Effect of magnetic field on the onset of thermal convection in a Jeffery nanofluid layer saturated by a porous medium: free-free, rigid-rigid and rigid-free boundary conditions

Authors

  • Ajit Kumar
    Department of Mathematics & Statistics, Himachal Pradesh University, Summer Hill, Shimla, India
  • Pushap Lata Sharma
    Department of Mathematics & Statistics, Himachal Pradesh University, Summer Hill, Shimla, India
  • Praveen Lata
    Department of Mathematics & Statistics, Himachal Pradesh University, Summer Hill, Shimla, India
  • Deepak Bains
    Department of Mathematics & Statistics, Himachal Pradesh University, Summer Hill, Shimla, India
    https://orcid.org/0000-0001-8078-923X
  • Pankaj Thakur
    Faculty of Science and Technology, ICFAI University, Baddi, Solan, India

Keywords:

Magnetic field; thermal convection; Jeffery nanofluid; normal mode technique

Abstract

The effect of the magnetic field on the onset of thermal convection in a porous layer saturated by Jeffrey nanofluid is studied. Three distinct boundary conditions are considered to be free-free, rigid-rigid and rigid-free boundaries. The model used for Jeffrey nanofluid includes the effect of Brownian motion and thermophoresis. The normal mode analysis as well as the Galerkin first approximation technique is used. The effects of the Rayleigh number of nanoparticles, Lewis number, modified diffusivity ratio, Jeffery parameter, porosity and Chandrasekhar number are investigated analytically and graphically. It is discovered that the Chandrasekhar number, Lewis number and modified diffusivity ratio have a stabilizing effect while the Jeffery parameter, nanoparticles Rayleigh number and porosity have a destabilizing effect. This study induces the effect of Chandrasekhar number and Jeffrey nanofluid. We have analyzed that Chandrasekhar number produces a stabilizing effect on the onset of convection i.e. it delays the onset of convection whereas the Jeffrey parameter which comes from Jeffrey nanofluid shows the destabilizing effect on the onset of convection i.e. it accelerates the onset of convection. The influence of a magnetic field on the commencement of nanofluid convection is significant in magnetohydrodynamic power generators, electrical equipment, petroleum reservoirs, nuclear reactors, biochemical engineering, chemical engineering and geophysics.

Dimensions

S.U. Choi & J. A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, Technical report, Argonne National Lab.(ANL), Argonne, IL (United States), 1995. https://www.osti.gov/servlets/purl/196525.

J. Buongiorno, “Convective transport in nanofluids”, Transactions of the ASME 128 (2006) 240. https://doi.org/10.1115/1.2150834.

S. Chandrasekhar, “Hydrodynamic and hydromagnetic stability”, Dover Publications, Inc., New York, U.S.A., 2013, pp. 1-704. https://www.google.co.in/books/edition/Hydrodynamic_and_Hydromagnetic_Stability/Mg3CAgAAQBAJ?hl=en&gbpv=1&dq=Hydrodynamic+and+Hydromagnetic+Stability&pg=PP1&printsec=frontcover

D. 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. https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.023.

D. Tzou, “Instability of nanofluids in natural convection”, Journal of Heat Transfer 130 (2008) 072401. https://doi.org/10.1115/1.2908427.

D. Y. Tzou, “Thermal instability of nanofluids in natural convection”, International Journal of Heat and Mass Transfer 51 (2008) 2967. https://doi.org/10.1016/j.ijheatmasstransfer.2007.09.014.

D. A. Nield & A. Bejan, “Convection in Porous Media”, Springer Cham, Switzerland, 2006, pp. 1-988. https://doi.org/10.1007/978-3-319-49562-0

L. J. Sheu, “Thermal instability in a porous medium layer saturated with a viscoelastic nanofluid”, Transport in Porous Media 88 (2011) 461. https://doi.org/10.1007/s11242-011-9749-2.

G. C. Rana & P. K. Gautam, “On the onset of thermal instability of a porous medium layer saturating a Jeffrey nanofluid”, Engineering Transactions 70 (2022) 123. https://doi.org/10.24423/EngTrans.1387. 20220609.

P. L. Sharma, Deepak & A. Kumar, “Effects of rotation and magnetic field on thermosolutal convection in elastico- viscous Walters‘ (Model B‘) nanofluid with porous medium”, Stochastic Modeling & Applications 26 (2022) 21. https://www.researchgate.net/publication/371416130_EFFECTS_OF_ROTATION_AND_MAGNETIC_FIELD_ON_THERMOSOLUTAL_CONVECTION_IN_ELASTICO-_VISCOUS_WALTERS_MODEL_B_NANOFLUID_WITH_POROUS_MEDIUM

P. L. Sharma, M. Kapalta, A. Kumar, D. Bains & P. Thakur, “Electrohydro dynamics convection in dielectric rotating Oldroydian nanofluid in porous medium”, Journal of the Nigerian Society of Physical Sciences 5 (2023) 1231. https://doi.org/10.46481/jnsps.2023.1231

A. Kuznetsov & D. Nield, “Thermal instability in a porous medium layer saturated by a nanofluid: Brinkman model”, Transport in Porous Media 81 (2010) 409. https://doi.org/10.1007/s11242-009-9413-2.

