Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium

Harsha S. V.; Chandra Shekara; Hemanth Kumar C.

doi:10.14744/thermal.0000926

Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium

Abstract

This study investigates the stability of a mixed convective flow of a nanofluid through a horizontal porous layer using an unsteady Jeffrey-Darcy model. Linear stability theory is employed to assess the stability of a system, where the base fluid is modeled as a Jeffrey fluid with dispersed nanoparticles in a state of thermal equilibrium. The stability equations are derived as an eigenvalue problem using Fourier decomposition, solved using the higher order Weighted Residual Galerkin Method (WRGM), and validated analytically. The results are presented in terms of critical values of the Darcy-Rayleigh number, wave number, and wave speed over nondimensional parameters. Further, the impact of nondimensional numbers like horizontal pressure gradient, thermal diffusivity ratio, and nanoparticle volume fraction has stabilizing effects, whereas the Jeffrey parameter and the Vadasz number have the opposite effect. Moreover, it has been observed that the increase in the Jeffrey parameter reduces the stability region. The variation Jeffrey parameter causes a change in the flow and thereby discards the analytical proof of stability even under the limit of an infinite Vadasz number. The inquiry into the stability or instability of the fundamental flow is addressed by solving the eigenvalue problem numerically over a finite range of the Jeffrey parameter and horizontal pressure gradient. These results indicate that the oscillatory convection mode is advantageous for estimating the required volume fraction of nanoparticles in the base fluid to improve the thermal efficiency of Jeffrey nanofluids. Numerical and graphical analyses explore the impacts of dimensionless parameters on physical systems, providing insights into the system’s stability properties under varying conditions.

Keywords

References

[1] Prasad V, Lai FC, Kulacki FA. Mixed convection in horizontal porous layers heated from below. J Heat Transf 1988;395–402. [CrossRef]
[2] Sphaier LA, Barletta A. Unstable mixed convection in a heated horizontal porous channel. Int J Therm Sci 2014;78:77–89. [CrossRef]
[3] Ozgen F, Varol Y. Numerical study of mixed convection in a channel filled with a porous medium. Appl Sci 2019;9:211. [CrossRef]
[4] Vafai K. Handbook of Porous Media. New York: CRC Press; 2005. [CrossRef]
[5] Kim Y, Vafai K. Buoyancy-driven heat transfer enhancement in a two-dimensional porous enclosure utilizing nanofluids. Int J Heat Mass Transf 2006;49:2402–2414.
[6] Abu-Nada E, Chamkha AJ. Mixed convection flow in a lid-driven cavity filled with a fluid-saturated porous medium: effect of a conducting vertical solid plate on the left wall. Int J Heat Mass Transf 2007;50:727–735.
[7] Nield DA, Bejan A. Convection in Porous Media. New York: Springer; 2006.
[8] Ingham DB, Pop I. Transport Phenomena in Porous Media III. Amsterdam: Elsevier; 2013.

