Skip to main content
Log in

Hybrid nanofluid flow around a triangular-shaped obstacle inside a split lid-driven trapezoidal cavity

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

Abstract

Numerical simulation analyzes the mixed convection flow of \(\hbox {Al}_{2}\hbox {O}_{3}{-}\hbox {Cu}{-}\hbox {H}_{2}\hbox {O}\) (aluminium oxide–copper–water) hybrid nanofluid inside a split lid-driven trapezoidal cavity. A triangular-shaped cold obstacle is placed inside the cavity. The horizontal base of the cavity is kept cold, whereas the side walls are chosen adiabatic. The thermally active upper wall maintained at a constant temperature is split into halves, and each half moves opposite to the other with constant velocity. Modeled equations are converted into a nonlinear system of partial differential equations. This system, along with incorporated physical boundary constraints, is solved numerically via Galerkin finite-element method. Attained results are also compared with the earlier publications to ensure validation and accuracy. To examine the effects of various pertinent parameters, various flow and heat transfer attributes like dimensionless velocity, stream contours, temperature, and isotherms, and local and average Nusselt numbers are critically analyzed. The outcomes of this examination will provide qualitative suggestions to improve the cooling mechanism of several electronic gadgets and thermal devices.

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

Access this article

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

Instant access to the full article PDF.

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

Similar content being viewed by others

Availability of data and materials

The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. M.K. Moallemi, K.S. Jang, Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. Int. J. Heat Mass Transf. 35, 1881–1892 (1992)

    Article  MATH  Google Scholar 

  2. O. Aydin, W.J. Yang, Mixed convection in cavities with a locally heated lower wall and moving sidewalls. Numer. Heat Transf. A 37, 695–710 (2000)

    Article  ADS  Google Scholar 

  3. A.J. Chamkha, Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation of absorption. Numer. Heat Transf. Part A 41, 529–546 (2002)

    Article  ADS  Google Scholar 

  4. H.F. Oztop, I. Dagtekin, Mixed convection in two-sided lid-driven differentially heated square cavity. Int. J. Heat Mass Transf. 47, 1761–1769 (2004)

    Article  MATH  Google Scholar 

  5. T. Basak, S. Roy, P.K. Sharma, I. Pop, Analysis of mixed convection flows within a square cavity with linearly heated sidewall(s). Int. J. Heat Mass Transf. 52, 2224–2242 (2009)

    Article  MATH  Google Scholar 

  6. L.M. González, M. Ahmed, J. Kühnen, H.C. Kuhlmann, V. Theofilis, Three-dimensional flow instability in a lid-driven isosceles triangular cavity. J. Fluid Mech. 675, 369–396 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. M.A. Ismael, I. Pop, A.J. Chamkha, Mixed convection in a lid-driven square cavity with partial slip. Int. J. Therm. Sci. 82, 47–61 (2014)

    Article  Google Scholar 

  8. M. Nasir Uddin, A. Farhana, Md. AbdulAlim, Numerical study of magnetohydrodynamic (MHD) mixed convection flow in a lid-driven triangular cavity. J. Naval Archit. Mar. Eng. 12, 21–32 (2015)

    Article  Google Scholar 

  9. T. Javed, Z. Mehmood, Ioan Pop, MHD-Mixed convection flow in a lid-driven trapezoidal cavity under uniformly/non-uniformly heated bottom wall. Int. J. Numer. Methods Heat Fluid Flow 27, 1–20 (2017)

    Article  Google Scholar 

  10. H.F. Oztop, Z. Zhao, B. Yu, Fluid flow due to combined convection in a lid-driven enclosure having a circular body. Int. J. Heat Fluid Flow 30, 886–901 (2009)

    Article  Google Scholar 

  11. M.M. Rahman, M.A. Alim, M.M.A. Sarker, Numerical study on the conjugate effect of joule heating and magnetohydrodynamics mixed convection in an obstructed lid-driven square cavity. Int. Commun. Heat Mass Transf. 37, 524–534 (2010)

    Article  Google Scholar 

  12. M. Billah, M. Rahman, J. Ahamed, M. Bhuiya, MHD mixed convection heat transfer enhancement in a lid-driven enclosure having a heat-generating body: aspect ratio and Prandtl number effect. Int. J. Energy Technol. 3, 1–8 (2011)

    Google Scholar 

  13. A.W. Islam, M.A.R. Sharif, E.S. Carlson, Mixed convection in a lid-driven square cavity with an isothermally heated square blockage inside. Int. J. Heat Mass Transf. 55, 5244–5255 (2012)

    Article  Google Scholar 

  14. K. Khanafer, S.M. Aithal, Laminar mixed convection flow and heat transfer characteristics in a lid-driven cavity with a circular cylinder. Int. J. Heat Mass Transf. 66, 200–209 (2013)

