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Mathematical and Computational Analysis of MHD Viscoelastic Fluid Flow and Heat Transfer Over Stretching Surface Embedded in a Saturated Porous Medium

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Stochastic Processes, Statistical Methods, and Engineering Mathematics (SPAS 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 408))

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Abstract

The study of MHD flow and heat transfer over a stretching sheet in presence of saturated porous media with the effect of space and temperature dependent internal heat source/sink. Two different heating process has been considered namely, Prescribed surface temperature (PST) and Prescribe heat flux (PHF). The nonlinear boundary layer equations of momentum, which are nonlinear partial differential equations are converted into nonlinear ordinary differential equations by means of suitable similarity transformation. Similarly, the heat transfer equations, which are partial differential equations, are converted into ordinary differential equations introducing a similarity transformation. The resultant flow and heat transfer has been solved analytically. The effects of viscoelastic parameter, porous parameter, Magnetic field, suction, space and temperature dependent heat source/sink on both flow and heat transfer characteristics are presented graphically.

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References

  1. Aiboud, S., Saouli, S.: Entropy analysis for viscoelastic magnetogydrodynamic flow over a stretching surface. Int. J. Non-Lin. Mech. 45, 482–489 (2010)

    Article  Google Scholar 

  2. Baag, S., Mishra, S.R., Dash, G.C., Acharya, M.R.: Entropy generation analysis for viscoelastic MHD flow over a stretching sheet embedded in a porous medium. Ain Shams Eng. J. 8, 623-632 (2017)

    Google Scholar 

  3. Babaelahi, M., Domairry, G., Joneidi, A.A.: Viscoelastic MHD flow boundary layer over a stretching surface with viscous and ohmic dissipation. Meccanica 45, 817–827 (2010)

    Article  MATH  Google Scholar 

  4. Beard, D.W., Walters, K.: Elasto-viscous boundary layer flow. Proc. Camb. Phil. Soc. 60, 667–674 (1964)

    Article  MATH  Google Scholar 

  5. Eswaramoorth, S., Bhuvaneshwari, M., Sivasankaran, S., Rajan, S.: Effect of radiation on MHD convective flow and heat transfer of a viscoelastic fluid over a stretching surface. Proc. Eng. 127, 916–923 (2015)

    Article  Google Scholar 

  6. Hsiao, K.L.: Heat and mass mixed convection for MHD viscoelastic fluid past a stretching sheet with ohmic dissipation. Comm. Non Lin. Sci. Num. Sim. 15, 1803–1812 (2010)

    Article  MATH  Google Scholar 

  7. Ingham, D.B., Pop, I.: Transport Phenomena in Porous Media. Pergmon, Oxford (1988)

    MATH  Google Scholar 

  8. Mahapatra, T.R., Dholey, S., Gupta, A.S.: Momentum and heat transfer in the magnetohydrodynamic stagnation point flow of a viscoelastic fluid towards a stretching surface. Meccanica 42, 263–272 (2007)

    Article  MATH  Google Scholar 

  9. Metri, P.G., Abel, M.S., Silvestrov, S.: Heat transfer in MHD mixed convection viscoelastic fluid flow over a stretching sheet embedded in a porous medium with viscous dissipation and non-uniform heat source/sink. Proc. Eng. 157, 309–316 (2016)

    Article  MATH  Google Scholar 

  10. Metri, P.G., Bablad, V.M., Metri, P.G., Abel, M.S., Silvestrov, S.: Mixed convection heat transfer in MHD non-Darcian flow due to an exponential stretching sheet embedded in a porous medium in presence of non-uniform heat source/sink. In: Silvestrov, S., Rancic, M. (eds.) Engineering Mathematics I. Springer Proceedings in Mathematics and Statistics, vol 178, pp. 187–201. Springer, Cham (2016)

    Chapter  Google Scholar 

  11. Metri, P.G., Abel, M.S., Silvestrov, S.: Heat and mass transfer in MHD boundary layer flow over a nonlinear stretching sheet in a nanofluid with convective boundary condition and viscous dissipation. In: Silvestrov, S., Rancic, M. (Eds.), Engineering Mathematics I. Springer Proceedings in Mathematics and Statistics, vol 178. Springer, Cham, pp. 203–219 (2016)

    Google Scholar 

  12. Metri, P.G., Abel, M.S.: Hydromagnetic flow of a thin nanoliquid film over an unsteady stretching sheet. Int. J. Adv. Appl. Math. Mech. 3(4), 121–134 (2016)

    Google Scholar 

  13. Metri, P.G., Abel, M.S., Tawade, J., Metri, P.G.: Fluid flow and radiative nonlinear heat transfer in a liquid film over an unsteady stretching sheet. In: Proceedings of 2016 7th International Conference on Mechanical and Aerospace Engineering (ICMAE), London. IEEE, pp. 83–87 (2016)

    Google Scholar 

  14. Metri, P.G., Guariglia, E., Silvestrov, S.: Lie group analysis for MHD boundary layer flow and heat transfer over stretching sheet in presence of viscous dissipation and uniform heat source/sink. AIP Conf. Proc. 1798, 020096 (2017)

    Article  Google Scholar 

  15. Metri, P.G., Narayana, M., Silvestrov, S.: Hypergeometric steady solution of hydromagnetic nano liquid film flow over an unsteady stretching sheet. AIP Conf. Proc. 1798, 020097 (2017)

