Skip to main content

A Note on Vorticity of Hydromagnetic Two-Phase Flow Through Two Parallel Plates in a Rotating System

  • Conference paper
  • First Online:
Proceedings of Integrated Intelligence Enable Networks and Computing

Part of the book series: Algorithms for Intelligent Systems ((AIS))

  • 881 Accesses

Abstract

In the present paper, an attempt has been made to find the vorticity of incompressible fluid in the hydromagnetic two-phase flow through two parallel plates in a rotating system. Variations in the vorticity are studied through vorticity profiles, and some very important conclusions are drawn. It is also observed that the flow in both the regions is self-superposable. The conditions for the flow in both regions to become irrotational are found.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R.N. Barik, G.C. Dash, P.K. Rath, Steady laminar MHD flow of viscoelastic fluid through a porous pipe embedded in a porous medium. Alexandria Eng. J. 57, 973–982 (2018)

    Article  Google Scholar 

  2. R. Ballabh, Two dimensional superposable motions. J. Indian Math. Soc. 16, 191–197 (1952)

    MathSciNet  MATH  Google Scholar 

  3. R.C. Chaudhary, A.K. Jha, Effects of chemical reaction on MHD micropolar fluid flow past a vertical plate in slip-flow regime. Appl. Math. Mech. 29(9), 1179–1194 (2008)

    Article  Google Scholar 

  4. A.J. Chamkha, Hydromagnetic two-phase flow in a channel. Int. J. Eng. Sci. 33(3), 437–446 (1995)

    Article  Google Scholar 

  5. A.J. Chamkha, H.M. Ramadan, Analytical solutions for free convection flow of a particulate suspension past an infinite vertical surface. Int. J. Eng. Sci. 36, 49–60 (2000)

    Article  Google Scholar 

  6. El-Amin, A. Salam, S. Sun, Numerical and dimensional investigation of two-phase countercurrent imbibitions in porous media. J. Comput. Appl. Mathe. 242, 285–296 (2013)

    Google Scholar 

  7. El-Amin, Magnetohydrodynamic free convection and mass transfer flow in micropolar fluid with constant suction. J. Magn. Magn. Mater. 234(3), 567–574 (2001)

    Google Scholar 

  8. A.S. Gupta, Hydrodynamic flow past a porous flat plate with Hall effects. Acta Mech. 22, 281–287 (1975)

    Article  Google Scholar 

  9. A.S. Gupta, J.C. Misra, M. Reza, Magnetohaydrodynamic shear flow a flat plat with uniform suction or blowing. Z. Angew. Math. Phys. 56, 1030–1047 (2005)

    Article  MathSciNet  Google Scholar 

  10. S.K. Ghosh, J. Zueco, Hydromagnetic free convection flow with induction magnetic field effects. Meccanica 45, 175–185 (2009)

    Article  Google Scholar 

  11. R.R. Gold, M.Z. Krzywoblocki, On superposability and self-superposability conditions for hydrodynamic equations based on continuum—II. J. Reine Angew. Math. 199, 139–164 (1958)

    MATH  Google Scholar 

  12. J.N. Kapur, Superposability in MHD flows. J. Appl. Sci. Res. 8, 198–208 (1959)

    Article  Google Scholar 

  13. J.N. Kapur, B.L. Bhatia, Superposability and self-superposability in fluid dynamics—II. Proc. Natl. Inst. Sci. India 31A, 126–151 (1965)

    MATH  Google Scholar 

  14. J.N. Kapur, Superposability in magnetohydrodynamics. Applied scientific research 8, 198–208 (1959)

    Article  Google Scholar 

  15. J.N. Kapur, Superposability and self-superposability in fluid dynamics. Math. Semin. 2, 1–31 (1961)

    MathSciNet  Google Scholar 

  16. P.K. Mittal, On some magnetohydrostatic configurations a parabolic coordinates. Bull. Calcutta Math. Soc. 75, 339–352 (1983)

    MATH  Google Scholar 

  17. P.K. Mittal, M.I. Khan, On some self- superposable flows in conical ducts. Int. J. Theor. Phys. 34, 181–191 (1986)

    MATH  Google Scholar 

  18. A. Raptis, C. Massalas, G. Tzivanidis, Hydromagnetic free convection flow through a porous medium between two parallel plates. Phys. Lett. 90A, 288–289 (1982)

    Article  Google Scholar 

  19. B.P. Reddy, Radiation and chemical reaction effects on unsteady MHD free convection parabolic flow past an infinite isothermal vertical plate with viscous dissipation. Int. J. Appl. Mech. Eng. 24(2), 343–358 (2019)

    Google Scholar 

  20. G.T. Rao, Superpoasability of the equations of MHD. Math. Soc. Jpn. 12(1), 97–103 (1960)

    Google Scholar 

  21. S. Rastogi, B.N. Kaul, S. Ranjan, Superposability in hydrodynamic and MHD flows. J. Fluid Dyn. 5, 151–170 (2015)

    Google Scholar 

  22. Z. Recebli, H. Kurt, Two-phase steady flow along a glass pipe in the presence of magnetic and electric field. Int. J. Heat Fluid Flow 29, 263–268 (2008)

    Article  Google Scholar 

  23. P.K. Sharma, B.K. Sharma, R.C. Chaudhary, Unsteady free convection oscillatory Couette flow through a porous medium with periodic wall temperature. Tamkang J. Math. 38(1), 93–102 (2007)

    Article  MathSciNet  Google Scholar 

  24. Z. Shao, N.A. Shah, I. Tlili, U. Afzal, Hydromagnetic free convection flow of viscous fluid between vertical parallel plates with damped thermal and mass fluxes. Alexandria Eng. J. 58, 989–1000 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

One of the authors (Dr. Alok Darshan Kothiyal) is thankful to Mr. Sandeep Kumar (Registrar GBPIET Pauri Garhwal, Uttarakhand) for his constant support during this work.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alok Darshan Kothiyal .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kothiyal, A.D., Kumar, R., Bhatt, S., Dobhal, G., Uniyal, N. (2021). A Note on Vorticity of Hydromagnetic Two-Phase Flow Through Two Parallel Plates in a Rotating System. In: Singh Mer, K.K., Semwal, V.B., Bijalwan, V., Crespo, R.G. (eds) Proceedings of Integrated Intelligence Enable Networks and Computing. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-33-6307-6_79

Download citation

Publish with us

Policies and ethics