    Article  Google Scholar 

  15. S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticle, in Developments and Applications of Non-Newtonian Flows, vol. 66, ed. by D.A. Signer, H.P. Wang (ASME FED, 1995), pp. 99–105

    Google Scholar 

  16. W.J. Minkowycz, E.M. Sparrow, J.P. Abraham, Nanoparticle Heat Transfer and Fluid Flow (CRC Press)

  17. M. Sheikholeslami, Nanofluid Heat and Mass Transfer in Engineering Problems (Intech Open, London, 2017)

    Google Scholar 

  18. Y. Menni, A.J. Chamkha, A. Azzi, Nanofluid flow in complex geometries—a review. J. Nanofluids 8, 893–916 (2019)

    Article  Google Scholar 

  19. A. Hussain, M.Z. Salleh, I. Khan, S. Shafie, Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene, and engine oil. J. Mol. Liq. 229, 482–488 (2017)

    Article  Google Scholar 

  20. A.J. Chamkha, A.S. Dogonchi, D.D. Ganji, Magnetohydrodynamic flow and heat transfer of a hybrid nanofluid in a rotating system among two surfaces in the presence of thermal radiation and Joule heating. AIP Adv. 9, 025103 (2019)

    Article  ADS  Google Scholar 

  21. S. Suresh, K.P. Venkitaraj, P. Selvakumar, M. Chandrasekar, Effect of \(\text{ Al}_{2}\text{ O}_{3}\)–Cu/water hybrid nanofluid in heat transfer. Exp. Therm. Fluid Sci. 38, 54–60 (2012)

    Article  Google Scholar 

  22. S. Senthilaraja, K. Vijayakumar, R. Ganadevi, A comparative study on thermal conductivity of Al\(_2\)O\(_3\) /water, CuO/water, and Al\(_2\)O\(_3\)–CuO/water nanofluids. Dig. J. Nanomater. Biostruct. 10, 1449–1458 (2015)

    Google Scholar 

  23. J. Sarkar, P. Ghosh, A. Adil, A review on hybrid nanofluids: recent research, development and applications. Renew. Sustain. Energy Rev. 43, 164–177 (2015)

    Article  Google Scholar 

  24. M.I. Afridi, I. Tlili, M. Goodarzi, M. Osman, N.A. Khan, Irreversibility analysis of hybrid nanofluid flow over a thin needle with effects of energy dissipation. Symmetry 11, 663 (2019)

    Article  MATH  Google Scholar 

  25. A.A. Mehrizi, M. Farhadi, H.H. Afroozi, K. Sedighi, A.A.R. Darz, Mixed convection heat transfer in a ventilated cavity with a hot obstacle: effect of nanofluid and outlet port location. Int. Commun. Heat Mass Transf. 39, 1000–1008 (2012)

    Article  Google Scholar 

  26. M. Hemmat Esfe, M. Akbari, A. Karimipour, Mixed convection in a lid-driven cavity with an inside hot obstacle-filled by an \(\text{ Al}_{2}\text{ O}_{3}\)-water nanofluid. J. Appl. Mech. Tech. Phys. 56, 443–453 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. M.H. Esfe, H.A. Refahi, H. Teimouri, M.J. Noroozi, M. Afrand, K. Arash, mixed convection fluid flow and heat transfer of the Al\(_{2}\)O\(_{3}\)–water nanofluid with variable properties in a cavity with an inside quadrilateral obstacle. Heat Transf. Res. 46, 465–482 (2015)

    Google Scholar 

  28. S. Hussain, S.E. Ahmed, T. Akbar, Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle. Int. J. Heat Mass Transf. 114, 1054–1066 (2017)

    Article  Google Scholar 

  29. F. Selimefendigil, Mixed convection in a lid-driven cavity filled with single and multiple-walled carbon nanotubes nanofluid having an inner elliptic obstacle. Propuls. Power Res. 8, 128–137 (2019)

    Article  Google Scholar 

  30. M.N. Rostami, S. Dinarvand, I. Pop, Dual solutions for mixed convective stagnation-point flow of an aqueous silica–alumina hybrid nanofluid. Chin. J. Phys. 56(5), 2465–2478 (2018)

    Article  Google Scholar 

  31. P. Sreenivasulu, T. Poornima, N.B. Reddy, Influence of joule heating and nonlinear radiation on MHD 3D dissipating flow of Casson nanofluid past a nonlinear stretching sheet. Nonlinear Eng. 8(1), 661–72 (2019)

    Article  ADS  Google Scholar 

  32. P. Sreenivasulu, T. Poornima, N.B. Reddy, M.G. Reddy, A numerical analysis on UCM dissipated nanofluid imbedded carbon nanotubes influenced by inclined Lorentzian force along with non-uniform heat source/sink. J. Nanofluids 8(5), 1076–84 (2019)

