Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation

S. Vigneshwari; B. Reddappa; B. Rushi Kumar

Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation

Abstract

The primary objective of the present study is to investigate the influence of magnetohydrodynamic (MHD) flow and heat transfer behavior of Jeffrey fluid under natural convection within a square cavity filled with a permeable matrix. This investigation is significant because enhancing heat transfer capabilities in systems such as nuclear reactor cooling is crucial for ensuring efficient thermal management. The cavity is configured with cold vertical walls, an adiabatic top surface, and a heated bottom surface, while a constant vertical magnetic field is applied at the left wall. The momentum transfer in the permeable matrix is modelled using the Darcy–Forchheimer approach, and the Galerkin finite element method (GFEM) is employed within COMSOL Multiphysics 6.1 to solve the governing equations. The study examines a range of Rayleigh numbers (10³ ≤ Ra ≤ 106), Darcy numbers (10-5 ≤ Da ≤ 10-3), and Hartmann numbers (10 ≤ Ha ≤ 40), providing a detailed analysis of the Nusselt number, velocity distribution, isocontours, isotherms, temperature profiles, and stream functions. Key findings of the study reveal that as the Hartmann number increases, the velocity distribution exhibits a monotonic rise which indicating the strong influence of the magnetic field on flow dynamics. Numerical results of the study demonstrate that with an increase in the Hartmann number (Ha) from 10 to 40, the average Nusselt number on the hot wall decreases from 13.645 to 12.380 at a Rayleigh number (Ra) of 106 indicate a reduction in heat transfer efficiency due to the damping effect of the magnetic field. For lower Rayleigh numbers (Ra = 103) the Nusselt number remains nearly constant around 5.728 across varying Hartmann numbers which shows that the magnetic field’s impact is less significant under weaker convective conditions. The results of the study show a high degree of consistency with previous studies, demonstrating the robustness of the numerical approach. This work advances the understanding of MHD natural convection with Jeffrey fluids by offering specific, quantitative insights that go beyond previous literature, particularly in the context of optimizing heat transfer in engineering applications. The novelty of present findings are particularly relevant to geophysical applications, such as modeling the movement of magma in volcanic cavities, as well as industrial processes like polymer mixing.

Keywords

References

[1] Mullick SH, Kumar A, Kundu PK. Numerical study of natural convection inside a square cavity with non-uniform heating from top. J Inst Eng (India) Ser C 2020;101:1043–1050.[CrossRef]
[2] Selimefendigil F, Senol G, Öztop HF, Abu-Hamdeh NH. A review on non-Newtonian nanofluid applications for convection in cavities under magnetic field. Symmetry 2023;15:41.[CrossRef]
[3] Hamid M, Usman M, Khan ZH, Haq RU, Wang W. Heat transfer and flow analysis of Casson fluid in a partially heated trapezoidal cavity. Int Commun Heat Mass Transf 2019;108:104284.[CrossRef]
[4] Anthony AS, Verma TN. Numerical analysis of natural convection in a heated room and its implication on thermal comfort. J Therm Eng 2021;7:37–53.[CrossRef]
[5] Hussien AA, Al-Kouz W, El Hassan M, Janvekar AA, Chamkha AJ. A review of flow and heat transfer in cavities and their applications. Eur Phys J Plus 2021;136:353.[CrossRef]
[6] Babu DH, Tarakaramu N, Narayana PVS, Sarojamma G, Makinde OD. MHD flow and heat transfer of a Jeffrey fluid over a porous stretching/shrinking sheet with a convective boundary condition. Int J Heat Technol 2021;39:885–894.[CrossRef]
[7] Makkar V, Poply V, Goyal R, Sharma N. Numerical investigation of MHD Casson nanofluid flow towards a nonlinear stretching sheet in the presence of double-diffusive effects along with viscous and Ohmic dissipation. J Therm Eng 2021;7:1–17.[CrossRef]
[8] Prasad A, Rajkumar S, Teklemariam A, Tafesse D, Tufa M, Bejaxhin BH. Influence of nano additives on performance and emissions characteristics of a diesel engine fueled with watermelon methyl ester. J Therm Eng 2023;9:395–400.[CrossRef]

