Engineering Transactions, 70, 2, pp. 123-139, 2022

On the Onset of Thermal Instability of a Porous Medium Layer Saturating a Jeffrey Nanofluid

NSCBM Govertment College

Poonam Kumari GAUTAM
Career Point University

The onset of stationary convection in thermal instability of porous layer saturating a Jeffrey nanofluid is studied. The behaviour of nanofluid is described by a Jeffrey fluid model and the porous layer is assumed to follow Darcy’s law. Due to the presence of the Jeffrey parameter and nanoparticles, the momentum-balance equation of fluid is modified. The linear stability analysis and normal modes analysis method are utilised to derive the dispersion relation for the Rayleigh number in terms of various parameters for free-free boundaries. The effects of the Jeffrey parameter, Lewis number, modified diffusivity ratio, nanoparticles’ Rayleigh number and medium porosity on the physical system are discussed analytically and graphically.
Keywords: nanofluid; Jeffrey model; Rayleigh number; porous medium; convection.
Full Text: PDF


Jeffreys H., The stability of a layer of fluid heated below, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2: 833–844, 1926, doi: 10.1080/14786442608564114.

Chandrasekhar S., Hydrodynamic and hydromagnetic stability, Dover Publication, New York, 1981.

Martinez-Mardones J., Perez-Garcia C., Linear instability in viscoelastic fluid convection, Journal of Physics: Condensed Matter, 2(5): 1281, 1990, doi: 10.1088/0953-8984/2/5/019.

Nadeem S., Akbar N.S., Peristaltic flow of a Jeffrey fluid with variable viscosity in an asymmetric channel, Zeitschrift f¨ur Naturforschung A, 64(11): 713–722, 2009, doi: 10.1515/zna-2009-1107.

Akbar N.S., Nadeem S., Mixed convective magnetohydrodynamic peristaltic flow of a Jeffrey nanofluid with Newtonian heating, Zeitschrift f¨ur Naturforschung A, 68(6–7): 433–441, 2013, doi: 10.5560/zna.2013-0029.

Akbar N.S., Nadeem S., Lee C., Characteristics of Jeffrey fluid model for peristaltic flow of chyme in small intestine with magnetic field, Results in Physics, 3: 152–160, 2013, doi: 10.1016/j.rinp.2013.08.006.

Nallapu S., Radhakrishnamacharya G., Chamkha A.J., Flow of a Jeffrey fluid through a porous medium in narrow tubes, Journal of Porous Media, 18(1): 71–78, 2015, doi: 10.1615/JPorMedia.v18.i1.60.

Shehzad S.A., Hayat T., Alsaedi A., MHD flow of Jeffrey nanofluid with convective boundary conditions, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 37: 873–883, 2015, doi: 10.1007/s40430-014-0222-3.

Imtiaz M., Hayat T., Alsaedi A., MHD convective flow of Jeffrey fluid due to a curved stretching surface with homogeneous-heterogeneous reactions, PLOS ONE, 11(9): e0161641, 2016, doi: 10.1371/journal.pone.0161641.

Sushma K., Sreenadh S., Dhanalakshmi P., Mixed convection flow of a Jeffrey nanofluid in a vertical channel, Middle-East Journal of Scientific Research, 25(5): 950–959, 2017, doi: 10.5829/idosi.mejsr.2017.950.959.

Lapwood E.R., Convection of a fluid in porous medium, Proc. Camb. Phil. Soc., 44(4): 508–521, 1948, doi: 10.1017/S030500410002452X.

Wooding R.A., Rayleigh instability of a thermal boundary layer in flow through a porous medium, Journal of Fluid Mechanics, 9(2): 183–192, 1960, doi: 10.1017/S0022112060001031.

Nield D.A., Bejan A., Convection in porous media, 5th ed., Springer International Publishing, 2017.

Buongiorno J., Convective transport in nanofluids, ASME Journal of Heat Transfer, 128(3): 240–250, 2005, doi: 10.1115/1.2150834.

