Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
Special Topics & Reviews in Porous Media: An International Journal
ESCI SJR: 0.277 SNIP: 0.52 CiteScore™: 1.3

ISSN Imprimir: 2151-4798
ISSN On-line: 2151-562X

Special Topics & Reviews in Porous Media: An International Journal

DOI: 10.1615/SpecialTopicsRevPorousMedia.2020030166
pages 539-553

ON THE ONSET OF ELECTROHYDRODYNAMIC INSTABILITY IN A COUPLE-STRESS NANOFLUID SATURATING A POROUS MEDIUM

Gian C. Rana
Department of Mathematics, NSCBM Government College, Hamirpur-177005, Himachal Pradesh, India
Ramesh Chand
Department of Mathematics, Government Degree College Sugh-Bhatoli, Himachal Pradesh, India
Hemlata Saxena
Department of Mathematics, Career Point University, Kota, Rajasthan, India
Poonam Kumari Gautam
Department of Mathematics, Career Point University, Kota, Rajasthan, India

RESUMO

In this paper, electrohydrodynamic thermal instability in a horizontal layer of an elastico-viscous nanofluid saturating a porous medium under the action of a vertical AC electric field is investigated. A couple-stress fluid model is used to describe the rheological behavior of nanofluid, and for a porous medium the Darcy model is employed. The model used for nanofluid includes the effects of thermophoresis and Brownian diffusion. Nanoparticle flux is assumed to be zero on the boundaries, and the temperature can be imposed on the boundaries. The problem is solved by applying linear stability analysis based upon perturbation theory and normal mode analysis for isothermal free-free boundaries analytically and numerically. The effects of the couple-stress parameter, AC electric field, Lewis number, modified diffusivity ratio, nanoparticle Rayleigh number, and medium porosity have been discussed for the case of stationary convection. Oscillatory convection does not exist under the present boundary conditions.

Referências

  1. Buongiorno, J., Convective Transport in Nanofluids, ASME J. Heat Transf., vol. 128, pp. 240-250,2006. Castellanos, A., Electrohydrodynamics, New York: Springer-Verlag Wien, 1998.

  2. 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, pp. 5417-5424,2012a.

  3. Chand, R. and Rana, G.C., Thermal Instability of Rivlin-Ericksen Elastico-Viscous Nanofluid Saturated by a Porous Medium, J. Fluids Eng., vol. 134, p. 121203,2012b.

  4. Chand, R. and Rana, G.C., Electrothermo Convection of Rotating Nanofluid in Brinkman Porous Medium, Spec. Topics Rev. Porous Media: Int. J, vol. 7, pp. 181-194,2016.

  5. Chand, R. and Rana, G.C., Thermal Instability of Maxwell Visco-Elastic Nanofluid in a Porous Medium with Thermal Conductivity and Viscosity Variation, Structural Integrity Life, vol. 17, pp. 113-120,2017.

  6. Chand, R.,Kango, S.K., and Rana, G.C., Thermal Instability in Anisotropic Porous Medium Saturated by aNanofluid-A Realistic Approach, NSNTAIJ, vol. 8, pp. 445-453,2014.

  7. Chand, R., Rana, G.C., and Yadav, D., Electrothermo Convection in a Porous Medium Saturated by Nanofluid, J. Appl. Fluid Mech., vol. 9, pp. 1081-1088,2016.

  8. Chand, R., Rana, G.C., and Yadav, D., Thermal Instability in a Layer of Couple-Stress Nanofluid Saturated Porous Medium, J. Theor. Appl. Mech, vol. 47, pp. 69-84,2017.

  9. Chandrasekhar, S., Hydrodynamic andHydromagnetic Stability, New York: Dover, 1961.

  10. Choi, S., Enhancing Thermal Conductivity of Fluids with Nanoparticles, in Developments and Applications of Non-Newtonian Flows, D.A. Siginer and H.P. Wang, Eds., pp. 99-105,1995.

  11. Jaimala, V. and Kumar, V., Thermal Convection in a Couple-Stress Fluid in the Presence of Horizontal Magnetic Field with Hall Currents, Appl. Appl. Math.: Int. J., vol. 8, pp. 161-177,2013.

  12. Jones, T.B., Electrohydrodynamically Enhanced Heat Transfer in Liquids-A Review, Adv. Heat Transf., vol. 14, pp. 107-148, 1979.

  13. 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, pp. 409-422,2009.

