Unsteady MHD Free Convective Flow of a Visco-Elastic Fluid Past an Infinite Vertical Porous Moving Plate with Variable Temperature and Concentration

  • K. Ramesh Babu
  • A. Parandhama
  • K. Venkateswara Raju
  • M. C. Raju
  • P. V. Satya Narayana
Original Paper
  • 188 Downloads

Abstract

The present study considers the effect unsteady MHD free convective flow of a viscoelastic incompressible electrically conducting fluid past a moving vertical plate through a porous medium with time dependent oscillatory permeability and suction in presence of a uniform transverse magnetic field and heat source and chemical reaction along with heat and mass transfer are reported. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The governing equations of the fluid flow, heat and mass transfer are solved by applying multi parameter perturbation technique. Comparison with previously published work have been conducted and the results are found to be in concordance with the previous study. A parametric study is performed on the influence of the visco-elastic fluid parameter, the magnetic field parameter, the permeability parameter, on the fluid velocity. The expressions for transient velocity, temperature, species concentration and non-dimensional skin friction at the plate are illustrated through tables to observe the visco-elastic effect in combination of other flow parameters involved in the solution.

Keywords

Chemical reaction Free convection Heat and mass transfer Heat source Mass diffusion Radiation absorption Visco-elastic 

Notes

Acknowledgements

Authors are grateful to the reviewers for their valuable comments and suggestions which helped them to improve the quality of the research paper.

