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Melting Heat Transfer of MHD Micropolar Fluid Flow Past An Exponentially Stretching Sheet with SLip and Thermal Radiation

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Abstract

The effects of velocity slip and radiation on MHD flow and melting heat transfer of a micropolar fluid due to an exponentially stretched sheet are presented. By means of similarity transformations the leading partial differential equations are changed to a set of ordinary differential equations which are nonlinear. Numerical solutions of the nonlinear system of equations are then obtained by changing the boundary value problem first to an initial value problem. It is observed that the pertaining parameters have significant effects on the flow and heat transfer characteristics, which are presented and talked about in detail through their illustrations. Due to boost in the melting parameter, the fluid velocity, angular velocity and temperature are found to decrease. Fluid velocity and angular velocity both decrease with a rise in slip at the boundary but quite opposite is the effect on the temperature.

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References

  1. Eringen, A.C.: Theory of m fs. J. Math. Mech 16, 1–18 (1966)

    MathSciNet  Google Scholar 

  2. Bhattacharyya, K., Mukhopadhyay, S., Layek, G.C., Pop, I.: 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 

  3. Turkyilmazoglu, M.: A note on micropolar fluid flow and heat transfer over a porous shrinking sheet. Int. J. Heat Mass Transf. 72, 388–391 (2014)

    Article  Google Scholar 

  4. Das, K., Duari, P.R.: Micropolar nanofluid flow over a stretching sheet with chemical reaction. Int. J. Appl. Comput. Math (2016). https://doi.org/10.1007/s40819-016-0294-0

    Article  MATH  Google Scholar 

  5. Mandal, I.C., Mukhopadhyay, S.: Nonlinear convection in micropolar fluid flow past an exponentially stretching sheet in an exponentially moving stream with thermal radiation. Mec. Adv. Mat. Struct. (2018). https://doi.org/10.1080/15376494.2018.1472325

    Article  Google Scholar 

  6. Hayat, T., Shafiq, A., Alsaedi, A.: Characteristics of magnetic field and melting heat transfer in stagnation point flow of Tangent hyperbolic liquid. J Magnetism Magnetic Mat (2016). https://doi.org/10.1016/j.jmmm.2015.10.080

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  8. Hayat, T., Farooq, M., Alsaedi, A.: Melting heat transfer in the stagnation point flow of Maxwell fluid with double diffusive Convection. Int. J. Numer. Meth. Heat Fluid Flow 24, 760–774 (2014)

    Article  MathSciNet  Google Scholar 

  9. Andersson, H.I.: Slip flow past a stretched sheet. Acta Mech. 158, 11–125 (2002)

    Article  Google Scholar 

  10. Aman, F., Ishak, A.: Boundary layer flow and heat transfer over a permeable shrinking sheet with partial slip. J. Appl. Sci. Res. 6(8), 111–115 (2010)

    Google Scholar 

  11. Nadeem, S., Mehmood, R., Akbar, N.S.: Combined effects of magnetic field and partial slip on obliquely striking rheological fluid over a stretched sheet. J. Magn. Magnet. Mat. (2014). https://doi.org/10.1016/j.jmmm.2014.11.043i

    Article  Google Scholar 

  12. Mukhopadhyay, S., Mandal, I.C.: Magnetohydrodynamic (MHD) mixed convection slip flow and heat transfer over a vertical porous plate. Engng. Sci. Tech. an Int. J. 18, 98–105 (2015)

    Article  Google Scholar 

  13. Ishak, A.: MHD boundary layer flow due to an exponentially stretched sheet with radiation effect. Sains Malays. 40(4), 391–395 (2011)

    Google Scholar 

  14. Fazle Mabood, W.A. Khan, A.I. Md. Ismail, MHD flow over exponential radiating stretched sheet using homotopy analysis method, J. of King Saud Univ. – Engng. Sci.29 (2017) 68–74.