[9] Nield DA. A note on a porous medium model with the Navier slip boundary condition. Int J Heat Mass Transf 2013;62:287–291.
[10] Postelnicu A. The effect of a horizontal pressure gradient on the onset of a Darcy-Bénard convection in thermal non-equilibrium conditions. Int J Heat Mass Transf 2010;53:68–75. [CrossRef]
[11] Buongiorno J. Convective transport in nanofluids. ASME J Heat Transf 2005;128:240–250. [CrossRef]
[12] Choi SU, Zhang ZG, Yu W, Lockwood FE, Grulke EA. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett 2019;79:2252–2254. [CrossRef]
[13] R Mostafizur RM, Saidur R, Abdul Aziz AR, Bhuiyan MHU. Thermophysical properties of methanol-based Al₂O₃ nanofluids. Int J Heat Mass Transf 2015;85:414–419. [CrossRef]
[14] Tzou DY. Thermal instability of nanofluids in natural convection. Int J Heat Mass Transf 2008;51:2967–2979.
[15] Nield DA, Kuznetsov AV. Thermal instability in a porous medium layer saturated by a nanofluid. Int J Heat Mass Transf 2009;52:5796–5801. [CrossRef]
[16] Kuznetsov AV, Nield DA. Effect of local thermal non-equilibrium on the onset of convection in a porous medium layer saturated by a nanofluid. Transp Porous Media 2010;83:425–436. [CrossRef]
[17] Bhadauria BS, Agarwal S. Convective transport in a nanofluid saturated porous layer with thermal nonequilibrium model. Transp Porous Media 2011;88:107–131. [CrossRef]
[18] Chand R, Rana GC. Oscillating convection of nanofluid in a porous medium. Transp Porous Media 2012;95:269–284. [CrossRef]
[19] Yadav D, Agrawal GS, Bhargava R. The onset of convection in a binary nanofluid saturated porous layer. Int J Theor Appl Multiscale Mech 2012;2:198–224. [CrossRef]
[20] Yadav D, Mohamed R, Lee J, Cho HH. Thermal convection in a Kuvshiniski viscoelastic nanofluid saturated porous layer. Ain Shams Eng J 2017;8:613–621. [CrossRef]
[21] Sheu LJ. Linear stability of convection in a viscoelastic nanofluid layer. World Acad Sci Eng Technol Int J Mech Mechatron Eng 2011;5:1970–1976.
[22] Chand R, Rana GC, Puigjaner D. Thermal instability analysis of an elastic-viscous nanofluid layer. Eng Trans 2018;66:301–324.
[23] Zangooee MR, Hosseinzadeh K, Ganji DD. Hydrothermal analysis of Ag and CuO hybrid NPs suspended in a mixture of water 20%+ EG 80% between two concentric cylinders. Case Stud Therm Eng 2023;50:103398. [CrossRef]
[24] Alipour N, Jafari B, Hosseinzadeh K. Optimization of the wavy trapezoidal porous cavity containing a mixture of hybrid nanofluid (water/ethylene glycol Go–Al₂O₃) by response surface method. Sci Rep 2023;13:1635. [CrossRef]
[25] Hosseinzadeh K, Mardani MR, Paikar M, Hasibi A, Tavangar T, Nimafar M, et al. Investigation of second-grade viscoelastic non-Newtonian nanofluid flow on the curve stretching surface in the presence of MHD. Results Eng 2023;17:100838. [CrossRef]
[26] Fallah Najafabadi M, Talebi Rostami H, Hosseinzadeh K, Ganji DD. Hydrothermal study of nanofluid flow in the channel by RBF method with exponential boundary conditions. Proc Inst Mech Eng E 2023;237:2268–2277. [CrossRef]
[27] Faghiri S, Akbari S, Shafii MB, Hosseinzadeh K. Hydrothermal analysis of non-Newtonian fluid flow (blood) through the circular tube under prescribed non-uniform wall heat flux. Theor Appl Mech Lett 2022;12:100360. [CrossRef]
[28] Zangooee MR, Hosseinzadeh K, Ganji DD. Hydrothermal analysis of hybrid nanofluid flow on a vertical plate by considering slip condition. Theor Appl Mech Lett 2022;12:100357. [CrossRef]
[29] Akbari S, Faghiri S, Poureslami P, Hosseinzadeh K, Shafii MB. Analytical solution of non-Fourier heat conduction in a 3-D hollow sphere under time-space varying boundary conditions. Heliyon 2022;8:e12496. [CrossRef]
[30] Attar MA, Roshani M, Hosseinzadeh K, Ganji DD. Analytical solution of fractional differential equations by Akbari–Ganji's method. Partial Differ Equ Appl Math 2022;6:100450. [CrossRef]
[31] Mahboobtosi M, Hosseinzadeh K, Ganji DD. Entropy generation analysis and hydrothermal optimization of ternary hybrid nanofluid flow suspended in polymer over a curved stretching surface. Int J Thermofluids 2023;20:100507. [CrossRef]
[32] Talebi Rostami H, Fallah Najafabadi M, Hosseinzadeh K, Ganji DD. Investigation of mixture-based dusty hybrid nanofluid flow in porous media affected by magnetic field using RBF method. Int J Amb Energy 2022;43:6425–6435. [CrossRef]
[33] Nadeem S, Akbar NS. Peristaltic flow of a Jeffrey fluid with variable viscosity in an asymmetric channel. Z Naturforsch A 2009;64:713–722. [CrossRef]
