Skip to main content
SpringerLink
Log in

Heat transfer enhancement analysis of mixed convection \({\text{Cu}}/{\text{CuO}}\)–water magneto-hybrid nanofluid flow in a square enclosure with hot and cold slits in non-Darcy porous medium

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

The fluid flow over an extending cavity has many applications in different fields which include manufacturing processes, treatment of various diseases, destruction of cancer tissue, artificial lungs and radiators, heat and mass transfer, biomedical applications, environmental science, and energy production. The heat transfer investigated mixed convection MHD with \({\text{Cu}}/{\text{CuO}}\)–water hybrid nanofluid flow in a square cavity with a non-Darcy porous medium. In this study, the MAC (Marker and Cell) technique is to solve the resulting governing non-dimensional partial differential equation within a staggered grid system. The \({{\text{MATLAB}}}^{\mathrm{\circledR }}\) software is used to obtain the contours of streamlines and isotherms. In comparison with prior research, the average Nusselt number obtained under identical conditions validates the accuracy of the current study’s findings. The impact of magnetic field \(({\text{Ha}})\), non-Darcy \(({\text{Da}})\), and heat sink/source \((Q)\) parameters are discussed. The results of the current study assert that the square cavity of heat and energy transfer increases as the non-Darcy parameter value \(({\text{Da}} = 0.001, \, 0.01, \, 0.1)\) increases. The heat transfer rate is very slow as the Hartmann number \(({\text{Ha}} = 0, \, 20, \, 40)\) increases. Finally, heat transfer increases as the influence of the heat generation/absorption parameter \((Q=-6, \, 0, \, 6)\) also increases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig.1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Data Availability Statement

Data will be made available on reasonable request.

Abbreviations

\({\text{Da}}\) :

Non-Darcy

\(g\) :

Gravitational \([{{\text{ms}}}^{-2}]\)

K :

Permeability of the porous medium \([{{\text{m}}}^{2}]\)

Gr:

Grashof number

\({\text{Nu}}\) :

Nusselt number

\({\text{Pr}}\) :

Prandtl number

\(P\) :

Pressure \([{\text{N}}/{{\text{m}}}^{2}]\)

\({\text{Re}}\) :

Reynold number

\({\text{Ri}}\) :

Richardson number

\({\text{Ra}}\) :

Rayleigh number

\({B}_{0}\) :

Strength of the constant magnetic field \([{{\text{kgs}}}^{-2}{{\text{A}}}^{-1}]\)

\(T\) :

Temperature \([{\text{K}}]\)

\(Q\) :

Heat sink/source

\(t\) :

Non-dimensional time \([{\text{s}}]\)

\({t}^{*}\) :

Time \([{\text{s}}]\)

\(X,Y\) :

Non-dimensional coordinate in horizontal and vertical direction

\(x,y\) :

Cartesian co-ordinates in horizontal and vertical direction \([{\text{m}}]\)

\(U,V\) :

Non-dimensional velocity component in \(X,Y\)-direction

\(u,v\) :

Dimensional velocity component in \(x\), \(y\)-direction \([{{\text{ms}}}^{-1}]\)

\({T}_{h}\) :

Hot wall

\({T}_{c}\) :

Cold wall

L:

Horizontal length of enclosure \([{\text{m}}]\)

H:

Height of enclosure \([{\text{m}}]\)

\(\beta\) :

Coefficient of thermal expansion \([{{\text{K}}}^{-1}]\)

\(\alpha\) :

Thermal diffusivity \({[{\text{m}}}^{2}{{\text{s}}}^{-1}]\)

\(v\) :

Kinematic viscosity \([{{\text{m}}}^{2}/{\text{s}}]\)

\(\varphi\) :

Solid volume fraction

\(\sigma\) :

Electric conductivity \({[\Omega }^{-1}{{\text{m}}}^{-1}]\)

\(\theta\) :

Dimensionless temperature

\(\mu\) :

Dynamic viscosity \([{{\text{kgm}}}^{-1}{{\text{s}}}^{-1}]\)

\(\rho\) :

Density \([{\text{kg}}/{{\text{m}}}^{3}]\)

C :

Cold

H :

Hot

\({\text{bf}}\) :

Base fluid

\({\text{nf}}\) :

