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Submitted
July 14, 2017
Accepted
July 3, 2019
Published
November 5, 2020
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Abstract

The steady two dimensional convective boundary layer flow of micropolar Jeffrey fluid past a permeable stretching sheet is studied in this paper. The governing boundary layer equation in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. The effects of Prandtl number, Deborah number, and material parameter with the boundary condition for microrotation, n = 0 (strong concentration of microelements) on the velocity, microrotation, temperature profiles as well as the skin friction and heat transfer coefficients are presented and discussed. An excellent agreement is observed between the present and earlier published results for some special cases. The results revealed that, the effect of Deborah number and stretching parameter are increased the heat transfer coefficient while the opposite trend is observed for the effects of material and velocity slip parameters. It was also observed that, the values of skin friction increased with the increment on the values of all studied parameters.

Keywords

Boundary layer flow Micropolar Jeffrey fluid Numerical solution.

Article Details

How to Cite
Rawi, N. A., Mohd Zin, N. A., Khalid, A., Mohd Kasim, A. R., Mat Isa, Z., & Shafie, S. (2020). Numerical Solutions for Convective Boundary Layer Flow of Micropolar Jeffrey Fluid with Prescribe Wall Temperature. Journal of the Indonesian Mathematical Society, 26(3), 286–298. https://doi.org/10.22342/jims.26.3.553.286-298
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References