P. K. Gautam, G. C. Rana & H. Saxena, “Stationary convection in the electrohydrodynamic thermal instability of Jeffrey nanofluid layer saturating a porous medium: free-free, rigid-free, and rigid-rigid boundary conditions”, Journal of Porous Media 23 (2020) 1043. https://doi.org/10.1615/JPorMedia.2020035061.

P. L. Sharma, D. Bains & P. Thakur, “Thermal instability of rotating Jeffrey nanofluids in porous media with variable gravity”, Journal of the Nigerian Society of Physical Sciences 5 (2023) 1366. https://doi.org/10.46481/jnsps.2023.1366

P. L. Sharma, D. Bains, A. Kumar & P. Thakur, “Effect of rotation on thermosolutal convection in Jeffrey nanofluid with porous medium”, Structural Integrity and Life 23 (2023) 299. http://divk.inovacionicentar.rs/ivk/ivk23/299-IVK3-2023-PLS-DB-AK-PT.pdf.

P. L. Sharma, A. Kumar, D. Bains, P. Lata & P. Thakur, “Thermal convective instability in a Jeffrey nanofluid saturating a porous medium: rigid-rigid and rigid-free boundary conditions”, Structural Integrity and Life 23 (2023) 351. http://divk.inovacionicentar.rs/ivk/ivk23/351-IVK3-2023-PLS-AK-DB-PL-GCR.pdf.

G. C. Rana, “Effects of rotation on Jeffrey nanofluid flow saturated by a porous medium”, Journal of Applied Mathematics and Computational Mechanics 20 (2021) 17. https://doi.org/10.17512/jamcm.2021.3.02.

S. U. Khan, Usman, A. Raza, A. Kanwal & K. Javid, “Mixed convection radiated flow of Jeffery-type hybrid nanofluid due to inclined oscillating surface with slip effects: a comparative fractional model”, Waves in Random and Complex Media (2022) 1. https://doi.org/10.1080/17455030. 2022.2122628.

A. K. Pati, A. Misra, S. K. Mishra, S. Mishra, R. Sahu & S. Panda, “Computational modelling of heat and mass transfer optimization in copper water nanofluid flow with nanoparticle ionization”, JP Journal of Heat and Mass Transfer 31 (2023) 1. https://doi.org/10.17654/0973576323001.

A. K. Pati, A. Misra & S. K. Mishra, “Effect of electrification of nanoparticles on heat and mass transfer in boundary layer flow of a copper water nanofluid over a stretching cylinder with viscous dissipation”, JP Journal of Heat and Mass Transfer 17 (2019) 97. http://dx.doi.org/10.17654/HM017010097.

M. B. Ashraf, A. Tanveer & S. Ulhaq, “Effects of Cattaneo-Christov heat flux on MHD Jeffery nano fluid flow past a stretching cylinder”, Journal of Magnetism and Magnetic Materials 565 (2019) 170154. https://doi.org/10.1016/j.jmmm.2022.170154.

P. L. Sharma, D. Bains & G. C. Rana, “Effect of variable gravity on thermal convection in Jeffrey nanofluid: Darcy-Brinkman Model”, Numerical Heat Transfer, Part B: Fundamentals (2023) 1. https://doi.org/10.1080/ 10407790.2023.2256970.

D. Bains, P. L. Sharma & G. C. Rana, “Effect of variable gravity on thermal convection in rotating Jeffrey nanofluid: Darcy-Brinkman model”, Special Topics & Reviews in Porous Media: An International Journal 15 (2024) 25. https://doi.org/10.1615/SpecialTopicsRevPorousMedia. 2023049875.

A. Garg, Y. D. Sharma & S. K. Jain, “Stability analysis of thermobioconvection flow of Jeffrey fluid containing gravitactic microorganism into an anisotropic porous medium”, Forces in Mechanics 10 (2023) 100152. https://doi.org/10.1016/j.finmec.2022.100152.

A. Garg, Y. D. Sharma & S. K. Jain, “Instability investigation of Thermobioconvection of oxytactic microorganism in Jeffrey nanoliquid with effects of internal heat source”, Journal of Porous Media 26 (2023) 13. https://doi.org/10.1615/JPorMedia.2023046406.

A. Garg, Y. D. Sharma & S. K. Jain, “Onset of triply diffusive thermobio-convection in the presence of gyrotactic microorganisms and internal heating into an anisotropic porous medium: oscillatory convection”, Chinese Journal of Physics 84 (2023) 173. https://doi.org/10.1016/j.cjph.2023.05.014.

A. Garg, Y. D. Sharma, S. K. Jain & S. Maheshwari, “Numerical study of the influence of magnetic field and throughflow on the onset of thermo-bio-convection in a Forchheimer-extended Darcy-Brinkman porous nanofluid layer containing gyrotactic microorganisms”, Journal of Porous Media (2024) 77. https://doi.org/10.1615/JPorMedia.2024049980.