  15. Ishak, A.N.: R. and I. Pop. Heat transfer over a stretching surface with variable surface heat flux in micropolar fluids. Phys. Lett: A 372, 559–561 (2008)

    Article  Google Scholar 

  16. Jena, S.K., Mathur, M.N.: Similarity solutions for laminar free convection flow of a thermo micropolar fluid past a non- isothermal vertical flat plate. Int. J. Engng. Sci. 19, 1431–1439 (1981)

    Article  Google Scholar 

  17. Elbashbeshy, E.M.A.: Heat transfer over an exponentially str. continuous s. with suction. Arch. Mech. 53(6), 643–651 (2001)

    MATH  Google Scholar 

  18. Hafidzuddin, E.H., Nazar, R., Arifin, N.M., Pop, I.: Numerical solutions of boundary layer flow over an exponentially str/shrinking sheet with generalized slip velocity. World. Academy Sci. Engng. Tech. Int. J. Math. Comput. Phy. Elect. Comput. Engng. 9(4), 244–249 (2015)

    Google Scholar 

  19. Ibrahim, W.: MHD boundary layer flow and heat transfer of micropolar fluid past a stretching sheet with second order slip. J. Braz. Soc. Mech. Sci. Eng. 39(3), 791–799 (2017). https://doi.org/10.1007/s40430-016-0621-8

    Article  Google Scholar 

  20. Ghosh, S., Mukhopadhyay, S.: Effects of slip on Cu–water or Fe3O4–water nanofluid flow over an exponentially stretched sheet, Pramana –. J. Phys. 92, 93–99 (2019)

    Google Scholar 

  21. Magyari, E., Keller, B.: H and mass t in the boundary layer on an exponentially str continuous s. J. Phy. D. Appl. Phy. 32(5), 577–585 (1999)

    Article  Google Scholar 

  22. Bidin, B., Nazar, R.: Numerical solution of the boundary layer flow over an exponentially stretched sheet with thermal radiation. Eur. J. Sci. Res. 33(4), 710–717 (2009)

    Google Scholar 

  23. Mukhopadhyay, S.: Slip effects on MHD boundary layer flow over an exponentially stretched sheet with suction/blowing and thermal radiation. Ain Shams Engng. J. 4, 485–491 (2013)

    Article  Google Scholar 

  24. Ghosh, S., Mukhopadhyay, S., Vajravelu, K.: Existence of dual solutions and melting phenomenon in unsteady nanofluid flow and heat transfer over a stretching surface. J. of Mechanics (online published) (2019). https://doi.org/10.1017/jmech.2018.44

    Article  Google Scholar 

  25. Ibrahim, W.: Passive control of nanoparticle of micropolar fluid past a stretching sheet with nanoparticles, convective boundary condition and second-order slip. Proc. Inst. Mech. Eng. Part E: J. Process Mech. Eng. 231(4), 704–719 (2016)

    Article  Google Scholar 

  26. Adegbie, S.K., Koriko, O.K., Animasaun, I.L.: Melting heat transfer effects on stagnation point flow of micropolar fluid with variable dynamic viscosity and thermal conductivity at constant vortex viscosity. J. of the Nigerian Math. Soc. 35, 34–47 (2016)

    Article  MathSciNet  Google Scholar 

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Thanks are due to the assessors for beneficial ideas which assisted a lot for the enhancement of the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, The University of Burdwan, Burdwan, West Bengal, 713104, India

    Iswar Chandra Mandal & Swati Mukhopadhyay

  2. Department of Mathematics, University of Central Florida, Orlando, FL, 32816-1364, USA

    Kuppalapalle Vajravelu

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  1. Iswar Chandra Mandal
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  2. Swati Mukhopadhyay
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  3. Kuppalapalle Vajravelu
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Correspondence to Kuppalapalle Vajravelu.

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Mandal, I.C., Mukhopadhyay, S. & Vajravelu, K. Melting Heat Transfer of MHD Micropolar Fluid Flow Past An Exponentially Stretching Sheet with SLip and Thermal Radiation. Int. J. Appl. Comput. Math 7, 31 (2021). https://doi.org/10.1007/s40819-021-00955-1

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