Skip to main content

Advertisement

Log in

Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The magnetohydrodynamic (MHD) mixed convection flow past a shrinking vertical sheet with thermal radiation is considered. Besides, the effects of Cu-Al2O3 nanoparticles and dust particles are considered. The similarity variables reduce the governing equations to the similarity equations, which are then solved numerically. The outcome shows that, for the shrinking case, the solutions are not unique. The rate of heat transfer and the friction factor enlarge with increasing the values of the copper nanoparticle volume fraction as well as the magnetic parameter. Meanwhile, the assisting flow and the rise of the thermal radiation reduce these quantities. Two solutions are found, and the boundary layer separation is dependent on the mixed convection parameter.

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.

Similar content being viewed by others

References

  1. KUMAR, K. G. and ARCHANA, M. Comparative study of SiO2 and TiO2 nanoparticles on flow and heat transfer of dusty fluid over a stretching sheet. Multidiscipline Modeling in Materials and Structures, 15, 990–1005 (2019)

    Article  Google Scholar 

  2. SAFFMAN, P. G. On the stability of laminar flow of a dusty gas. Journal of Fluid Mechanics, 13, 120–128 (1962)

    Article  MathSciNet  Google Scholar 

  3. DATTA, N. and MISHRA, S. K. Boundary layer flow of a dusty fluid over a semi-infinite flat plate. Acta Mechanica, 42, 71–83 (1982)

    Article  Google Scholar 

  4. GIREESHA, B. J., CHAMKHA, A. J., MANJUNATHA, S., and BAGEWADI, C. S. Mixed convective flow of a dusty fluid over a vertical stretching sheet with non-uniform heat source/sink and radiation. International Journal of Numerical Methods for Heat and Fluid Flow, 23, 598–612 (2013)

    Article  MathSciNet  Google Scholar 

  5. ROOPA, G. S., GIREESHA, B. J., and BAGEWADI, C. S. Numerical investigation of mixed convection boundary layer flow of a dusty fluid over a vertical surface with radiation. Afrika Matematika, 24, 487–502 (2013)

    Article  MathSciNet  Google Scholar 

  6. JALIL, M., ASGHAR, S., and YASMEEN, S. An exact solution of MHD boundary layer flow of dusty fluid over a stretching surface. Mathematical Problems in Engineering, 2017, 2307469 (2017)

    Article  MathSciNet  Google Scholar 

  7. SIDDIQA, S., HOSSAIN, M. A., and SAHA, S. C. Two-phase natural convection flow of a dusty fluid. International Journal of Numerical Methods for Heat and Fluid Flow, 25, 1542–1556 (2015)

    Article  MathSciNet  Google Scholar 

  8. TURKYILMAZOGLU, M. Magnetohydrodynamic two-phase dusty fluid flow and heat model over deforming isothermal surfaces. Physics of Fluids, 29, 013302 (2017)

    Article  Google Scholar 

  9. MISHRA, S. R., KHAN, M. I., and ROUT, B. C. Dynamics of dust particles in a conducting dusty nanomaterials: a computational approach. International Communications in Heat and Mass Transfer, 119, 104967 (2020)

    Article  Google Scholar 

  10. RADHIKA, M., PUNITH-GOWDA, R. J., NAVEENKUMAR, R., SIDDABASAPPA, B. C., and PRASANNAKUMARA, B. C. Heat transfer in dusty fluid with suspended hybrid nanoparticles over a melting surface. Heat Transfer, 50, 2150–2167 (2021)

    Article  Google Scholar 

  11. FAVRE-MARINET, M. and TARDU, S. Convective Heat Transfer: Solved Problem, Wiley, London (2009)

    Book  Google Scholar 

  12. CHOI, S. U. S. and EASTMAN, J. A. Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, American Society of Mechanical Engineers, San Francisco, 99–105 (1995)

    Google Scholar 

  13. OZTOP, H. F. and ABU-NADA, E. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow, 29, 1326–1336 (2008)

    Article  Google Scholar 

  14. TIWARI, R. K. and DAS, M. K. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. Journal of Heat and Mass Transfer, 50, 2002–2018 (2007)

    Article  Google Scholar 

  15. KHANAFER, K., VAFAI, K., and LIGHTSTONE, M. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. Journal of Heat and Mass Transfer, 46, 3639–3653 (2003)

    Article  Google Scholar 

  16. HAMAD, M. A. A. Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field. International Communications in Heat and Mass Transfer, 38, 487–492 (2011)

    Article  Google Scholar 

  17. KAMESWARAN, P. K., NARAYANA, M., SIBANDA, P., and MURTHY, P. V. S. N. Hydromagnetic nanofluid flow due to a stretching or shrinking sheet with viscous dissipation and chemical reaction effects. International Journal of Heat and Mass Transfer, 55, 7587–7595 (2012)

    Article  Google Scholar 

  18. KHAN, U., ZAIB, A., KHAN, I., and NISAR, K. S. Activation energy on MHD flow of titanium alloy (Ti6Al4V) nanoparticle along with a cross flow and streamwise direction with binary chemical reaction and non-linear radiation: dual solutions. Journal of Materials Research and Technology, 9, 188–199 (2020)

    Article  Google Scholar 

  19. WAINI, I., ISHAK, A., and POP, I. Dufour and Soret effects on Al2O3-water nanofluid flow over a moving thin needle: Tiwari and Das model. International Journal of Numerical Methods for Heat & Fluid Flow, 31, 766–782 (2021)

    Article  Google Scholar 

  20. JANA, S., SALEHI-KHOJIN, A., and ZHONG, W. H. Enhancement of fluid thermal conductivity by the addition of single and hybrid nano-additives. Thermochimica Acta, 462, 45–55 (2007)