  14. Landau, L.D., Electrodynamics of Continuous Media, New York, NY: Oxford, 1960.

  15. Lapwood, E.R., Convection of a Fluid in a Porous Medium, Math. Proc. Camb. Phil. Soc., vol. 44, pp. 508-521,1948.

  16. Malashetty, M.S. and Basavaraja, D., Effect of Thermal/Gravity Modulation on the Onset of Rayleigh-Benard Convection in a Couple-Stress Fluid, I. J. Transp. Phenomena, vol. 7, pp. 31-44,2005.

  17. Melcher, J.R. and Taylor, G.I., Electrohydrodynamics: A Review of the Role of Interfacial Shear Stresses, Annu. Rev. Fluid Mech, vol. 1,pp. 111-146,1969.

  18. Othman, M.I., Electrohydrodynamic Instability of a Rotating Layer of a Viscoelastic Fluid Heated from below, Zeitschriftfur Angewandte Mathematik und Physik, vol. 55, pp. 468-482,2004.

  19. 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, pp. 5796-5801,2009.

  20. 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.

  21. Rana, G.C., Chand, R., and Sharma, V, Onset of Electrohydrodynamic Instability of a Rotating Viscoelastic Fluid Layer Saturating a Porous Medium, Acta Technica, vol. 61, pp. 31-44,2016a.

  22. Rana, G.C., Chand, R., and Sharma, V., On the Onset of Instability of a Viscoelastic Fluid Saturating a Porous Medium in Elec-trohydrodynamics, Rev. Cubana Fis., vol. 33, pp. 89-94,2016b.

  23. Rana, G.C., Chand, R., and Yadav, D., The Onset of Electrohydrodynamic Instability of an Elastico-Viscous Walters' (Model B') Dielectric Fluid Layer, FME Transact, vol. 43, pp. 154-160,2015.

  24. Roberts, P.H., Electrohydrodynamic Convection, Quart. J. Mech. Appl. Math., vol. 22, pp. 211-220,1969.

  25. Sharma, R.C. and Thakur, K.D., Couple-Stress Fluid Heated from below in Hydromagnetics, Czech. J. Phys, vol. 50, pp. 753-758, 2000.

  26. Sheu, L.J., Thermal Instability in a Porous Medium Layer Saturated with a Viscoelastic Nanofluid, Transp. Porous Media, vol. 88, pp. 461-477,2011.

  27. Shivakumara, I.S., Akkanagamma, M., and Chiu-On, N., Electrohydrodynamic Instability of a Rotating Couple-Stress Dielectric FluidLayer, Int. J. HeatMass Transf., vol. 62, pp. 761-771,2013.

  28. Shivakumara, I.S., Nagashree, M.S., and Hemalatha, K., Electroconvective Instability in a Heat Generating Dielectric Fluid Layer, Int. Commun. HeatMass Transf, vol. 34, pp. 1041-1047,2007.

  29. Stokes, V.K., Couple-Stress in Fluids, Phys. Fluids, vol. 9, pp. 1709-1715,1966.

  30. Takashima, M., The Effect of Rotation on Electrohydrodynamic Instability, Can. J. Phys., vol. 54, pp. 342-347,2011.

  31. Takashima, M. and Ghosh, A.K., Electrohydrodynamic Instability in a Viscoelastic Liquid Layer, J. Phys. Soc. Japan, vol. 47, pp. 1717-1722,1979.

  32. Takashima, M. and Hamabata, H., The Stability of Natural Convection in a Vertical Layer of Dielectric Fluid in the Presence of a Horizontal AC Electric Field, J. Phys. Soc. Japan, vol. 53, pp. 1728-1736,1984.

  33. Tzou, D.Y., Thermal Instability of Nanofluids in Natural Convection, Int. J. Heat Mass Transf., vol. 51, pp. 2967-2979,2008a.

  34. Tzou, D.Y., Instability of Nanofluids in Natural Convection, ASMEJ. Heat Transf, vol. 130, pp. 072401-072410,2008b.

  35. Walicki, E. and Walicka, A., Inertial Effect in the Squeeze Film of Couple-Stress Fluids in Biological Bearings, Int. J. Appl. Mech. Eng., vol. 4, pp. 363-373,1999.

  36. Wooding, R.A., Rayleigh Instability of a Thermal Boundary Layer in Flow through a Porous Medium, J. Fluid Mech., vol. 9, pp. 183-192,1960.