[9] Basiri M, Goshayeshi H, Chaer I, Pourpasha H, Heris SZ. Experimental study on heat transfer from rectangular fins in combined convection. J Therm Eng 2023;9:1632–1642.[CrossRef]
[10] Mohammed AA. Natural convection heat transfer inside horizontal circular enclosure with triangular cylinder at different angles of inclination. J Therm Eng 2021;7:240–254.[CrossRef]
[11] Zhu L, He X, Wu X, Wu J, Hong T. Recent development of abrasive machining processes enhanced with non-Newtonian fluids. Coatings 2024;14:779.[CrossRef]
[12] Aman S, Al-Mdallal Q, Khan I. Heat transfer and second order slip effect on MHD flow of fractional Maxwell fluid in a porous medium. J King Saud Univ Sci 2018;32:450–458.[CrossRef]
[13] Shkarah AJ. Convective heat transfer and fully developed flow for circular tube Newtonian and non-Newtonian fluids condition. J Therm Eng 2021;7:409–414.[CrossRef]
[14] Anusha T, Mahabaleshwar US, Bhattacharyya S. An impact of MHD and radiation on flow of Jeffrey fluid with carbon nanotubes over a stretching/shrinking sheet with Navier’s slip. J Therm Anal Calorim 2023;148:12597–12607.[CrossRef]
[15] Siddique I, Adrees R, Ahmad H, Askar S. MHD free convection flows of Jeffrey fluid with Prabhakar-like fractional model subject to generalized thermal transport. Sci Rep 2023;13:9289.[CrossRef]
[16] Raisi A. Natural convection of non-Newtonian fluids in a square cavity with a localized heat source. J Mech Eng 2016;62:553–564.[CrossRef]
[17] Dimitrienko YI, Shuguang L. Numerical simulation of MHD natural convection heat transfer in a square cavity filled with Carreau fluids under magnetic fields in different directions. Comp Appl Math 2020;39:1–26.[CrossRef]
[18] Liao CC, Li WK, Chu CC. Analysis of heat transfer transition of thermally driven flow within a square enclosure under effects of inclined magnetic field. Int Comm Heat Mass Transf 2022;130:105817.[CrossRef]
[19] Sajjadi H, Amiri Delouei A, Sheikholeslami M, Atashafrooz M. Double MRT Lattice Boltzmann simulation of 3-D MHD natural convection in a cubic cavity with sinusoidal temperature distribution utilizing nanofluid. Int J Heat Mass Transf 2018;126:489–503.[CrossRef]
[20] Miroshnichenko V, Sheremet MA, Oztop HF, Abu-Hamdeh N. Natural convection of Al₂O₃/H₂O nanofluid in an open inclined cavity with a heat-generating element. Int J Heat Mass Transf 2018;126:184–191.[CrossRef]
[21] VahabzadehBozorg M, Siavashi M. Two-phase mixed convection heat transfer and entropy generation analysis of a non-Newtonian nanofluid inside a cavity with internal rotating heater and cooler. Int J Mech Sci 2019;151:842–857.[CrossRef]
[22] Abu-Nada E, Pop I, Mahian O. A dissipative particle dynamics two-component nanofluid heat transfer model: Application to natural convection. Int J Heat Mass Transf 2019;133:1086–1098.[CrossRef]
[23] Keyhani-Asl A, Hossainpour S, Rashidi MM, Sheremet MA, Yang Z. Comprehensive investigation of solid and porous fins' influence on natural convection in an inclined rectangular enclosure. Int J Heat Mass Transf 2019;133:729–744.[CrossRef]
[24] Sajjadi H, Amiri Delouei A, Sheikholeslami M, Atashafrooz M. Simulation of three-dimensional MHD natural convection using double MRT Lattice Boltzmann method. Physica A Stat Mech Appl 2019;515:474–496.[CrossRef]
[25] Pekmen Geridönmez B. Numerical simulation of natural convection in a porous cavity filled with ferrofluid in presence of magnetic source. J Therm Eng 2018;4:1756–1769.[CrossRef]
[26] Aneja M, Chandra A, Sharma S. Natural convection in a partially heated porous cavity to Casson fluid. Int Comm Heat Mass Transf 2020;114:104555.[CrossRef]
[27] Horimek A. Non-Newtonian natural-convection cooling of a heat source of variable length and position placed at the bottom of a square cavity. Therm Sci 2023;27:4161–4178.[CrossRef]
[28] Raje A, Ashlesha AB, Kulkarni A. Entropy analysis of the MHD Jeffrey fluid flow in an inclined porous pipe with convective boundaries. Int J Thermofluids 2023;17:100275.[CrossRef]
[29] Li Y, Wang Y, Pang L, Xiao L, Ding Z, Duan P. Research progress of plasma/MHD flow control in inlet. Chin J Theor Appl Mech 2019;51:311–321.
[30] Karimi MS, Oboodi MJ. Investigation and recent developments in aerodynamic heating and drag reduction for hypersonic flows. Heat Mass Transf 2019;55:547–569.[CrossRef]