[34] Nallapu S, Radha Krishnamacharya G, Chamkha AJ. Flow of a Jeffrey fluid through a porous medium in narrow tubes. J Porous Media 2015;18:71–78. [CrossRef]
[35] Yadav D. Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer. Heat Transf 2021;50:4595–4606. [CrossRef]
[36] Naganthran K, Nazar R, Pop I. Effects of heat generation/absorption in the Jeffrey fluid past a permeable stretching/shrinking disc. J Braz Soc Mech Sci Eng 2019;41:414. [CrossRef]
[37] Zhang J, Zheng L, Zhang X, Fang T. Free convection in Jeffrey nanofluid flow in a porous medium with convective boundary condition. Int J Heat Mass Transf 2018;116:240–248.
[38] Siddiqui AM, Haq RU, Khan MI. Effects of Darcy and Prandtl numbers on unsteady heat transfer of Jeffrey nanofluid through a porous medium. Eng Sci Technol Int J 2021;24:113–123.
[39] Sharma P, Kumar A, Bains D, Lata P, Rana G. Thermal convective instability in a Jeffrey nanofluid saturating a porous medium: Rigid-rigid and rigid-free boundary conditions. Struct Integ Life 2024;23:351–356. [40] Pushap PLS, Bains D, Lata P. Thermal instability of rotating Jeffrey nanofluids in porous media with variable gravity. J Niger Soc Phys Sci 2023;5:1366. [CrossRef]
[41] Gautam PK, Rana GC, Saxena H. Stationary convection in the electrohydrodynamic thermal instability of Jeffrey nanofluid layer saturating a porous medium: Free-free, rigid-free, and rigid-rigid boundary conditions. J Porous Media. 2020;23:1043. [CrossRef]
[42] Shehzad SA, Hayat T, Alsaedi A. MHD flow of Jeffrey nanofluid with convective boundary conditions. J Braz Soc Mech Sci Eng 2015;37:873–883. [CrossRef]
[43] 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 Adv 2018;8:065316. [CrossRef]
[44] 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. J Nanofluids 2018;7:62–71. [CrossRef]
[45] Devi J, Sharma V, Kapalta M. Electroconvection in rotating Jeffrey nanofluid saturating porous medium: Free-Free, Rigid-Free, Rigid-Rigid boundaries. J Nanofluids 2023;12:1554–1565. [CrossRef]
[46] Devi P, Rana GC, Sharma SR, Kumar S, Gautam PK. Impact of rotation on thermal instability of Darcy–Brinkman porous layer filled with a Jeffrey nanofluid. Numer Heat Transf Part A Appl 2023;2273456. [CrossRef]
[47] Sharma PL, Kumar A, Deepak D, Rana GC. Effect of magnetic field on thermosolutal convection in Jeffrey nanofluid with porous medium. Spec Top Rev Porous Media 2023;14:17–29. [CrossRef]
[48] Maatoug S, Babu KH, Deepthi VVL, Ghachem K, Raghunath K, Ganteda C, et al. Variable chemical species and thermo-diffusion Darcy–Forchheimer squeezed flow of Jeffrey nanofluid in horizontal channel with viscous dissipation effects. J Indian Chem Soc 2023;100:100831. [CrossRef]
[49] Sushma K, Sreenadh S, Dhanalakshmi P. Mixed convection flow of a Jeffrey nanofluid in a vertical channel. Middle-East J Sci Res 2017;25:950–959.
[50] Pallavi G, Hemanthkumar C, Shivakumara IS, Rushikumar B. Oscillatory Darcy-Bénard-Poiseuille mixed convection in an Oldroyd-B fluid-saturated porous layer. In: Rushi Kumar B, Sivaraj R, Prakash J, eds. Advances in Fluid Dynamics. Lecture Notes in Mechanical Engineering. Singapore: Springer; 2021. [CrossRef]
[51] Hemanthkumar C, Shivakumara IS. Thermal instability of an Oldroyd-B fluid saturated porous layer: Implications of pressure gradient and LTNE temperatures. SN Appl Sci 2020;2:566. [CrossRef]
[52] Singh N, Khandelwal MK. Linear stability perspective on mixed convection flow of nanofluids in a differentially heated vertical channel. Int Commun Heat Mass Transf 2022;134:105989. [CrossRef]
[53] Xuan Y, Li Q. Investigation on convective heat transfer and flow features of nanofluids. J Heat Transf 2003;125:151–155. [CrossRef]
[54] Brinkman HC. The viscosity of concentrated suspensions and solutions. J Chem Phys 1952;20:571–581. [CrossRef]
[55] Maxwell JC. A treatise on electricity and magnetism. Cambridge: Cambridge University Press; 2010. [CrossRef]
[56] Khanafer K, Vafai K, Lightstone M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int J Heat Mass Transf 2003;46:3639–3653. [CrossRef]
[57] Xuan Y, Roetzel W. Conceptions for heat transfer correlation of nanofluids. Int J Heat Mass Transf 2000;43: 3701–3707. [CrossRef]
[58] Shankar BM, Shivakumara IS. Gill's stability problem may be unstable with horizontal heterogeneity in permeability. J Fluid Mech 2022;943:A20. [CrossRef]