Nanofluid

Hnf:

Hybrid nanofluid

References

  1. M. Usman, M. Hamid, T. Zubair, R. UlHaq, W. Wang, Cu−Al2O3/Water hybrid nanofluid through a permeable surface in the presence of nonlinear radiation and variable thermal conductivity via LSM. Int. J. Heat Mass Transf. 126, 1347–1356 (2018). https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.005

    Article  Google Scholar 

  2. C. Yıldız, M. Arıcı, H. Karabay, Comparison of a theoretical and experimental thermal conductivity model on the heat transfer performance of Al2O3-SiO2/water hybrid-nanofluid. Int. J. Heat Mass Transf. 140, 598–605 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2019.06.028

    Article  Google Scholar 

  3. O. Cicek, M.A. Sheremet, A.C. Baytas, Effect of natural convection hybrid nanofluid flow on the migration and deposition of MWCNT-Fe3O4 in a square enclosure. Int. J. Therm. Sci. (2023). https://doi.org/10.1016/j.ijthermalsci.2023.108318

    Article  Google Scholar 

  4. M.A. Mansour, S. Siddiqa, R.S.R. Gorla, A.M. Rashad, Effects of heat source and sink on entropy generation and MHD natural convection of Al2O3-Cu/water hybrid nanofluid filled with square porous cavity. Therm. Sci. Eng. Prog. 6(October 2017), 57–71 (2018). https://doi.org/10.1016/j.tsep.2017.10.014

    Article  Google Scholar 

  5. K.D. Goswami, A. Chattopadhyay, S.K. Pandit, M.A. Sheremet, Transient thermogravitational convection for magneto hybrid nanofluid in a deep cavity with multiple isothermal source-sink pairs. Int. J. Therm. Sci. (2021). https://doi.org/10.1016/j.ijthermalsci.2021.107376

    Article  Google Scholar 

  6. R. Du, P. Gokulavani, M. Muthtamilselvan, F. Al-Amri, B. Abdalla, Influence of the Lorentz force on the ventilation cavity having a centrally placed heated baffle filled with the Cu–Al2O3–H2O hybrid nanofluid. Int. Commun. Heat Mass Transf. (2020). https://doi.org/10.1016/j.icheatmasstransfer.2020.104676

    Article  Google Scholar 

  7. S. Ahmed, H. Xu, Y. Zhou, Q. Yu, Modelling convective transport of hybrid nanofluid in a lid driven square cavity with consideration of Brownian diffusion and thermophoresis. Int. Commun. Heat Mass Transf. (2022). https://doi.org/10.1016/j.icheatmasstransfer.2022.106226

    Article  Google Scholar 

  8. S. Parthiban, V.R. Prasad, Magneto-convective Al2O3/Cu–Water hybrid nanofluid flow in a heated enclosure containing non-Darcy porous medium: lattice Boltzmann simulation. Eur. Phys. J. Plus 137(9), 1–20 (2022). https://doi.org/10.1140/epjp/s13360-022-03266-6

    Article  Google Scholar 

  9. S. Parthiban, V.R. Prasad, Thermal radiation and hall current effects in a MHD non-Darcy flow in a differentially heated square enclosure – lattice Boltzmann simulation. J. Porous Media 26(5), 37–56 (2023). https://doi.org/10.1615/JPORMEDIA.2022044054

    Article  Google Scholar 

  10. K. Venkatadri, H.F. Öztop, V.R. Prasad, S. Parthiban, A.O. Bég, RSM-based sensitivity analysis of hybrid nanofluid in an enclosure filled with non-Darcy porous medium by using LBM method. Numer. Heat Transf. Part A Appl. (2023). https://doi.org/10.1080/10407782.2023.2193708

    Article  Google Scholar 

  11. S.S. Shah, R. ulHaq, L.B. McCash, H.M.S. Bahaidarah, T. Aziz, Numerical simulation of lid driven flow in a curved corrugated porous cavity filled with CuO–water in the presence of heat generation/absorption. Alex. Eng. J. 61(4), 2749–2767 (2022). https://doi.org/10.1016/j.aej.2021.07.045