References

  1. 1.
    Beard, D.W., Walters, K.: Elastic-viscous boundary layer flow. Two dimensional flows near a stagnation point. Proc. Camb. Philos. Soc. 60(3), 667–674 (1964)CrossRefMATHGoogle Scholar
  2. 2.
    Angirasa, D., Peterson, P., Pop, I.: Combined heat and mass transfer by natural convection with opposing buoyancy effects in a fluid saturated porous medium. Int. J. Heat Mass Trans. 40(12), 2755–2773 (1997)CrossRefMATHGoogle Scholar
  3. 3.
    Chowdhury, M.K., Islam, M.N.: MHD free convection flow of visco-elastic fluid past an infinite vertical porous plate. Heat Mass Transf. 36(5), 439–447 (2000)CrossRefGoogle Scholar
  4. 4.
    Subhash, A.M., Joshi, A., Sonth, R.M.: Heat transfer in MHD visco-elastic fluid flow over a stretching surface. Zeitschrift frangewandte Mathematikund Mechanik 81(10), 691–698 (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Abel, M.S., Khan, S.K., Prasad, K.V.: Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity. Int. J. Non-Linear Mech. 37(1), 81–88 (2002)CrossRefMATHGoogle Scholar
  6. 6.
    Khan, S.K., Sanjayanand, E.: Visco-elastic boundary layer MHD flow through a porous medium over a porous quadratic stretching sheet. Arch. Mech. 56(3), 191–204 (2004)MATHGoogle Scholar
  7. 7.
    Makinde, O.D.: Free convection flow with thermal radiation and mass transfer past a moving vertical porous plate. Int. Commun. Heat Mass Transf. 32, 1411–1419 (2005)CrossRefGoogle Scholar
  8. 8.
    Kandasamy, R., Periasamy, K., Raghu, K.K.S.: Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects. Int. J. Heat Mass Transf. 48(21–22), 4557–4561 (2005)CrossRefMATHGoogle Scholar
  9. 9.
    Khan, S.K.: Heat transfer in visco-elastic fluid flow over a stretching surface with heat source/sink, suction/blowing and radiation. Int. J. Heat Mass Transf. 49(3), 628–639 (2006)CrossRefMATHGoogle Scholar
  10. 10.
    Muthucumaraswamy, R., Meenakshisundaram, S.: Theoretical study of chemical reaction effects on vertical oscillating plate with variable temperature. Theoret. Appl. Mech. 33(3), 245–257 (2006)CrossRefMATHGoogle Scholar
  11. 11.
    Ibrahim, F.S., Elaiwm, A.M., Bakr, A.A.: Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow Past a semi-infinite vertical permeable moving plate with heat source and suction. Commun. Nonlinear Sci. Numer. Simul. 13(6), 1056–1066 (2008)Google Scholar
  12. 12.
    Massoudi, M., Phuoe, T.X.: Unsteady motion of a non-linear visco-elastic fluid. Int. J. Non-Linear Mech. 44(10), 1063–1072 (2009)CrossRefGoogle Scholar
  13. 13.
    Sochi, T.: Non-Newtonian flow in porous media. Polymer 51(22), 5007–5023 (2010)CrossRefGoogle Scholar
  14. 14.
    Raju, M.C., Varma, S.V.K., Ramakoteswara Rao, R.: Unsteady MHD free convection and chemically reactive flow past an infinite vertical porous plate, i-manager’s. J. Future Eng. Technol. 8(3), 35–40 (2013)Google Scholar
  15. 15.
    Satya Narayana, P.V., Harish Babu, D.: MHD free convective heat and mass transfer past a vertical porous plate with variable temperature. Int. J. Appl. Math Mech. 9(7), 66–94 (2013)Google Scholar
  16. 16.
    Mishra, S.R., Dash, G.C., Acharya, M.: Mass and heat transfer effect on MHD flow of a visco-elastic fluid through porous medium with oscillatory suction and heat source. Int. J. Heat Mass Transf. 57, 433–438 (2013)CrossRefGoogle Scholar
  17. 17.
    Ravikumar, V., Raju, M.C., Raju, G.S.S.: Combined effects of eat absorption and MHD on convective Rivlin-Ericksen flow past a semi-infinite vertical porous plate with variable temperature and suction. Ain Shams Eng. J. 5, 867–875 (2014)CrossRefGoogle Scholar
  18. 18.
    Raju, M.C., Vidya sagar, B., Varma, S.V.K.: Radiation absorption effect on MHD free convective chemically reacting visco-elastic fluid past an oscillatory vertical porous plate in slip flow regime. Int. J. Eng. Comput. Sci. 3(9), 8212–8221 (2014). ISSN:2319-7242Google Scholar
  19. 19.
    Acharya, A.K., Dash, G.C., Mishra, S.R.: Free convective fluctuating MHD flow through porous media past a vertical porous plate with variable temperature and heat source. Phys. Res. Int. 2014, 1–8, Article ID: 587367 (2014)Google Scholar
  20. 20.
    Venkateswarlu, Bhumarapu, Narayana, Panyam Venkata Satya: MHD visco- elastic fluid flow over a continuously moving vertical surface with chemical reaction. Walailak J. Sci. Technol. 12(9), 775–783 (2015)Google Scholar
  21. 21.
    Makanda, G., Shaw, S., Sibanda, P.: Effects of radiation on MHD free convection of a Casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation. Bound. Value Probl. 75, 1–14 (2015)Google Scholar
  22. 22.
    Baag, S., Acharya, M.R., Dash, G.C., Mishra, S.R.: MHD flow of a visco-elastic fluid through a porous medium between infinite parallel plates with time dependent suction. J. Hydrodyn. 27(5), 738–747 (2015)CrossRefGoogle Scholar
  23. 23.
    Umamaheswar, M., Raju, M.C., Varma, S.V.K.: Effects of time dependent variable Temperature and concentration boundary layer on MHD free convection flow past a vertical porous plate in the presence of thermal radiation and chemical reaction. Int. J. Appl. Comput. Math. (2015). doi: 10.1007/s40819-015-0124-9
  24. 24.
    Seth, G.S., Hussain, S.M., Sarkar, S.: Hydro-magnetic natural convection flow with heat and mass transfer of a chemically reacting and heat absorbing fluid past an accelerated moving vertical plate with ramped temperature and ramped surface concentration through a porous medium. J. Egypt. Math. Soc. 23, 197–207 (2015)CrossRefMATHGoogle Scholar
  25. 25.
    Seth, G.S., Sharma, S., Sarkar, S.: Natural convection heat and mass transfer flow with Hall current. Rotation, radiation and heat absorption past an accelerated moving vertical plate with ramped temperature. J. Appl. Fluid Mech. 8(1), 7–20 (2015)Google Scholar
  26. 26.
    Seth, G.S., Sarkar, S.: MHD natural convection heat and mass transfer flow past a time dependent moving vertical plate with ramped temperature in a rotating medium with Hall effects, radiation and chemical reaction. J. Mech. 31(1), 91–104 (2015)CrossRefGoogle Scholar
  27. 27.
    Seth, G.S., Kumbhakar, B., Sharma, R.: Unsteady MHD free convection flow with Hall effect of a radiating and heat absorbing fluid past a moving vertical plate with variable ramped temperature. J. Egypt. Math. Soc. 24, 471–478 (2016)CrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    Seth, G.S., Sharma, R., Kumbhakar, B.: Heat and mass transfer effects on unsteady MHD natural convection flow of a chemically reactive and radiating fluid through a Porous medium past a moving vertical plate with arbitrary ramped temperature. J. Appl. Fluid Mech. 9(1), 103–117 (2016)CrossRefGoogle Scholar
  29. 29.
    Gurivireddy, P., Raju, M.C., Mamatha, B., Varma, S.V.K.: Thermal diffusion effect on MHD heat and mass transfer flow past a semi-infinite moving vertical porous plate with heat generation and chemical reaction. Appl. Math. (Scientific Research Publishing) 7, 638–649 (2016)Google Scholar
  30. 30.
    Phan-Thein, N.: Understanding Viscoelasticity. An Introduction to Rheology, 2nd edn. Springer, Berlin (2013)CrossRefGoogle Scholar
  31. 31.
    Raju, M.C., Chamkha, A.J., Philip, J., Varma, S.V.K.: Soret effect due to mixed convection on unsteady magneto hydrodynamic flow past a semi infinite vertical permeable moving plate in presence of thermal radiation, heat absorption and homogenous chemical reaction. Int. J. Appl. Comput. Math. (2016). doi: 10.1007/s40819-016-0147-x

Copyright information

© Springer India Pvt. Ltd. 2017

Authors and Affiliations

  • K. Ramesh Babu
    • 1
  • A. Parandhama
    • 1
  • K. Venkateswara Raju
    • 1
  • M. C. Raju
    • 2
  • P. V. Satya Narayana
    • 3
  1. 1.Department of MathematicsSree Vidyanikethan Engineering College (Autonomous)TirupatiIndia
  2. 2.Department of MathematicsAnnamacharya Institute of Technology and ScienceRajampetIndia
  3. 3.Department of MathematicsVIT UniversityVelloreIndia

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