[31] Nazee M, Ali N, Javed T, Nazir MW. Numerical analysis of the full MHD model with the Galerkin finite-element method. Eur Phys J Plus 2019;134:204.[CrossRef]
[32] Mwapinga A, Mureithi E, Makungu J, Masanja V. MHD arterial blood flow and mass transfer under the presence of stenosis, body acceleration and chemical reaction: a case of magnetic therapy. J Math Informatics 2020;18:85–103.[CrossRef]
[33] Dharmaiah G, Rama Prasad JL, Balamurugan KS, Nurhidayat I, Fernandez-Gamiz U, Noeiaghdam S. Performance of magnetic dipole contribution on ferromagnetic non-Newtonian radiative MHD blood flow: an application of biotechnology and medical sciences. Heliyon 2023;9:e13369.[CrossRef]
[34] Chen X, Zhao L, Wang F, Peng A. Numerical analysis of the self-propulsion performance of seawater MHD propulsion underwater vehicle. Magnetohydrodynamics 2023;59:7.[CrossRef]
[35] Selvi RK, Muthuraj R. MHD oscillatory flow of a Jeffrey fluid in a vertical porous channel with viscous dissipation. Ain Shams Eng J 2018;9:2503–2516.[CrossRef]
[36] Sarada K, Gowda RJP, Sarris IE, Kumar RN, Prasannakumara BC. Effect of magnetohydrodynamics on heat transfer behaviour of a non-Newtonian fluid flow over a stretching sheet under local thermal non-equilibrium condition. Fluids 2021;6:264.[CrossRef]
[37] Shaheen S, Bég OA, Gul F, Maqbool K. Electro-osmotic propulsion of Jeffrey fluid in a ciliated channel under the effect of nonlinear radiation and heat source/sink. J Biomech Eng 2021;143:051008.[CrossRef]
[38] Ahmed SY, Al-Amir QR, Hamzah HK, Ali FH, Abed AM, Al-Manea AA, et al. Investigation of natural convection and entropy generation of non-Newtonian flow in molten polymer-filled odd-shaped cavities using finite difference lattice Boltzmann method. Numer Heat Transf Part B Fundam 2024;1–26.[CrossRef]
[39] Yasmeen S, Asghar S, Anjum HJ, Ehsan T. Analysis of Hartmann boundary layer peristaltic flow of Jeffrey fluid: Quantitative and qualitative approaches. Comm Nonlinear Sci Numer Simul 2019;76:51–65.[CrossRef]
[40] Ali A, Maqsood M, Anjum HJ, Awais M, Sulaiman M. Analysis of heat transfer on MHD Jeffrey nanofluid flow over nonlinear elongating surface of variable thickness. J Appl Math Mech 2021;102:e202100250.[CrossRef]
[41] Reddappa B, Parandhama A, Venkateswara Raju K, Sreenadh S. Analysis of the boundary layer flow of thermally conducting Jeffrey fluid over a stratified exponentially stretching sheet. Turk J Comput Math Educ 2021;12:730–739.
[42] Ishtiaq F, Ellahi R, Bhatti MM, Alamri SZ. Insight in thermally radiative cilia-driven flow of electrically conducting non-Newtonian Jeffrey fluid under the influence of induced magnetic field. Mathematics 2022;10:2007.[CrossRef]
[43] Reddappa B, SudheerBabu M, Sreenadh S. Magnetohydrodynamic (MHD) Jeffrey nanofluid flow over an exponentially stretching sheet through a porous medium. AIP Conf Proc 2023;2649:030003.[CrossRef]
[44] Khan A, Gul T, Ali I, Abd El-Wahed HK, Taseer M, Alghamdi W, et al. Thermal examination for double diffusive MHD Jeffrey fluid flow through the space of disc and cone apparatus subject to impact of multiple rotations. Int J Heat Fluid Flow 2024;106:109295.[CrossRef]
[45] Yadav D. Effect of electric field on the onset of Jeffrey fluid convection in a heat-generating porous medium layer. Pramana J Phys 2022;96:23. [CrossRef]
[46] Basak T, Roy S. Natural convection in a square cavity filled with a porous medium: effects of various thermal boundary conditions. Int J Heat Mass Transf 2006;49:1430–1441.[CrossRef]
[47] Basak T, Roy S, Balakrishnan AR. Effects of thermal boundary conditions on natural convection flows within a square cavity. Int J Heat Mass Transf 2006;49:4525–4535.[CrossRef]
[48] Khan ZH, Khan WA, Hamid M. Non-Newtonian fluid flow around a Y-shaped fin embedded in a square cavity. J Therm Anal Calorim 2021;143:573–585.[CrossRef]
[49] Nield DA, Bejan A. Convection in Porous Media. 3rd ed. New York: Springer; 2006.
[50] Dimitrienko YI, Li S. Numerical simulation of MHD natural convection heat transfer in a square cavity filled with Carreau fluids under magnetic fields in different directions. Comput Appl Math 2020;39:252.[CrossRef]