    Article  Google Scholar 

  12. M. Rajarathinam, N. Nithyadevi, Heat transfer enhancement of nanofluid in an inclined porous cavity. Spec. Top. Rev. Porous Media 9(2), 101–116 (2018). https://doi.org/10.1615/SpecialTopicsRevPorousMedia.v9.i2.10

    Article  Google Scholar 

  13. A.M. Aly, S.E. Ahmed, An incompressible smoothed particle hydrodynamics method for natural/mixed convection in a non-Darcy anisotropic porous medium. Int. J. Heat Mass Transf. 77, 1155–1168 (2014). https://doi.org/10.1016/j.ijheatmasstransfer.2014.06.044

    Article  Google Scholar 

  14. N. Vinodhini, V. Ramachandra Prasad, Numerical study of magneto convective Buongiorno nanofluid flow in a rectangular enclosure under oblique magnetic field with heat generation/absorption and complex wall conditions. SSRN Electron. J. 9(7), 17669 (2022). https://doi.org/10.2139/ssrn.4301336

    Article  Google Scholar 

  15. N. Vinodhini, R. Prasad, numerical study of free convection ag-water nanofluid flow in a square enclosure with viscous dissipation and heat generation/absorption effects in a porous medium with comple. J. Porous Media 26(9), 77–99 (2023). https://doi.org/10.1615/jpormedia.2023044454

    Article  Google Scholar 

  16. N. Vinodhini, V. Ramachandra Prasad, Magneto-hybrid nanofluid (Al2O3/Cu-Oil) flow in a porous square enclosure with Cattaneo-Christov heat flow model-sensitivity analysis. Indian J. Chem. Technol. 30(5), 714–730 (2023). https://doi.org/10.56042/ijct.v30i5.5194

    Article  Google Scholar 

  17. C.C. Cho, Effects of porous medium and wavy surface on heat transfer and entropy generation of Cu-water nanofluid natural convection in square cavity containing partially-heated surface. Int. Commun. Heat Mass Transf. (2020). https://doi.org/10.1016/j.icheatmasstransfer.2020.104925

    Article  Google Scholar 

  18. A. Sumithra, R. Sivaraj, Chemically reactive magnetohydrodynamic mixed convective nanofluid flow inside a square porous enclosure with viscous dissipation and Ohmic heating. Eur. Phys. J. Plus. 137, 10 (2022). https://doi.org/10.1140/epjp/s13360-022-03409-9

    Article  Google Scholar 

  19. N. Santhosh, R. Sivaraj, Comparative heat transfer performance of hydromagnetic mixed convective flow of cobalt-water and cobalt-kerosene ferro-nanofluids in a porous rectangular cavity with shape effects. Eur. Phys. J. Plus 138, 240 (2023). https://doi.org/10.1140/epjp/s13360-023-03837-1

    Article  Google Scholar 

  20. S.A. Khan et al., Computational analysis of natural convection with water based nanofluid in a square cavity with partially active side walls: applications to thermal storage. J. Mol. Liq. (2023). https://doi.org/10.1016/j.molliq.2023.122003

    Article  Google Scholar 

  21. G.A. Sheikhzadeh, A. Arefmanesh, M.H. Kheirkhah, R. Abdollahi, Natural convection of Cu water nanofluid in a cavity with partially active side walls. Eur. J. Mech. B/Fluids 30(2), 166–176 (2011). https://doi.org/10.1016/j.euromechflu.2010.10.003

    Article  ADS  Google Scholar 

  22. K. Khanafer, K. Vafai, M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Int. J. Heat Mass Transf. 46(19), 3639–3653 (2003). https://doi.org/10.1016/S0017-9310(03)00156-X

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Advances Sciences, Vellore Institute of Technology, Vellore, 632014, India

    K. Seenuvasan & V. Ramachandra Prasad

Authors
  1. K. Seenuvasan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Ramachandra Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Ramachandra Prasad.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Seenuvasan, K., Prasad, V.R. Heat transfer enhancement analysis of mixed convection \({\text{Cu}}/{\text{CuO}}\)–water magneto-hybrid nanofluid flow in a square enclosure with hot and cold slits in non-Darcy porous medium. Eur. Phys. J. Plus 139, 313 (2024). https://doi.org/10.1140/epjp/s13360-024-05113-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-024-05113-2

Search

Navigation