Details

Primary Language

English

Subjects

Fluid Mechanics and Thermal Engineering (Other)

Journal Section

Research Article

Authors

Harsha S. V. This is me
0000-0001-5640-8222
India

Chandra Shekara ^*
0000-0002-4259-6784
India

Hemanth Kumar C. This is me
0000-0001-5802-8303
India

Publication Date

March 24, 2025

Submission Date

January 16, 2024

Acceptance Date

June 10, 2024

Published in Issue

Year 2025 Volume: 11 Number: 2

DOI

https://doi.org/10.14744/thermal.0000926

IZ

https://izlik.org/JA98ZN88AF

Cite

RIS / Bibtex

APA

V., H. S., Shekara, C., & C., H. K. (2025). Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium. Journal of Thermal Engineering, 11(2), 448-463. https://doi.org/10.14744/thermal.0000926

AMA

1.V. HS, Shekara C, C. HK. Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium. Journal of Thermal Engineering. 2025;11(2):448-463. doi:10.14744/thermal.0000926

Chicago

V., Harsha S., Chandra Shekara, and Hemanth Kumar C. 2025. “Stability Analysis of the Mixed Convective Flow of Jeffrey Nanofluid through a Porous Medium”. Journal of Thermal Engineering 11 (2): 448-63. https://doi.org/10.14744/thermal.0000926.

EndNote

V. HS, Shekara C, C. HK (March 1, 2025) Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium. Journal of Thermal Engineering 11 2 448–463.

IEEE

[1]H. S. V., C. Shekara, and H. K. C., “Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium”, Journal of Thermal Engineering, vol. 11, no. 2, pp. 448–463, Mar. 2025, doi: 10.14744/thermal.0000926.

ISNAD

V., Harsha S. - Shekara, Chandra - C., Hemanth Kumar. “Stability Analysis of the Mixed Convective Flow of Jeffrey Nanofluid through a Porous Medium”. Journal of Thermal Engineering 11/2 (March 1, 2025): 448-463. https://doi.org/10.14744/thermal.0000926.

JAMA

1.V. HS, Shekara C, C. HK. Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium. Journal of Thermal Engineering. 2025;11:448–463.

MLA

V., Harsha S., et al. “Stability Analysis of the Mixed Convective Flow of Jeffrey Nanofluid through a Porous Medium”. Journal of Thermal Engineering, vol. 11, no. 2, Mar. 2025, pp. 448-63, doi:10.14744/thermal.0000926.

Vancouver

1.Harsha S. V., Chandra Shekara, Hemanth Kumar C. Stability analysis of the mixed convective flow of Jeffrey nanofluid through a porous medium. Journal of Thermal Engineering. 2025 Mar. 1;11(2):448-63. doi:10.14744/thermal.0000926