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An MHD Navier’s Slip Flow Over Axisymmetric Linear Stretching Sheet Using Differential Transform Method

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Abstract

The magnetohydrodynamics boundary layer flows with Naviers’ slip condition are mathematically modelled into highly nonlinear partial differential equations which are then transformed into highly nonlinear ordinary differential equations. The similarity solutions are obtained and are analysed means of differential transform method and with an application of Pade approximants to the highly nonlinear ordinary differential equation. The effects of suction/injection, magnetic field, slip and other parameters on the flow for two-dimensional and axisymmetric stretching are evaluated in relation to existing studies. The present study has potential application to magnetic nano fluids in wound medicines, skin repair and specialised coatings for devices such as audio/video diskettes and optical fibre filters.

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References

  1. Sakiadis, B.C.: Boundary layer behavior on continuous solid surface: I. Boundary-layer equations for two-dimensional and axisymmetric flow. J. AIChE 7, 26–28 (1961)

    Article  Google Scholar 

  2. Sakiadis, B.C.: Boundary layer behavior on continuous solid surface: II. Boundary-layer equations for two-dimensional and axisymmetric flow. J. AIChE 7, 221–225 (1961)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Navier, C.L.M.H.: Mémoire sur les lois du mouvement des fluids. Mém. Acad. R. Sci. Inst. Fr. 6, 389 (1823)

    Google Scholar 

  5. Gorder, R.A.V., Sweet, E., Vajravelu, K.: Nano boundary layers over stretching surfaces. Commun. Nonlinear Sci. Numer. Simul. 15, 1494–1500 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Wang, C.Y.: Flow due to a stretching boundary with partial slip—an exact solution of the Navier–Stokes equations. Chem. Eng. Sci. 57(17), 3745–3747 (2002)

    Article  Google Scholar 

  7. Pukhov, G.E.: Differential transforms and circuit theory. Int. J. Circ. Theor. Appl. 10, 265 (1982)

    Article  MATH  Google Scholar 

  8. Zhou, J.K.: Differential Transformation and Its Application for Electrical Circuits. Huazhong University Press, Wuhan (1986)

    Google Scholar 

  9. Baker, G.A., Graves-Marris, P.: Pade Approximants. Cambridge University Publications, Cambridge (1996)

    Book  MATH  Google Scholar 

  10. Peker, H.A., Karaoglu, O., Oturanc, O.: The differential transformation method and Pade approximant for a form of MHD Blasius flow. Math. Comput. Appl. 16(2), 507–513 (2011)

    MathSciNet  MATH  Google Scholar 

  11. Jang, M.J., Chen, C.L., Liu, Y.C.: On solving the initial value problems using the differential transformation method. Appl. Math. Comput. 115, 145–160 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Arikoglu, A., Ozkol, I.: Solution of difference equations by using differential transform method. Appl. Math. Comput. 174, 1216–1228 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kurnaz, A., Oturanc, G.: The differential transform approximation for system of ordinary differential equations. Int. J. Comput. Math. 82, 709–719 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hassan, I.H.A.H.: Application to differential transformation method for solving systems of differential equations. Appl. Math. Model. 32, 2552–2559 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Rashidi, M.M.: The modified differential transform method for solving MHD boundary-layer equations. Comput. Phys. Commun. 180, 2210–2217 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Fang, T., Zhang, J., Yao, S.: Slip MHD viscous flow over a stretching sheet—an exact solution. Commun. Nonlinear Sci. Numer. Simul. 14, 3731–3737 (2009)

    Article  Google Scholar 

  17. Andersson, H.I.: Slip flow past a stretching surface. Acta Mech. 158, 121–125 (2002)

    Article  MATH  Google Scholar 

  18. Wang, C.Y.: Analysis of viscous flow due to a stretching sheet with surface slip and suction. Nonlinear Anal. Real World Appl. 10(1), 375–380 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pop, I., Na, T.Y.: A note on MHD flow over a stretching permeable surface. Mech. Res. Commun. 25(3), 263–269 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. Gupta, P.S., Gupta, A.S.: Heat and mass transfer on a stretching sheet with suction/blowing. Can. J. Chem. Eng. 55, 744–746 (1977)

    Article  Google Scholar 

  21. Mahabaleshwar, U.S., Vinay Kumar, P.N., Sheremet, M.: Magnetohydrodynamics flow of a nanofluid driven by a stretching/shrinking sheet with suction. Springer Plus 5(1), 1901–1908 (2016)

    Article  Google Scholar 

  22. Pavlov, K.B.: Magnetohydrodynamic flow of an incompressible viscous liquid caused by deformation of plane surface. Magn. Gidrodin 4, 146–147 (1974)

    Google Scholar 

  23. Siddappa, B., Abel, M.S.: Non-Newtonian flow past a stretching plate. Zeitschrift für angewandte Math. Phys. 36, 890–892 (1985)

    Article  MATH  Google Scholar 

  24. Siddheshwar, P.G., Mahabaleshwar, U.S.: Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet. Int. J. Non-Linear Mech. 40, 807–820 (2005)

    Article  MATH  Google Scholar 

  25. Boyd, J.P.: Padé approximant algorithm for solving nonlinear ordinary differential equation boundary value problems on an unbounded domain. Comput. Phys. 11, 299–303 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Government First Grade College for Women, Hassan, India

    U. S. Mahabaleshwar

  2. Department of Mathematics, Government Engineering College, Hassan, India

    K. R. Nagaraju

  3. Department of Mathematics, SHDD Government First Grade College, Paduvalahippe, Hassan, India

    P. N. Vinay Kumar

  4. HPC and Research Support Group, Queensland University of Technology (QUT), 2 George St, GPO Box 2434, Brisbane, 4001, Australia

    N. A. Kelson

Authors
  1. U. S. Mahabaleshwar
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  2. K. R. Nagaraju
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  3. P. N. Vinay Kumar
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  4. N. A. Kelson
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Correspondence to U. S. Mahabaleshwar.

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Mahabaleshwar, U.S., Nagaraju, K.R., Vinay Kumar, P.N. et al. An MHD Navier’s Slip Flow Over Axisymmetric Linear Stretching Sheet Using Differential Transform Method. Int. J. Appl. Comput. Math 4, 30 (2018). https://doi.org/10.1007/s40819-017-0446-x

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  • DOI: https://doi.org/10.1007/s40819-017-0446-x

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