Tzou D.Y., Thermal instability of nanofluids in natural convection, International Journal of Heat and Mass Transfer, 51(11–12): 2967–2979, 2008, doi: 10.1016/j.ijheatmasstransfer.2007.09.014.

Nield D.A., Kuznetsov A.V., Thermal instability in a porous medium layer saturated by a nanofluid, International Journal of Heat and Mass Transfer, 52(25–26): 5796–5801, 2009, doi: 10.1016/j.ijheatmasstransfer.2009.07.023.

Kuznetsov A.V., Nield D.A., Effect of local thermal non-equilibrium on the onset of convection in a porous medium layer saturated by a nanofluid, Transport in Porous Media, 83: 425–436, 2010, doi: 10.1007/s11242-009-9452-8.

Bhadauria B.S., Agarwal S., Convective transport in a nanofluid saturated porous layer with thermal non equilibrium model, Transport in Porous Media, 88: 107–131, 2011, doi: 10.1007/s11242-011-9727-8.

Chand R., Rana G.C., On the onset of thermal convection in rotating nanofluid layer saturating a Darcy-Brinkman porous medium, International Journal of Heat and Mass Transfer, 55(21–22): 5417–5424, 2012, doi: 10.1016/j.ijheatmasstransfer.2012.04.043.

Chand R., Rana G.C., Oscillating convection of nanofluid in porous medium, Transport in Porous Media, 95: 269–284, 2012, doi: 10.1007/s11242-012-0042-9.

Yadav D., Agrawal G.S., Bhargava R., The onset of convection in a binary nanofluid saturated porous layer, International Journal of Theoretical and Applied Multiscale Mechanics, 2(3): 198–224, 2012, doi: 10.1504/IJTAMM.2012.049931.

Yadav D., Bhargava R., Agrawal G.S., Numerical solution of a thermal instability problem in a rotating nanofluid layer, International Journal of Heat and Mass Transfer, 63: 313–322, 2013, doi: 10.1016/j.ijheatmasstransfer.2013.04.003.

Yadav D., Mohamed R.A., Lee J., Cho H.H., Thermal convection in a Kuvshiniski viscoelastic nanofluid saturated porous layer, Ain Shams Engineering Journal, 8(4): 613–621, 2017, doi: 10.1016/j.asej.2015.11.023.

Sheu L.J., Linear stability of convection in a viscoelastic nanofluid layer, World Academy of Science, Engineering and Technology, International Journal of Mechanical and Mechatronics Engineering, 5(10): 1970–1976, 2011, doi: 10.5281/zenodo.1072493.

Sheu L.J., Thermal instability in a porous medium layer saturated with a viscoelastic nanofluid, Transport in Porous Media, 88: 461–477, 2011, doi: 10.1007/s11242-011-9749-2.

Chand R., Rana G.C., Thermal instability of Rivlin-Ericksen elastico-viscous nanofluid saturated in porous medium, Journal of Fluid Engineering, 134(12): 121203 (7 pages), 2012, doi: 10.1115/1.4007901.

Chand R., Rana G.C., Yadav D., Thermal instability of couple-stress nanofluid with vertical rotation in a porous medium, Journal of Porous Media, 20(7): 635–648, 2017, doi: 10.1615/JPorMedia.v20.i7.50.

Chand R., Rana G.C., Puigjaner D., Thermal instability analysis of an elastico-viscous nanofluid layer, Engineering Transactions, 66(3): 301–324, 2018, doi: 10.24423/engtrans.401.2018092.

Shahzad F., Sagheer M., Hussain S., Numerical simulation of magnetohydrodynamic Jeffrey nanofluid flow and heat transfer over a stretching sheet considering Joule heating and viscous dissipation, AIP Advances, 8: 065316, 2018, doi: 10.1063/1.5031447.

Sreelakshmi K., Sarojamma G., Murthy J., Ramana V., Homotopy analysis of an unsteady flow heat transfer of a Jeffrey nanofluid over a radially stretching convective surface, Journal of Nanofluids, 7(1): 62–71, 2018, doi: 10.1166/jon.2018.1432.

DOI: 10.24423/EngTrans.1387.20220609

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland