Skip to main content
SpringerLink
Log in

Effects of viscous dissipation and chemical reaction on MHD squeezing flow of Casson nanofluid between parallel plates in a porous medium with slip boundary condition

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

Abstract

The present numerical study investigates magnetohydrodynamic squeezing flow of Casson nanofluid embedded in a porous medium with velocity slip under the influence of viscous dissipation and chemical reaction. Buongiorno’s nanofluid model is considered in this study. Suitable similarity transformations are used to convert the governing nonlinear partial differential equations into the system of nonlinear ordinary differential equations. Then, the equations are solved using an implicit finite difference scheme known as Keller-box method. The present method is validated by comparing the numerical results of skin friction coefficient, Nusselt and Sherwood numbers with previous published results and found to be in good agreement. Graphical results for velocity, temperature and nanoparticles concentration as well as wall shear stress, heat and mass transfer rate are examined with pertinent parameters. Findings reveal that fluid velocity and wall shear stress increase when the plates move closer. Also, increment of Casson and Hartmann number reduce the fluid velocity, temperature and nanoparticles concentration. The presence of viscous dissipation and thermophoresis enhance the fluid temperature and the convective heat transfer rate. Moreover, the rate of convective mass transfer decrease when Brownian motions of nanoparticles occurs, while it rises with increase in chemical reaction and thermophoresis.

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
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. S.U.S. Choi, J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles, in Proc ASME International Mechanical Engineering Congress Expo. ASME, FED231/MD66, San Francisco (1995), pp. 99–105

  2. J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl. Phys. Lett. 78, 718–720 (2001). https://doi.org/10.1063/1.1341218

    Article  ADS  Google Scholar 

  3. S. Senthilraja, M. Karthikeyan, R. Gangadevi, Nanofluid applications in future automobiles: comprehensive review of existing data. Nano-Micro Lett. 2, 306–310 (2010). https://doi.org/10.3786/nml.v2i4.p306-310

    Article  Google Scholar 

  4. K.V. Wong, O. De Leon, Applications of nanofluids: current and future. Adv. Mech. Eng. (2010). https://doi.org/10.1155/2010/519659

    Article  Google Scholar 

  5. J. Buongiorno, Convective transport in nanofluids. ASME J. Heat Transf. 128, 240–250 (2006). https://doi.org/10.1115/1.2150834

    Article  Google Scholar 

  6. M. Sheikholeslami, M. Hatami, G. Domairry, Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in presence of time dependent magnetic field. J. Taiwan Inst. Chem. Eng. 46, 43–50 (2015). https://doi.org/10.1016/j.jtice.2014.09.025

    Article  Google Scholar 

  7. M. Usman, M. Hamid, U. Khan, S.T. Mohyud-Din, M.A. Iqbal, W. Wang, Differential transform method for unsteady nanofluid flow and heat transfer. Alex. Eng. J. 57, 1867–1875 (2017). https://doi.org/10.1016/j.aej.2017.03.052

    Article  Google Scholar 

  8. U. Shankar, N.B. Naduvinamani, Magnetized impacts of Brownian motion and thermophoresis on unsteady squeezing flow of nanofluid between two parallel plates with chemical reaction and Joule heating. Heat Transf. Asian Res. 48, 4174–4202 (2019). https://doi.org/10.1002/htj.21587

    Article  Google Scholar 

  9. M. Stefan, Experiments on apparent adhesion. London Edinburgh Dublin Philos. Mag. J. Sci. 47, 465–466 (1874). https://doi.org/10.1002/htj.21587

    Article  Google Scholar 

  10. O. Reynolds, On the theory of lubrication and its application to Mr. Beauchamp tower’s experiments, including an experimental determination of the viscosity of olive oil. Philos. Trans. R. Soc. Lond. 177, 157–234 (1886). https://doi.org/10.1098/rstl.1886.0005

    Article  ADS  MATH  Google Scholar 

  11. F.R. Archibald, Load capacity and time relations for squeeze films. Trans. ASME 78, 231–245 (1956). https://doi.org/10.1016/0043-1648(73)90161-0

    Article  Google Scholar 

  12. J.D. Jackson, A study of squeezing flow. Appl. Sci. Res. 11, 148–152 (1963). https://doi.org/10.1007/BF03184719

    Article  MATH  Google Scholar 

  13. R. Usha, R. Sridharan, Arbitrary squeezing of a viscous fluid between elliptic plates. Fluid Dyn. Res. 18, 35–51 (1996). https://doi.org/10.1016/0169-5983(96)00002-0

    Article  ADS  Google Scholar 

  14. D.C. Kuzma, Fluid inertia effects in squeeze films. Appl. Sci. Res. 18, 15–20 (1968). https://doi.org/10.1007/BF00382330

    Article  Google Scholar 

  15. J.A. Tichy, W.O. Winer, Inertial considerations in parallel circular squeeze film bearings. J. Lubr. Technol. 92, 588–592 (1970). https://doi.org/10.1115/1.3451480

    Article  Google Scholar 

  16. R.J. Grimm, Squeezing flows of Newtonian liquid films: an analysis including fluid inertia. Appl. Sci. Res. 32, 149–166 (1976). https://doi.org/10.1007/BF00383711

    Article  ADS  Google Scholar 

  17. C.Y. Wang, The squeezing of a fluid between two plates. J. Appl. Mech. 43, 579–583 (1976). https://doi.org/10.1115/1.3423935

    Article  ADS  MATH  Google Scholar 

  18. A. Cameron, Basic Lubrication Theory (Prentice Hall Europe, Upper Saddle River, 1981)

    Google Scholar 

  19. N.M. Bujurke, P.K. Achar, N.P. Pai, Computer extended series for squeezing flow between plates. Fluid Dyn. Res. 16, 173–187 (1995). https://doi.org/10.1016/0169-5983(94)00058-8

    Article  ADS  Google Scholar 

  20. M. Rashidi, H. Shahmohamadi, S. Dinarvand, Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates. Math. Probl. Eng. (2008). https://doi.org/10.1155/2008/935095

    Article  MathSciNet  MATH  Google Scholar 

  21. U. Khan, N. Ahmed, S.I. Khan, Z.A. Zaidi, Y. Xiao-Jun, S.T. Mohyud-Din, On unsteady two-dimensional and axisymmetric squeezing flow between parallel plates. Alex. Eng. J. 53, 463–468 (2014). https://doi.org/10.1016/j.aej.2014.02.002

    Article  Google Scholar 

  22. N.A.M. Noor, S. Shafie, M.A. Admon, Unsteady MHD flow of Casson nanofluid with chemical reaction, thermal radiation and heat generation/absorption. MATEMATIKA 35, 33–52 (2019). https://doi.org/10.11113/matematika.v35.n4.1262

    Article  Google Scholar 

  23. N. Casson, A flow equation for the pigment oil suspensions of the printing ink type, in rheology of disperse systems (Pergamon, New York, 1959)

    Google Scholar 

  24. U. Khan, N. Ahmed, S.I. Khan, S. Bano, S.T. Mohyud-Din, Unsteady squeezing flow of a Casson fluid between parallel plates. World J. Model. Simul. 10, 308–319 (2014)

    Google Scholar 

  25. N. Ahmed, U. Khan, S.I. Khan, S. Bano, S.T. Mohyud-Din, Effects on magnetic field in squeezing flow of a Casson fluid between parallel plates. J. King Saud Univ. Sci. 29, 119–125 (2015). https://doi.org/10.1016/j.jksus.2015.03.006

    Article  Google Scholar 

  26. H. Khan, M. Qayyum, O. Khan, M. Ali, Unsteady squeezing flow of Casson fluid with magnetohydrodynamic effect and passing through porous medium. Math. Probl. Eng. (2016). https://doi.org/10.1155/2016/4293721

    Article  MathSciNet  MATH  Google Scholar 

  27. S.T. Mohyud-Din, M. Usman, W. Wang, M. Hamid, A study of heat transfer analysis for squeezing flow of a Casson fluid via differential transform method. Neural Comput. Appl. 30, 3253–3264 (2017). https://doi.org/10.1007/s00521-017-2915-x

    Article  Google Scholar 

  28. N.B. Naduvinamani, U. Shankar, Thermal-diffusion and thermo-diffusion effects on squeezing flow of unsteady magnetohydrodynamic Casson fluid between two parallel plates with thermal radiation. Sadhana (2019). https://doi.org/10.1007/s12046-019-1154-5

    Article  Google Scholar 

  29. M. Sheikholeslami, D.D. Ganji, H.R. Ashorynejad, Investigation of squeezing unsteady nanofluid flow using ADM. Powder Technol. 239, 259–265 (2013). https://doi.org/10.1016/j.powtec.2013.02.006

    Article  Google Scholar 

  30. A. Dib, A. Haiahem, B. Bou-said, Approximate analytical solution of squeezing unsteady nanofluid flow. Powder Technol. 269, 193–199 (2014). https://doi.org/10.1016/j.powtec.2014.08.074

    Article  MATH  Google Scholar 

  31. A.K. Gupta, S.S. Ray, Numerical treatment for investigation of squeezing unsteady nanofluid flow between two parallel plates. Powder Technol. 279, 282–289 (2015). https://doi.org/10.1016/j.powtec.2015.04.018

    Article  Google Scholar 

  32. S.H. Seyedi, B.N. Saray, A. Ramazani, On the multiscale simulation of squeezing nanofluid flow by a high precision scheme. Powder Technol. 340, 264–273 (2018). https://doi.org/10.1016/j.powtec.2018.08.088

    Article  Google Scholar 

  33. M.G. Sobamowo, A.T. Akinshilo, On the analysis of squeezing flow of nanofluid between two parallel plates under the influence of magnetic field. Alex. Eng. J. 57, 1413–1423 (2017). https://doi.org/10.1016/j.aej.2017.07.001

    Article  Google Scholar 

  34. I. Celik, Squeezing flow of nanofuids of Cu–water and kerosene between two parallel plates by Gegenbauer wavelet collocation method. Eng. Comput. (2019). https://doi.org/10.1007/s00366-019-00821-1

    Article  Google Scholar 

  35. M. Sheikholeslami, M. Hatami, G. Domairry, Numerical simulation of two phase unsteady nanofluid flow and heat transfer between parallel plates in presence of time dependent magnetic field. J. Taiwan Inst.Chem. Eng. 46, 43–50 (2015). https://doi.org/10.1016/j.jtice.2014.09.025

    Article  Google Scholar 

  36. M. Azimi, R. Riazi, MHD unsteady GO-water squeezing nanofluid flow heat and mass transfer between two infinite parallel moving plates: analytical investigation. Sadhana 42, 335–341 (2017). https://doi.org/10.1007/s12046-017-0605-0

    Article  MathSciNet  MATH  Google Scholar 

  37. M. Sheikholeslami, D.D. Ganji, M.M. Rashidi, Magnetic field effect on unsteady nanofluid flow and heat transfer using Buongiorno model. J. Magn. Magn. Mater. 416, 164–173 (2016). https://doi.org/10.1016/j.jmmm.2016.05.026

    Article  ADS  Google Scholar 

  38. A.G. Madaki, R. Roslan, M.S. Rusiman, C.S.K. Raju, Analytical and numerical solutions of squeezing unsteady Cu and TiO2-nanofluid flow in the presence of thermal radiation and heat generation/absorption. Alex. Eng. J. 57, 1033–1040 (2017). https://doi.org/10.1016/j.aej.2017.02.011

    Article  Google Scholar 

  39. G. Sobamowo, L. Jayesimi, D. Oke, A. Yinusa, O. Adedibu, Unsteady Casson nanofluid squeezing flow between two parallel plates embedded in a porous medium under the influence of magnetic field. Open J. Math. Sci. 3, 59–73 (2019). https://doi.org/10.30538/oms2019.0049

    Article  Google Scholar 

  40. U. Khan, N. Ahmed, M. Asadullah, S.T. Mohyud-din, Effects of viscous dissipation and slip velocity on two-dimensional and axisymmetric squeezing flow of Cu–water and Cu–kerosene nanofluids. Propuls. Power Res. 4, 40–49 (2015). https://doi.org/10.1016/j.jppr.2015.02.004

    Article  Google Scholar 

  41. K. Singh, S.K. Rawat, M. Kumar, Heat and mass transfer on squeezing unsteady MHD nanofluid flow between parallel plates with slip velocity effect. J. Nanosci. (2016). https://doi.org/10.1155/2016/9708562

    Article  Google Scholar 

  42. M. Qayyum, H. Khan, O. Khan, Slip analysis at fluid-solid interface in MHD squeezing flow of Casson fluid through porous medium. Results Phys. 7, 732–750 (2017). https://doi.org/10.1016/j.rinp.2017.01.033

    Article  ADS  Google Scholar 

  43. I. Ullah, S. Shafie, I. Khan, Heat generation and absorption in MHD flow of Casson fluid past a stretching wedge with viscous dissipation and newtonian heating. Jurnal Teknologi 80, 77–85 (2018). https://doi.org/10.11113/jt.v80.11138

    Article  Google Scholar 

  44. M. Mustafa, T. Hayat, S. Obaidat, On heat and mass transfer in the unsteady squeezing flow between parallel plates. Meccanica 47, 1581–1589 (2012). https://doi.org/10.1007/s11012-012-9536-3

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author would like to acknowledge Ministry of Education (MOE) and Research Management Centre of Universiti Teknologi Malaysia (UTM) for the financial support through vote number 07G77 for this research.

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, Johor Bahru, Johor, Malaysia

    Nur Azlina Mat Noor, Sharidan Shafie & Mohd Ariff Admon

Authors
  1. Nur Azlina Mat Noor
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sharidan Shafie
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohd Ariff Admon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohd Ariff Admon.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mat Noor, N.A., Shafie, S. & Admon, M.A. Effects of viscous dissipation and chemical reaction on MHD squeezing flow of Casson nanofluid between parallel plates in a porous medium with slip boundary condition. Eur. Phys. J. Plus 135, 855 (2020). https://doi.org/10.1140/epjp/s13360-020-00868-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00868-w

Search

Navigation