Publication de 6 numéros par an
ISSN Imprimer: 1940-2503
ISSN En ligne: 1940-2554
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THE EFFECT OF CHANGEABLE GRAVITY FIELD ON THE STABILITY OF CONVECTION IN A POROUS LAYER FILLED WITH NANOFLUID: BRINKMAN MODEL
RÉSUMÉ
The onset of convective instability in a horizontal nanofluid filled porous layer is investigated for the changeable gravity field. The Buongiorno model for the nanofluid and the Brinkman model for the flow through the porous layer are employed. Three cases of boundaries viz., free−free, rigid−free, and rigid−rigid, are considered in this observation. Also, linear, quadratic, cubic, and exponentially varying gravity fields have been taken to present this problem. The linear stability of the basic state is studied for the normal mode perturbations and, the solution for the corresponding eigenvalue problem is obtained using the bvp4c routine inMATLAB. The critical Rayleigh number and corresponding wavenumber have been calculated and shown graphically for various aspects due to the influence of the governing parameters. It is noted that the basic density Rayleigh number, Lewis number, and modified diffusivity ratio advance the convective motion; whereas the Darcy number and gravity variation parameter postpone the onset of convection. When both boundaries are rigid or free, the modified particle density increment acts as a stabilizing factor; however, when the lower boundary is rigid and the upper boundary is free, it plays the role as a destabilising factor. The flow in a cubic varying gravity field with free-free boundaries is more unstable; whereas the flow in an exponentially varying gravity field with rigid-rigid boundaries is more stable.
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Alloui, Z., Vasseur, P., and Reggio, M., Natural Convection of Nanofluids in a Shallow Cavity Heated from below, Int. J. Thermal Sci., vol. 50, no. 3, pp. 385-393, 2011.
-
Barman, D. and Srinivasacharya, D., The Variable Gravity Field and Viscous Dissipation Effects on the Convective Instability in a Porous Layer with Throughflow: Brinkman Model, J. Porous Media, vol. 24, no. 6, pp. 1-13, 2021.
-
Buongiorno, J., Convective Transport in Nanofluids, J. Heat Transf., vol. 128, no. 3, pp. 240-250, 2006.
-
Chand, R. and Rana, G.C., On the Onset of Thermal Convection in Rotating Nanofluid Layer Saturating a Darcy-Brinkman Porous Medium, Int. J. Heat Mass Transf., vol. 55, nos. 21-22, pp. 5417-5424, 2012.
-
Chand, R., Rana, G.C., and Kango, S.K., Effect of Variable Gravity on Thermal Instability of Rotating Nanofluid in Porous Medium, FME Transact., vol. 43, no. 1, pp. 62-69, 2015.
-
Chand, R., Rana, G.C., and Kumar, S., Variable Gravity Effects on Thermal Instability of Nanofluid in Anisotropic PorousMedium, Int. J. Appl. Mech. Eng., vol. 18, no. 3, pp. 631-642, 2013.
-
Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, North Chelmsford, MA: Courier Corporation, 2013.
-
Choi, S.U.S. and Eastman, J.A., Enhancing Thermal Conductivity of Fluids with Nanoparticles, Tech. Rep., Argonne National Lab., Lemont, IL, 1995.
-
Cordell, L., Gravity Analysis Using an Exponential Density-Depth Function, San Jacinto Graben, California, Geophys., vol. 38, no. 4, pp. 684-690, 1973.
-
Das, S.K., Choi, S.U.S., Yu, W., and Pradeep, T., Nanofluids: Science and Technology, Hoboken, NJ: Wiley, 2007.
-
Guo, J. and Kaloni, P.N., Double-Diffusive Convection in a Porous Medium, Nonlinear Stability and the Brinkman Effect, Stud. Appl. Math., vol. 94, no. 3, pp. 341-358, 1995.
-
Horton, C.W. and Rogers, F.T., Convection Currents in a Porous Medium, J. Appl. Phys., vol. 16, no. 6, pp. 367-370, 1945.
-
Kuznetsov, A.V., Nanofluid Bioconvection inWater-Based Suspensions Containing Nanoparticles and Oxytactic Microorganisms: Oscillatory Instability, Nanoscale Res. Lett., vol. 6, no. 1, pp. 1-13, 2011.
-
Kuznetsov, A.V. and Nield, D.A., The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated PorousMedium, Transp. Porous Media, vol. 85, no. 3, pp. 941-951, 2010a.
-
Kuznetsov, A.V. and Nield, D.A., Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model, Transp. Porous Media, vol. 81, no. 3, pp. 409-422, 2010b.