    Article  Google Scholar 

  33. P. Sreenivasulu, T. Poornima, B. Malleswari, N.B. Reddy, B. Souayeh, Viscous dissipation impact on electrical resistance heating distributed Carreau nanoliquid along stretching sheet with zero mass flux. Eur. Phys. J. Plus 135(9), 1–25 (2020)

    Article  Google Scholar 

  34. S. Pandikunta, P. Tamalapakula, Reddy N. Bhaskar, Inclined Lorentzian force effect on tangent hyperbolic radiative slip flow imbedded carbon nanotubes: Lie group analysis. J. Comput. Appl. Res. Mech. Eng. (JCARME) 10(1), 85–99 (2020)

    Google Scholar 

  35. P. Sreenivasulu, T. Poornima, B. Vasu, R.S. Reddy Gorla, Reddy N. Bhaskar, Nonlinear radiation and Navier-slip effects on UCM nanofluidý flow past a stretching sheet under Lorentzian force. J. Appl. Comput. Mech. 7(2), 638–45 (2021)

    Google Scholar 

  36. W. Aftab, A. Usman, J. Shi, K. Yuan, M. Qin, R. Zou, Phase change material-integrated latent heat storage systems for sustainable energy solutions. Energy Environ. Sci. 14(8), 4268–91 (2021)

  37. M. Yousaf, U. Naseer, Y. Li, Z. Ali, N. Mahmood, L. Wang, P. Gao, S. Guo, A mechanistic study of electrode materials for rechargeable batteries beyond lithium ions by in situ transmission electron microscopy. Energy Environ. Sci. 14(5), 2670–707 (2021)

    Article  Google Scholar 

  38. W. Aftab, X. Huang, R. Zou, The application of carbon materials in latent heat thermal energy storage (LHTES), in Thermal Transport in Carbon-Based Nanomaterials. (Elsevier, Amsterdam, 2017), pp. 243–265

    Chapter  Google Scholar 

  39. M. Usman, M. Hamid, T. Zubair, R.U. Haq, 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. 1(126), 1347–56 (2018)

    Article  Google Scholar 

  40. J.N. Reddy, An Introduction to Finite Element Analysis (McGraw-Hill, New York, 1993)

    Google Scholar 

  41. O.C. Zienkiewicz, R.L. Taylor, J.M. Too, Reduced integration technique in general analysis of plates and shells. Int. J. Numer. Methods Eng. 3, 275–290 (1971)

    Article  MATH  Google Scholar 

  42. Z.H. Khan, W.A. Khan, M.A. Sheremet, M. Hamid, M. Du, Irreversibilities in natural convection inside a right-angled trapezoidal cavity with sinusoidal wall temperature. Phys. Fluids 33(8), 083612 (2021)

    Article  ADS  Google Scholar 

  43. M. Usman, M. Hamid, Z.H. Khan, R.U. Haq, W.A. Khan, Finite element analysis of water-based Ferrofluid flow in a partially heated triangular cavity. Int. J. Numer. Methods Heat Fluid Flow 31(10), 3132–3147 (2021)

    Article  Google Scholar 

  44. Z.H. Khan, W.A. Khan, R.U. Haq, M. Usman, M. Hamid, Effects of volume fraction on water-based carbon nanotubes flow in a right-angle trapezoidal cavity: FEM based analysis. Int. Commun. Heat Mass Transf. 1(116), 104640 (2020)

    Article  Google Scholar 

  45. M. Hamid, Z.H. Khan, W.A. Khan, R.U. Haq, Natural convection of water-based carbon nanotubes in a partially heated rectangular fin-shaped cavity with an inner cylindrical obstacle. Phys. Fluids 31(10), 103607 (2019)

    Article  ADS  Google Scholar 

  46. R. Iwatsu, J.M. Hyun, K. Kuwahara, Mixed convection in a driven cavity with a stable vertical temperature gradient. Int. J. Heat Mass Transf. 36(6), 1601–1608 (1993)

    Article  Google Scholar 

Download references

Acknowledgements

The first author is profoundly grateful for the financial support of the Thousand Talents Plan 2019 “for the Introduction of High-level Talents at Home and Abroad in Sichuan Province.” The corresponding author is grateful to the financial support of the National Natural Science Foundation of China (Grant nos. 51709191). The author (M. Hamid) acknowledges the support of Fudan University through the International Exchange Fellowship and China Postdoctoral Science Foundation (No. 2020M681135).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Du.

Ethics declarations

Conflict of interest

All the authors declare that there is no actual or potential conflict of interest, including any financial, personal, or other relationships with other people or organizations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, Z.H., Khan, W.A., Qasim, M. et al. Hybrid nanofluid flow around a triangular-shaped obstacle inside a split lid-driven trapezoidal cavity. Eur. Phys. J. Spec. Top. 231, 2749–2759 (2022). https://doi.org/10.1140/epjs/s11734-022-00607-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjs/s11734-022-00607-5

Navigation