Details

Primary Language

English

Subjects

Fluid Mechanics and Thermal Engineering (Other)

Journal Section

Research Article

Authors

S. Vigneshwari This is me
0009-0001-7501-4488
India

B. Reddappa ^* This is me
0000-0002-6048-9069
India

B. Rushi Kumar This is me
0000-0001-8391-098X
India

Publication Date

May 16, 2025

Submission Date

April 12, 2024

Acceptance Date

September 21, 2024

Published in Issue

Year 2025 Volume: 11 Number: 3

IZ

https://izlik.org/JA87YS93CZ

Cite

RIS / Bibtex

APA

Vigneshwari, S., Reddappa, B., & Rushi Kumar, B. (2025). Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation. Journal of Thermal Engineering, 11(3), 780-799. https://izlik.org/JA87YS93CZ

AMA

1.Vigneshwari S, Reddappa B, Rushi Kumar B. Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation. Journal of Thermal Engineering. 2025;11(3):780-799. https://izlik.org/JA87YS93CZ

Chicago

Vigneshwari, S., B. Reddappa, and B. Rushi Kumar. 2025. “Magnetohydrodynamic Natural Convection of Complex Fluids in a Square Porous Cavity: A Numerical Simulation”. Journal of Thermal Engineering 11 (3): 780-99. https://izlik.org/JA87YS93CZ.

EndNote

Vigneshwari S, Reddappa B, Rushi Kumar B (May 1, 2025) Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation. Journal of Thermal Engineering 11 3 780–799.

IEEE

[1]S. Vigneshwari, B. Reddappa, and B. Rushi Kumar, “Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation”, Journal of Thermal Engineering, vol. 11, no. 3, pp. 780–799, May 2025, [Online]. Available: https://izlik.org/JA87YS93CZ

ISNAD

Vigneshwari, S. - Reddappa, B. - Rushi Kumar, B. “Magnetohydrodynamic Natural Convection of Complex Fluids in a Square Porous Cavity: A Numerical Simulation”. Journal of Thermal Engineering 11/3 (May 1, 2025): 780-799. https://izlik.org/JA87YS93CZ.

JAMA

1.Vigneshwari S, Reddappa B, Rushi Kumar B. Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation. Journal of Thermal Engineering. 2025;11:780–799.

MLA

Vigneshwari, S., et al. “Magnetohydrodynamic Natural Convection of Complex Fluids in a Square Porous Cavity: A Numerical Simulation”. Journal of Thermal Engineering, vol. 11, no. 3, May 2025, pp. 780-99, https://izlik.org/JA87YS93CZ.

Vancouver

1.S. Vigneshwari, B. Reddappa, B. Rushi Kumar. Magnetohydrodynamic natural convection of complex fluids in a square porous cavity: A numerical simulation. Journal of Thermal Engineering [Internet]. 2025 May 1;11(3):780-99. Available from: https://izlik.org/JA87YS93CZ