-
Lapwood, E.R., Convection of a Fluid in a Porous Medium, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 44, Cambridge, UK: Cambridge University Press, pp. 508-521, 1948.
-
Li, Q., Wang, J., Wang, J., Baleta, J., Min, C., and Sunden, B., Effects of Gravity and Variable Thermal Properties on Nanofluid Convective Heat Transfer Using Connected and UnconnectedWalls, Energy Convers. Manag., vol. 171, pp. 1440-1448, 2018.
-
Liu, X., Pu, J., Wang, L., and Xue, Q., Novel DLC/Ionic Liquid/GrapheneNanocomposite Coatings towards High-Vacuum Related Space Applications, J. Mater. Chem. A, vol. 1, pp. 3797-3809, 2013.
-
Matsuda, H., Ebata, A., Teramae, K., and Hishinuma,N., Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles, Netsu Bussei, vol. 7, pp. 227-233, 1993.
-
Nield, D.A. and Kuznetsov, A.V., Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid, Int. J. Heat Mass Transf., vol. 52, nos. 25-26, pp. 5796-5801, 2009.
-
Nield, D.A. and Kuznetsov, A.V., The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid, Transp. Porous Media, vol. 87, no. 3, pp. 765-775, 2011.
-
Nield, D.A. and Kuznetsov, A.V., Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: A Revised Model, Int. J. Heat Mass Transf., vol. 68, pp. 211-214, 2014.
-
Pradhan, G.K. and Samal, P.C., Thermal Stability of a Fluid Layer Under Variable Body Forces, J. Math. Anal. Appl., vol. 122, no. 2, pp. 487-495, 1987.
-
Rana, G.C. and Chand, R., Onset of Thermal Convection in a Rotating Nanofluid Layer Saturating a Darcy-Brinkman Porous Medium: A More Realistic Model, J. Porous Media, vol. 18, no. 6, pp. 629-635, 2015.
-
Rionero, S. and Straughan, B., Convection in a Porous Medium with Internal Heat Source and Variable Gravity Effects, Int. J. Eng. Sci., vol. 28, no. 6, pp. 497-503, 1990.
-
Shivakumara, I.S. and Dhananjaya, M., Penetrative Brinkman Convection in an Anisotropic Porous Layer Saturated by a Nanofluid, Ain Shams Eng J., vol. 6, no. 2, pp. 703-713, 2015.
-
Srinivasacharya, D. and Barman, D., The Variable Gravity Field and Viscous Dissipation Effects on the Double Diffusive and Soret Driven Convective Instability in a Porous Layer with Throughflow, Int. Commun. Heat Mass Transf., vol. 120, p. 105050, 2021.
-
Sui, D., Langaker, V.H., and Yu, Z., Investigation of Thermophysical Properties of Nanofluids for Application in Geothermal Energy, Energy Proc., vol. 105, pp. 5055-5060, 2017.
-
Suma, S.P. and Gangadharaiah, Y.H., Effect of Throughflow and Variable Gravity Field on Thermal Convection in a Porous Layer, Int. J. Eng. Sci. Tech., vol. 3, pp. 7657-7668, 2011.
-
Tzou, D.Y., Instability of Nanofluids in Natural Convection, J. Heat Transf., vol. 130, no. 7, p. 072401, 2008a.
-
Tzou, D.Y., Thermal Instability of Nanofluids in Natural Convection, Int. J. Heat Mass Transf., vol. 51, nos. 11-12, pp. 2967-2979, 2008b.
-
Wong, K.V. and De Leon, O., Applications of Nanofluids: Current and Future, Adv. Mech. Eng., vol. 2010, 2010.
-
Yadav, D., Numerical Investigation of the Combined Impact of Variable Gravity Field and Throughflowon the Onset of Convective Motion in a Porous Medium layer, Int. Commun. Heat Mass Transf., vol. 108, p. 104274, 2019.
-
Yadav, D., Numerical Examination of the Thermal Instability in an Anisotropic Porous Medium Layer Subjected to Rotation and Variable Gravity Field, Spec. Topics Rev. Porous Media: Int. J., vol. 11, no. 4, pp. 395-407, 2020a.
-
Yadav, D., Numerical Solution of the Onset of Buoyancy-Driven Nanofluid Convective Motion in an Anisotropic PorousMedium Layer with Variable Gravity and Internal Heating, Heat Transf., vol. 49, no. 3, pp. 1170-1191, 2020b.
-
Yadav, D., Chu, Y.M., and Li, Z., Examination of the Nanofluid Convective Instability of Vertical Constant Throughflow in a Porous Medium Layer with Variable Gravity, Appl. Nanosci., pp. 1-14, 2021.