A. Garg, Y. D. Sharma & S. K. Jain, “Impact of an anisotropic porous media on thermobioconvection instability in the presence of gyrotacticmicroorganisms and heating from below”, Special Topics & Reviews in Porous Media: An International Journal 15 (2024) 1. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.2023048137.

D. Bains & P. L. Sharma, “Thermal instability of hydro-magnetic Jeffrey nanofluids in porous media with variable gravity for: free-free, rigidrigid and rigid-free boundaries”, Special Topics & Reviews in Porous Media: An International Journal 15 (2023) 51. https://doi.org/10.1615/SpecialTopicsRevPorousMedia.2023048444.

P. L. Sharma, A. Kumar, D. Bains & G. C. Rana, “Effect of magnetic field on thermosolutal convection in Jeffrey nanofluid with porous medium”, Special Topics & Reviews in Porous Media: An International Journal 14 (2023) 17. https://doi.org/10.1615/SpecialTopicsRevPorousMedia. 2023046929.

P. L. Sharma, A. Kumar, M. Kapalta & D. Bains, “Effect of magnetic field on thermosolutal convection in a rotating non-Newtonian nanofluid with porous medium”, International Journal of Applied Mathematics & Statistical Sciences 12 (2023) 19. https://www.researchgate.net/publication/374616576_EFFECT_OF_MAGNETIC_FIELD_ON_THERMOSOLUTAL_CONVECTION_IN_A_ROTATING_NON-NEWTONIAN_NANOFLUID_WITH_POROUS_MEDIUM

D. Yadav, “Influence of anisotropy on the Jeffrey fluid convection in a horizontal rotary porous layer”, Heat Transfer 50 (2021) 4595. https://doi.org/10.1002/htj.22090.

D. Yadav, “Effect of electric field on the onset of Jeffery fluid convection in a heat-generating porous medium layer”, Pramana 96 (2022) 19. https: //doi.org/10.1007/s12043-021-02242-6.

D. Yadav, “Thermal non-equilibrium effects on the instability mechanism in a non-Newtonian Jeffrey fluid saturated porous layer”, Journal of Porous Media 25 (2022) 1. https://doi.org/10.1615/JPorMedia. 2021038392.

D. Yadav, “Numerical treatment on the convective instability in a Jeffrey fluid soaked permeable layer with through-flow”, Mathematical Modeling for Intelligent Systems 1 (2022) 11. https://www.taylorfrancis.com/chapters/edit/10.1201/978100329191610/numerical-treatment-convective-instability-jeffrey-fluid-soakedpermeable-layer-flow-dhananjay-yadav-mukesh-kumar-awasthimahabaleshwar-krishnendu-bhattacharyya.

D. Yadav, A. A. Mohamad & M. K. Awasthi, “The Horton–Rogers–Lapwood problem in a Jeffrey fluid influenced by a vertical magnetic field. Proceedings of the Institution of Mechanical Engineers”, Part E: Journal of Process Mechanical Engineering 235 (2021) 2119. https://doi.org/10.1177/09544089211031108.

D. Yadav, S. Al-Balushi, M. K. Awasthi, T. Al-Hadi, R. Al-Abri, J. AlWahaibi, F. Al-Nasseri, S. Al-Siyabi, R. Ragoju & K. Bhattacharyya, “Convective flow of ethylene glycol-silver Jeffery nanofluid in a HeleShaw cell with an influence of external magnetic field”, Asia-Pacific Journal of Chemical Engineering 18 (2023) 2884. https://doi.org/10.1002/apj. 2884.

U. Gupta, J. Ahuja & R. K. Wanchoo, “Magneto convection in a nanofluid layer.”, International Journal of Heat and Mass Transfer 64 (2013) 1163. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.035.

D. 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. https://doi.org/10.1016/j.euromechflu.2010.02.003.

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. https://doi.org/10.1016/j.ijthermalsci.2012.05.011.

Published

2024-04-21

How to Cite

Effect of magnetic field on the onset of thermal convection in a Jeffery nanofluid layer saturated by a porous medium: free-free, rigid-rigid and rigid-free boundary conditions. (2024). Journal of the Nigerian Society of Physical Sciences, 6(2), 1934. https://doi.org/10.46481/jnsps.2024.1934

Issue

Volume 6, Issue 2, May 2024

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2024 Ajit Kumar, Pushap Lata Sharma, Praveen Lata, Deepak Bains, Pankaj Thakur

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Effect of magnetic field on the onset of thermal convection in a Jeffery nanofluid layer saturated by a porous medium: free-free, rigid-rigid and rigid-free boundary conditions. (2024). Journal of the Nigerian Society of Physical Sciences, 6(2), 1934. https://doi.org/10.46481/jnsps.2024.1934

Similar Articles

21-30 of 218

You may also start an advanced similarity search for this article.