 726-740.
 J.C. Umavathi, D. Yadav, M.B. Mohite, Linear and nonlinear stability analyses of double-diffusive convection in a porous medium layer saturated in a Maxwell nanofluid with variable viscosity and conductivity, Elixir Mech. Eng., 79, 2015, 30407-30426.
 I.S. Shivakumara, M. Dhananjaya, C.-O. Ng, Thermal convective instability in an Oldroyd-B nanofluid saturated porous layer, International Journal of Heat and Mass Transfer, 84, 2015, 167-177.
 P. Olson, P.G. Silver, R.W. Carlson, The large-scale structure of convection in the Earth's mantle, Nature, 344, 1990, 209.
 M. Fedi, F. Cella, M.D Antonio, G. Florio, V. Paoletti, V. Morra, Gravity modeling finds a large magma body in the deep crust below the Gulf of Naples, Italy, Scientific Reports, 8, 2018, 8229.
 C. Hirt, S. Claessens, T. Fecher, M. Kuhn, R. Pail, M. Rexer, New ultrahigh‐resolution picture of Earth's gravity field, Geophysical Research Letters, 40, 2013, 4279-4283.
 B.D. Tapley, S. Bettadpur, J.C. Ries, P.F. Thompson, M.M. Watkins, GRACE measurements of mass variability in the Earth system, Science, 305, 2004, 503-505.
 S.M. Alex, P.R. Patil, Effect of variable gravity field on soret driven thermosolutal convection in a porous medium, International Communications in Heat and Mass Transfer, 28, 2001, 509-518.
 S.M. Alex, P.R. Patil, Effect of a variable gravity field on convection in an anisotropic porous medium with internal heat source and inclined temperature gradient, Journal of Heat Transfer, 124, 2002, 144-150.
 S. Govender, Coriolis effect on convection in a rotating porous layer subjected to variable gravity, Transport in Porous Media, 98, 2013, 443-450.
 U.S. Mahabaleshwar, D. Basavaraja, S. Wang, G. Lorenzini, E. Lorenzini, Convection in a porous medium with variable internal heat source and variable gravity, International Journal of Heat and Mass Transfer, 111, 2017, 651-656.
 D. Yadav, Numerical Investigation of the Combined Impact of Variable Gravity Field and Throughflow on the Onset of Convective Motion in a Porous Medium layer, International Communications in Heat and Mass Transfer,108, 2019, 104274.
 X. Liu, J. Pu, L. Wang, Q. Xue, Novel DLC/ionic liquid/graphene nanocomposite coatings towards high-vacuum related space applications, Journal of Materials Chemistry A, 1, 2013, 3797-3809.
 K.V. Wong, O. De Leon, Applications of nanofluids: current and future, in Nanotechnology and Energy, Jenny Stanford Publishing, 2017, pp. 105-132.
 D. Sui, V.H. Langåker, Z. Yu, Investigation of thermophysical properties of Nanofluids for application in geothermal energy, Energy Procedia, 105, 2017, 5055-5060.
 Q. Li, J. Wang, J. Wang, J. Baleta, C. Min, B. Sundén, Effects of gravity and variable thermal properties on nanofluid convective heat transfer using connected and unconnected walls, Energy Conversion and Management, 171, 2018, 1440-1448.
 R. Chand, G.C. Rana, S. Kumar, Variable gravity effects on thermal instability of nanofluid in anisotropic porous medium, International Journal of Applied Mechanics and Engineering, 18, 2013, 631-642.
 A. Mahajan, M.K. Sharma, Convection in a magnetic nanofluid saturating a porous medium under the influence of a variable gravity field, Engineering Science and Technology, an International Journal, 21, 2018, 439-450.
 D.A. Nield, A.V. Kuznetsov, Thermal instability in a porous medium layer saturated by a nanofluid: a revised model, International Journal of Heat and Mass Transfer, 68, 2014, 211-214.
 D. Yadav, D. Nam, J. Lee, The onset of transient Soret-driven MHD convection confined within a Hele-Shaw cell with nanoparticles suspension, Journal of the Taiwan Institute of Chemical Engineers, 58, 2016, 235-244.
 J. Buongiorno, Convective transport in nanofluids, Journal of Heat Transfer, 128, 2006, 240-250.
 D.A. Nield, A.V. Kuznetsov, The onset of convection in a horizontal nanofluid layer of finite depth, European Journal of Mechanics - B/Fluids, 29, 2010, 217-223.
 D. Yadav, Hydrodynamic and hydromagnetic instability in nanofluids, Lap Lambert Academic Publishing, 2014.
 P.G. Siddheshwar, C. Kanchana, Unicellular unsteady Rayleigh–Bénard convection in Newtonian liquids and Newtonian nanoliquids occupying enclosures: new findings, International Journal of Mechanical Sciences, 131, 2017, 1061-1072.
 M. Bouhalleb, H. Abbassi, Natural convection of nanofluids in enclosures with low aspect ratios, International Journal of Hydrogen Energy, 39, 2014, 15275-15286.
 S. Rionero, B. Straughan, Convection in a porous medium with internal heat source and variable gravity effects, International Journal of Engineering Science, 28, 1990, 497-503.
 M.S. Malashetty, M. Swamy, The effect of rotation on the onset of convection in a horizontal anisotropic porous layer, International Journal of Thermal Sciences, 46, 2007, 1023-1032.