    Article  Google Scholar 

  21. SURESH, S., VENKITARAJ, K. P., SELVAKUMAR, P., and CHANDRASEKAR, M. Synthesis of Al2O3-Cu/water hybrid nanofluids using two step method and its thermo physical properties. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 388, 41–48 (2011)

    Article  Google Scholar 

  22. SIDIK, N. A. C., ADAMU, I. M., JAMIL, M. M., KEFAYATI, G. H. R., MAMAT, R., and NAJAFI, G. Recent progress on hybrid nanofluids in heat transfer applications: a comprehensive review. International Communications in Heat and Mass Transfer, 78, 68–79 (2016)

    Article  Google Scholar 

  23. TAKABI, B. and SALEHI, S. Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid. Advances in Mechanical Engineering, 6, 147059 (2014)

    Article  Google Scholar 

  24. KHAN, U., ZAIB, A., KHAN, I., BALEANU, D., and NISAR, K. S. Enhanced heat transfer in moderately ionized liquid due to hybrid MoS2/SiO2 nanofluids exposed by nonlinear radiation: stability analysis. Crystals, 10, 142 (2020)

    Article  Google Scholar 

  25. KHAN, U., WAINI, I., ISHAK, A., and POP, I. Unsteady hybrid nanofluid flow over a radially permeable shrinking/stretching surface. Journal of Molecular Liquids, 331, 115752 (2021)

    Article  Google Scholar 

  26. WAINI, I., ISHAK, A., and POP, I. Hiemenz flow over a shrinking sheet in a hybrid nanofluid. Results in Physics, 19, 103351 (2020)

    Article  Google Scholar 

  27. WAINI, I., ISHAK, A., and POP, I. MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge. Applied Mathematics and Mechanics (English Edition), 41, 507–520 (2020) https://doi.org/10.1007/s10483-020-2584-7

    Article  MathSciNet  Google Scholar 

  28. YASHKUN, U., ZAIMI, K., ISHAK, A., POP, I., and SIDAOUI, R. Hybrid nanofluid flow through an exponentially stretching/shrinking sheet with mixed convection and Joule heating. International Journal of Numerical Methods for Heat & Fluid Flow, 31, 1930–1950 (2021)

    Article  Google Scholar 

  29. ZAINAL, N. A., NAZAR, R., NAGANTHRAN, K., and POP, I. Impact of anisotropic slip on the stagnation-point flow past a stretching/shrinking surface of the Al2O3-Cu/H2O hybrid nanofluid. Applied Mathematics and Mechanics (English Edition), 41, 1401–1416 (2020) https://doi.org/10.1007/s10483-020-2642-6

    Article  MathSciNet  Google Scholar 

  30. SARKAR, J., GHOSH, P., and ADIL, A. A review on hybrid nanofluids: recent research, development and applications. Renewable and Sustainable Energy Reviews, 43, 164–177 (2015)

    Article  Google Scholar 

  31. BABU, J. A. R., KUMAR, K. K., and RAO, S. S. State-of-art review on hybrid nanofluids. Renewable and Sustainable Energy Reviews, 77, 551–565 (2017)

    Article  Google Scholar 

  32. HUMINIC, G. and HUMINIC, A. Entropy generation of nanofluid and hybrid nanofluid flow in thermal systems: a review. Journal of Molecular Liquids, 302, 112533 (2020)

    Article  Google Scholar 

  33. YANG, L., JI, W., MAO, M., and HUANG, J. An updated review on the properties, fabrication and application of hybrid-nanofluids along with their environmental effects. Journal of Cleaner Production, 257, 120408 (2020)

    Article  Google Scholar 

  34. ROSSELAND, S. Astrophysik auf Atomtheoretischer Grundlage, Springer-Verlag, Berlin (1931)

    Book  Google Scholar 

  35. WAINI, I., ISHAK, A., and POP, I. Hybrid nanofluid flow over a permeable non-isothermal shrinking surface. Mathematics, 9, 538 (2021)

    Article  Google Scholar 

  36. HUSSAIN, S., AHMED, S. E., and AKBAR, T. Entropy generation analysis in MHD mixed convection of hybrid nanofluid in an open cavity with a horizontal channel containing an adiabatic obstacle. International Journal of Heat and Mass Transfer, 114, 1054–1066 (2017)

    Article  Google Scholar 

  37. MERKIN, J. H. On dual solutions occurring in mixed convection in a porous medium. Journal of Engineering Mathematics, 20, 171–179 (1986)

    Article  Google Scholar 

  38. WEIDMAN, P. D., KUBITSCHEK, D. G., and DAVIS, A. M. J. The effect of transpiration on self-similar boundary layer flow over moving surfaces. International Journal of Engineering Science, 44, 730–737 (2006)

    Article  Google Scholar 

  39. HARRIS, S. D., INGHAM, D. B., and POP, I. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transport in Porous Media, 77, 267–285 (2009)

    Article  Google Scholar 

  40. MIKLAVČIČ, M. and WANG, C. Y. Viscous flow due to a shrinking sheet. Quarterly of Applied Mathematics, 64, 283–290 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Universiti Teknikal Malaysia Melaka and Universiti Kebangsaan Malaysia (No. DIP-2020-001) for funds.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Ishak.

Additional information

Citation: WAINI, I., ISHAK, A., and POP, I. Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation. Applied Mathematics and Mechanics (English Edition), 43(1), 12–-140 (2022) https://doi.org/10.1007/s10483-022-2807-8

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Waini, I., Ishak, A. & Pop, I. Magnetohydrodynamic flow past a shrinking vertical sheet in a dusty hybrid nanofluid with thermal radiation. Appl. Math. Mech.-Engl. Ed. 43, 127–140 (2022). https://doi.org/10.1007/s10483-022-2807-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-022-2807-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Navigation