Skip to main content
SpringerLink
Log in

Free Convective Flow, Heat and Mass Transfer in a Micropolar Fluid Over a Shrinking Sheet in the Presence of a Heat Source

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

The paper considers a free convective flow of a micropolar fluid in the presence of a heat source/sink over a shrinking sheet. Similarity transformations are used to reduce the governing coupled nonlinear partial differential equations, namely, the momentum and concentration equations, as well as the nonhomogeneous heat equation, to a set of nonlinear ordinary differential equations. Their numerical solution is obtained by the Runge–Kutta fourth-order method accompanied by the shooting technique. The effects of various physical parameters characterizing the flow are studied. The validation of the present results by the earlier published ones is performed in a particular case, and good agreement is obtained.

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

Similar content being viewed by others

References

  1. A. C. Eringen, Theory of micropolar fluids, J. Math. Mech., 16, 1–18 (1966).

    MathSciNet  Google Scholar 

  2. G. Ahmadi, Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate, Int. J. Eng. Sci., 14, 639–646 (1976).

    Article  MATH  Google Scholar 

  3. R. S. R. Gorla, Micropolar boundary layer flow at a stagnation on a moving wall, Int. J. Eng. Sci., 21, 25–33 (1983).

    Article  MATH  Google Scholar 

  4. L. J. Crane, Flow past a stretching plate, Z. Angew. Math. Phys., 21, 645–647 (1970).

    Article  Google Scholar 

  5. C. Y. Wang, Liquid film on an unsteady stretching sheet, Q. Appl. Math., 48, 601–610 (1990).

    Article  MATH  Google Scholar 

  6. T. Hayat and M. Qasim, Radiation and magnetic field effects on the unsteady mixed convection flow of a second grade fluid over a vertical stretching sheet, Int. J. Numer. Methods Fluids, 66, 820–832 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  7. D. Pal and H. Mondal, MHD non-Darcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with non-uniform heat source/sink, variable viscosity and Soret effect, Commun. Nonlinear Sci. Numer. Simul., 17, 672–684 (2012).

    Article  MathSciNet  Google Scholar 

  8. R. Cortell, Analysing flow and heat transfer of a viscoelastc fluid over a semi-infinite horizontal moving flat plate, Int. J. Non-Linear Mech., 43, 772–778 (2008).

    Article  MATH  Google Scholar 

  9. K. Bhattacharya, Boundary layer stagnation-point flow of Casson fluid and heat transfer towards a shrinking/stretching sheet, Front. Heat Mass Transf., 4, No. 023003, 1–9 (2013).

    Google Scholar 

  10. N. A. Yacob, A. Ishak, and I. Pop, Melting heat transfer in boundary layer stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid, Comput. Fluids, 47, 16–21 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Miklavčič and C. Y. Wang, Viscous flow due a shrinking sheet, Q. Appl. Math., 64, 283–290 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  12. B. Mohanty, S. R. Mishra, and H. B. Pattnaik, Numerical investigation on heat and mass transfer effect of micropolar fluid over a stretching sheet, Alexandria Eng. J., 54, No. 2, 223–232 (2015).

    Article  Google Scholar 

  13. S. R. Mishra, G. C. Dash, and P. K. Pattnaik, Flow of heat and mass transfer on MHD free convection in a micropolar fluid with heat source, Alexandria Eng. J., 54, No. 3, 681–689 (2015).

    Article  Google Scholar 

  14. P. K. Rout, G. C. Dash, S. N. Sahoo, and S. R. Mishra, Chemical reaction effect on MHD free convection flow in a micropolar fluid, Alexandria Eng. J., 55, No. 3, 2967–2973 (2016).

    Article  Google Scholar 

  15. N. F. M. Noor, S. A. Kechil, and I. Hashim, Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet, Commun. Nonlinear Sci. Numer. Simul., 15, 144–148 (2010).

    Article  MATH  Google Scholar 

  16. A. Ishak, Y. Y. Lok, and I. Pop, Stagnation-point flow over a shrinking sheet in a micropolar fluid, Chem. Eng. Commun., 197, 1417–1427 (2010).

    Article  Google Scholar 

  17. A. Ishak, Y. Y. Lok, and I. Pop, Non-Newtonian power-law fluid flow past a shrinking sheet with suction, Chem. Eng. Commun., 199, 142–150 (2012).

    Article  Google Scholar 

  18. S. Nadeem, Rizwan Ul Haq, and C. Lee, MHD flow of a Casson fluid over an exponentially shrinking sheet, Sci. Iran. Trans. B: Mech. Eng. B, 19, No. 6, 1550–1553 (2012).

    Article  Google Scholar 

  19. G. C. Dash, R. S. Tripathy, M. M. Rashidi, and S. R. Mishra, Numerical approach to boundary layer stagnation-point flow past a stretching/shrinking sheet, J. Mol. Liquids, 221, 860–866 (2016).

    Article  Google Scholar 

  20. T. Fang, S. Yao, J. Zhang, and A. Aziz, Viscous flow over a shrinking sheet with a second order slip flow model, Commun. Nonlinear Sci. Numer. Simul., 15, 1831–1842 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  21. C. Y. Wang, Stagnation flow towards a shrinking sheet, Int. J. Non-Linear Mech., 43, 377–382 (2008).

    Article  Google Scholar 

  22. T. Fang, J. Zhang, and S. Yao, Viscous flow over an unsteady shrinking sheet with mass transfer, Chin. Phys. Lett., 26, No. 1, 014703 (2009).

    Article  Google Scholar 

  23. T. R. Mahapatra, S. K. Nandy, and A. S. Gupta, Momentum and heat transfer in MHD stagnation-point flow over a shrinking sheet, ASME J. Appl. Mech., 78, 021015 (2011).

    Article  Google Scholar 

  24. K. Bhattacharyya, S. Mukhopadhyay, G. C. Layek, and I. Pop, Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet, Int. J. Heat Mass Transf., 55, 2945–2952 (2012).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Siksha ‘O’ Anusandhan Deemed to be University, -751030, Bhubaneswar, Odisha, India

    S. R. Mishra

  2. Department of Physics, Stewart Science College, Cuttack, India

    J. Mohanty & J. K. Das

Authors
  1. S. R. Mishra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Mohanty
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. K. Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. R. Mishra.

Additional information

Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 91, No. 4, pp. 1043–1049, July–August, 2018.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishra, S.R., Mohanty, J. & Das, J.K. Free Convective Flow, Heat and Mass Transfer in a Micropolar Fluid Over a Shrinking Sheet in the Presence of a Heat Source. J Eng Phys Thermophy 91, 983–990 (2018). https://doi.org/10.1007/s10891-018-1824-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-018-1824-x

Keywords

Search

Navigation