    Article  Google Scholar 

  16. Mishra, S.R., Tripathy, R.S., Dash, G.G.: MHD viscoelastic fluid flow through porous medium over a stretching sheet in presence of non-uniform heat source/sink. Rend. Circ. Mat. Palermo II(67), 129–143 (2018)

    Article  MATH  Google Scholar 

  17. Narayana, M., Metri, P.G., Silvestrov, S.: Thermocapillary flow of a non-Newtonian nanoliquid film over an unsteady stretching sheet. AIP Conf. Proc. 1798, 020109 (2017)

    Article  Google Scholar 

  18. Nayak, M.K., Dash, G.C., Sing, L.P.: Heat and mass transfer effects on MHD viscoelastic fluid over a stretching sheet through porous medium in presence of chemical reaction. Propuls. Power Res. 5(1), 70–80 (2016)

    Article  Google Scholar 

  19. Nayak, M.K.: Chemical reaction effect on MHD viscoelastic fluid over a stretching sheet through porous medium. Meccanica 51, 1699–1711 (2016)

    Article  MATH  Google Scholar 

  20. Nield, D.A., Bejan, A.: Convection in Porous Media, 2nd edn. Springer (1999)

    Google Scholar 

  21. Pratap Kumar, J., Umavathi, J.C., Metri, P.G., Silvestrov, S.: Effect of first order chemical reaction on magneto convection in a vertical double passage channel. In: Silvestrov, S., Rancic, M. (eds.) Engineering Mathematics I. Springer Proceedings in Mathematics and Statistics, vol. 178. Springer, Cham, pp. 247–279 (2016)

    Google Scholar 

  22. Ramesh, G.K.: Analysis of active and passive control of nanoparticles in viscoelastic nanomaterial inspired by activation energy and chemical reaction. Phys. A 550, 123964 (2020)

    Article  MATH  Google Scholar 

  23. Rushi Kumar, B., Sivaraj, R.: Heat and mass transfer in MHD viscoelastic fluid flow over a vertical cone and flat plate with variable viscosity. Int. J. Heat Mass Transf. 56, 370–379 (2013)

    Article  Google Scholar 

  24. Seth, G.S., Mishra, M.K., Tripathy, R.S.: MHD free convective heat transfer in Walter’s liquid-B fluid past a convectively heated stretching sheet with partial slip. J. Braz. Soc. Mech. Sci. Eng. 40(103) (2018)

    Google Scholar 

  25. Sureshkumar Raju, S., Ganesh Kumar. K., Rahimi-Gorji, M., Khan, I.: Darcy-Forchheimer flow and heat transfer augumentation of a viscoelastic fluid over an incessant moving needle in the presence of viscous dissipation. Microsyst. Technol. 25, 3399–3405 (2019)

    Google Scholar 

  26. Tawade, J., Metri, P.G., Abel, M.S.: Thin film flow and heat transfer over an unsteady stretching sheet with thermal radiation, internal heating in presence of external magnetic field. Int. J. Adv. Appl. Math. Mech. 3(4), 29–40 (2016). arXiv:1603.03664

  27. Turkyilmazoglu, M.: Multiple solutions of heat and mass transfer of MHD slip flow for viscoelastic fluid over a stretching sheet. Int. J. Therm. Sci. 50, 2264–2275 (2011)

    Article  Google Scholar 

  28. Turkyilmazoglu, M.: Multiple analytical solutions solutions of heat and mass transfer of magnetohydrodynamic slip flow for two types of viscoelastic fluid over a stretching surface. J. Heat Transf. 134(7), 071701, 9 pp. (2012)

    Google Scholar 

  29. Turkyilmazoglu, M.: Three diemensional MHD flow and heat transfer over a stretching/shrinking surface in a viscoelastic fluid with various physical effects. Int. J. Heat Mass Transf. 78, 150–155 (2014)

    Article  Google Scholar 

  30. Umavathi, J.C., Vajravelu, K., Metri, P.G., Silvestrov, S.: Effect of time-periodic boundary temperature modulations on the onset of convection in a Maxwell fluid nanofluid saturated porous layer. In: Silvestrov, S., Rancic, M. (eds.) Engineering Mathematics I. Springer Proceedings in Mathematics and Statistics, vol. 178. Springer, Cham, pp. 221–245 (2016)

    Google Scholar 

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Acknowledgements

Prashant Metri is also grateful to FUSION network and its Swedish node, MAM research milieu in Mathematics and Applied Mathematics, Division of Mathematics and Physics, School of Education, Culture and Communication at Mälardalen University for support and excellent research and research education environment during his visits.

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Authors and Affiliations

  1. Faculty of Science and Technology, Vishwakarma University, Pune, 411048, Maharashtra, India

    Jagadish Tawade

  2. Department of Mechanical Engineering and Mathematics, Walchand Institute of Technology, Solapur, Maharashtra, India

    Prashant G. Metri

Authors
  1. Jagadish Tawade
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  2. Prashant G. Metri
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Correspondence to Jagadish Tawade .

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Editors and Affiliations

  1. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Anatoliy Malyarenko

  2. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Ying Ni

  3. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Milica Rančić

  4. Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden

    Sergei Silvestrov

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Tawade, J., Metri, P.G. (2022). Mathematical and Computational Analysis of MHD Viscoelastic Fluid Flow and Heat Transfer Over Stretching Surface Embedded in a Saturated Porous Medium. In: Malyarenko, A., Ni, Y., Rančić, M., Silvestrov, S. (eds) Stochastic Processes, Statistical Methods, and Engineering Mathematics . SPAS 2019. Springer Proceedings in Mathematics & Statistics, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-031-17820-7_36

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