  37. Yadav, D., The Effect of Pulsating Throughflow on the Onset of Electro-Thermo-Convection in a Horizontal Porous Medium Saturated by a Dielectric Nanofluid, J. Appl. Fluid Mech, vol. 11, pp. 1679-1689,2018.

  38. Yadav, D., The Onset of Longitudinal Convective Rolls in a Porous Medium Saturated by a Nanofluid with Non-Uniform Internal Heating and Chemical Reaction, J. Therm. Anal. Calorim., vol. 135, pp. 1107-1117,2019.

  39. Yadav, D., Bhargava, R., and Agrawal, G.S., Numerical Solution of a Thermal Instability Problem in a Rotating Nanofluid Layer, Int. J. HeatMass Transf., vol. 63, pp. 313-322,2013.

  40. Yadav, D. and Lee J., The Onset of MHD Nanofluid Convection with Hall Current Effect, Euro. Phys. J. Plus, vol. 130, pp. 162-184,2015a.

  41. Yadav, D., Cho, H.H., and Lee, J., Brinkman Convection Induced by Purely Internal Heating in a Rotating Porous Medium Layer Saturated by a Nanofluid, Powder Technol, vol. 286, pp. 592-601,2015b.

  42. Yadav, D., Lee, D., Cho, H.H., and Lee, J., The Onset of Double-Diffusive Nanofluid Convection in a Rotating Porous Medium Layer with Thermal Conductivity and Viscosity Variation: A Revised Model, J. Porous Media, vol. 19, pp. 31-46,2016a.

  43. Yadav, D., Wang, J., Bhargava, R., and Cho, H.H., Numerical Investigation of the Effect of Magnetic Field on the Onset of Nanofluid Convection, Appl. Therm. Eng., vol. 103, pp. 1441-1449,2016b.

  44. Yadav, D., Nam, D., and Lee, J., The Onset of Transient Soret-Driven MHD Convection Confined within a Hele-Shaw Cell with Nanoparticles Suspension, J. Taiwan Inst. Chem. Eng., vol. 58, pp. 235-244,2016c.

  45. Yadav, D., Agrawal, G.S., and Lee, J., Thermal Instability in a Rotating Nanofluid Layer: A Revised Model, Ain Shams Eng. J, vol. 7, pp. 431-440,2016d.

  46. Yadav, D., Mohamed, R.A., Cho, H.H., and Lee, J., Effect of Hall Current on the Onset of MHD Convection in a Porous Medium Layer Saturated by a Nanofluid, J. Appl. FluidMech, vol. 9, pp. 2379-2389,2016e.

  47. Yadav, D., Mohamed, R.A., Lee, J., and Cho, H.H., Thermal Convection in a Kuvshiniski Viscoelastic Nanofluid Saturated Porous Layer, Ain Shams Eng. J., vol. 8, pp. 613-621,2017.


Articles with similar content:

ELECTROTHERMO CONVECTION OF ROTATING NANOFLUID IN BRINKMAN POROUS MEDIUM
Special Topics & Reviews in Porous Media: An International Journal, Vol.7, 2016, issue 2
Gian C. Rana, Ramesh Chand
MAGNETO-ROTATIONAL CONVECTION FOR FERROMAGNETIC FLUIDS IN THE PRESENCE OF COMPRESSIBILITY AND HEAT SOURCE THROUGH A POROUS MEDIUM
Special Topics & Reviews in Porous Media: An International Journal, Vol.5, 2014, issue 4
Seema Sharma, V. Singh, Kapil Kumar
LINEAR AND NONLINEAR DOUBLE-DIFFUSIVE CONVECTION IN A SATURATED POROUS LAYER WITH SORET EFFECT UNDER LOCAL THERMAL NON-EQUILIBRIUM MODEL
Journal of Porous Media, Vol.21, 2018, issue 13
I. Hashim, B. S. Bhadauria, Anas A. Altawallbeh
CONDITIONAL STABILITY FOR THERMAL CONVECTION IN A ROTATING COUPLE-STRESS FLUID SATURATING A POROUS MEDIUM
Special Topics & Reviews in Porous Media: An International Journal, Vol.5, 2014, issue 2
Sunil, Amit Mahajan, Shalu Choudhary
THERMAL INSTABILITY OF COUPLE-STRESS NANOFLUID WITH VERTICAL ROTATION IN A POROUS MEDIUM
Journal of Porous Media, Vol.20, 2017, issue 7
Gian C. Rana, Dhananjay Yadav, Ramesh Chand