  1. Eldabe, N. T., Moatimid, G. M. and Ali, H. S., “Magnetohydrodynamic flow of non-Newtonian visco-elastic fluid through a porous medium near an accelerated plate”, Can. J. Phys., 81(2003), 1249-1269.
  2. Hameed, M. and Nadeem, S., “Unsteady MHD flow of a non-Newtonian fluid on a porous plate”, J. Math. Anal. Appl., 325(2007), 724-733.
  3. Abel, M. S., Siddheshwar, P. G. and Nandeppanavar, M. M., “Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source”, Int. J. Heat Mass Transfer, 50(2007), 960-966.
  4. Das, K., “Slip effects on MHD mixed convection stagnation point flow of a micropolar fluid towards a shrinking vertical sheet”, Com. Math. Appl., 63(2012), 255-267.
  5. Kasim, A. R. M., Mohammad, N. F. , Aurangzaib and Shafie, S., “Natural convection boundary layer flow of a viscoelastic fluid on solid sphere with Newtonian heating”, World Academy Sc. Eng. Tech., 64(2012), 628-633.
  6. Ali, F., Khan, I. and Shafie, S., “Closed form solutions for unsteady free convection flow of a second grade fluid over an oscillating vertical plate”, PloS one, 9(2014), 1-15.
  8. Khan, I., Ali, F., Shafie, S. and Qasim, M., “Unsteady free convection flow in a Walters-B fluid and heat transfer analysis”, Bull. Malays. Math. Sci. Soc., 37(2014), 437-448.
  9. Ahmad, S., Vieru, D., Ilyas, I. and Shafie, S., “Unsteady magnetohydrodynamic free convection flow of a second grade fluid in a porous medium with ramped wall temperature”, PloS one, 9(2014), 1-9.
  10. Zaib, A. and Shafie, S., “Slip effect on an Unsteady MHD stagnation-point flow of a micropolar fluid towards a shrinking sheet with thermophoresis effect”, Int. J. Comput. Methods Eng. Sci. Mech., 16(2015), 285-291.
  11. Khalid, A., Khan, I. and Shafie, S., “Unsteady boundary layer flow of a Casson fluid past an oscillating vertical plate with constant wall temperature”, Malaysian J. Fundam. Appl. Sci., 11(2015), 28-32.
  12. Bird, R.B., Armstrong, R.C. and Hassager, O., Dynamics of polymeric liquids, John Wiley & Sons, 1987.
  13. Jeffreys, H., The Earth, Cambridge University Press, London, 1929.
  14. Nadeem, S. and Akbar, N.S., “Peristaltic flow of a Jeffrey fluid with variable viscosity in an asymmetric channel”, Z Naturforsch. A: Phys. Sci., 64(2009), 713-722.
  15. M. Khan, F. Iftikhar, A. Anjum, Some unsteady flows of a Jeffrey fluid between two side walls over a plane wall. Z Naturforsch. A: Phys. Sci. 66(2011), 745-752.
  16. Hayat, T., Asad, S., Qasim, M. and Hendi, A.A., “Boundary layer flow of a Jeffrey fluid with convective boundary conditions”, Int. J. Numer. Methods Fluids, 69(2012), 1350-1362.
  17. Hayat, T., Shehzad, S.A., Qasim, M. and Obaidat, S., “Thermal radiation effects on the mixed convection stagnation-point flow in a Jeffery fluid”, Z Naturforsch. A: Phys. Sci., 66(2011), 606-614.
  18. Hayat, T., Ahmad, N. and Ali, N., “Effects of an endoscope and magnetic field on the peristalsis involving Jeffrey fluid”, Commun. Nonlinear Sci. Numer. Simul., 13(2008), 1581-1591.
  19. Vajravelu, K., Sreenadh, S. and Lakshminarayana, P., “The influence of heat transfer on peristaltic transport of a Jeffrey fluid in a vertical porous stratum”, Commun. Nonlinear Sci. Numer. Simul., 16(2011), 3107-3125.
  20. Turkyilmazoglu, M. and Pop, I., “Exact analytical solutions for the flow and heat transfer near the stagnation point on a stretching/shrinking sheet in a Jeffrey fluid”, Int. J. Heat Mass Transfer, 57(2013), 82-88.
  21. Zin, N. A. M., Ilyas, I. and Shafie, S., “Exact and numerical solutions for unsteady heat and mass transfer problem of Jeffrey fluid with MHD and Newtonian heating effects”, Neural Comput. Appl., (2017), 1-17.
  22. Eringen, A. C., “Theory of micropolar fluids”, J. Math. Mech., 16(1966).
  23. Gorla, R. S. R., “Micropolar boundary layer flow at a stagnation point on a moving wall”, Int. J. Eng. Sci., 21(1983), 25-33.
  24. Agarwal, R. S. and Dhanapal, C., “Flow and heat transfer in a micropolar fluid past a flat plate with suction and heat sources”, Int. J. Eng. Sci., 26(1988), 1257-1266.
  25. Nazar, R. and Amin, N., “Free convection boundary layer on an isothermal sphere in a micropolar fluid”, Int. Commun. Heat Mass Transfer, 29(2002), 377-386.
  26. El-Arabawy, H. A., “Effect of suction/injection on the flow of a micropolar fluid past a continuously moving plate in the presence of radiation”, Int. J. Heat Mass Transfer, 46(2003), 1471-1477.
  27. Ishak, A., Nazar, R. and Pop, I., “Heat transfer over a stretching surface with variable heat flux in micropolar fluids”, Phys. Lett. A, 372(2008), 559-561.
  28. Cheng, C. Y., “Natural convection heat and mass transfer from a sphere in micropolar fluids with constant wall temperature and concentration”, Int. Commun. Heat Mass Transfer, 35(2008), 750-755.
  29. Nadeem, S., Hussain, M. and Naz. M., “MHD stagnation flow of a micropolar fluid through a porous medium”, Meccanica, 45(2010), 869-880.
  30. Aurangzaib, Kasim, A. R. M., Mohammad, N. F. and Shafie, S., “Unsteady MHD mixed convection flow with heat and mass transfer over a vertical plate in a micropolar fluid-saturated porous medium”, J. Appl. Sci. Eng., 16(2013), 141-150.
  31. Zaib, A. and Shafie, S., “Slip Effect on an Unsteady MHD Stagnation-Point Flow of a Micropolar Fluid towards a Shrinking Sheet with Thermophoresis Effect”, Int. J. Comput. Methods Eng. Sci. Mech., 16(2015), 285-291.
  32. Jena, S. K. and Mathur, M. N., “Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate”, Int. J. Eng. Sci., 19(1981), 1431-1439.
  33. Ahmadi, G., “Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate”, Int. J. Eng. Sci., 14(1976), 639-646.
  34. Rees, D. A. S. and Bassom, A. P., “The Blasius boundary-layer flow of a micropolar fluid”, Int. J. Eng. Sci., 34(1996), 113-124.
  35. Lok, Y. Y., Amin, N., Campean, D. and Pop, I., “Steady mixed convection flow of a micropolar fluid near the stagnation point on a vertical surface”, Int. J. Numer. Methods Heat Fluid Flow, 15(2005), 654-670.
  36. Rawi, N. A., Kasim, A. R. M., Isa, M. and Shafie, S. Shafie, “g-Jitter induced mixed convection flow of heat and mass transfer past an inclined stretching sheet”, Jurnal Teknologi, 71(2014), 27-31.
  37. Kasim, A. R. M., Jiann, L. Y., Rawi, N.A., Ali, A. and Shafie, S., “Mixed Convection Flow of Viscoelastic Fluid over a Sphere under Convective Boundary Condition Embedded in Porous Medium”, Defect Diffusion Forum, 362(2015), 67-75.