International Scientific Journal


The steady boundary-layer flow of a nanofluid past a moving semi-infinite flat plate in a uniform free stream in the presence of second order slip is studied using a second order slip flow model. The governing PDE are transformed into non-linear ODE by using appropriate similarity transformations, which are then solved numerically using bvp4c solver for different values of selected parameters. We found that the solutions existed for dual in a certain range of velocity ratio parameter. Therefore, a stability analysis has been analyzed to show which solutions are stable. The effects of velocity ratio parameter, Lewis number, Prandtl number, Brownian motion parameter, thermopherosis parameter, mass suction, first order slip parameter, and second order slip parameter on the skin friction coefficient, heat transfer coefficient, dimensionless velocity, temperature as well as nanoparticle volume fraction profiles are figured out graphically and discussed. These results reveals that the slip parameters expand the range of the solutions obtained. The increment of slip parameters lead to decrease the skin friction coefficient while increase the heat transfer coefficient. In addition, the value of Lewis nmber, Prandtl number, Brownian motion parameter, and thermopherosis parameter are significantly affected the heat transfer coefficient. Lastly, the first solution is stable and physically relevant, while the second solution is not.
PAPER REVISED: 2018-07-05
PAPER ACCEPTED: 2018-07-05
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  1. Wu, L., A slip model for rarefied gas flows at arbitrary Knudsen number. Applied Physics Letter 93 (2008), pp. 1-3, ID 253103
  2. Fang, T., et al., Viscous flow over a shrinking sheet with a second-order slip flow model. Comm. Nonlinear Sci Numer Simulat, 15 (2010), pp. 1831-1842
  3. Fang, T., Aziz, A., Viscous flow with second-order slip velocity over a stretching sheet. Z. Naturforsch. A, 65a (2010), pp. 1087-1092
  4. Roşca, A.V., Pop, I., Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. International Journal of Heat and Mass Transfer, 60 (2013), pp. 355 - 364
  5. Roşca, N.C., Pop, I., Mixed convection stagnation point flow past a vertical flat plate with a second order slip: heat flux case. International Journal of Heat and Mass Transfer, 65 (2013), pp. 102-109
  6. Mabood, F., Das, K., Melting heat transfer on hydromagnetic flow of a nanofluid over a stretching sheet with radiation and second order slip. The European Physical Journal Plus (2015), pp. 1-31
  7. Wu, L., Mass transfer induced slip effect on viscous gas flows above a shrinking/stretching sheet. International Journal of Heat and Mass Transfer, 93 (2016), pp. 17-22
  8. Sharma, R., Ishak, A., Second order slip flow of Cu-water nanofluid over a stretching sheet with heat transfer, WSEAS Transaction On Fluid Mechanics, 9 (2014), pp. 26-33
  9. Merkin, J. H., On Dual Solutions Occuring in Mixed Convection in a Porous Medium. Journal of Engineering Mathematics, 20 (1985), pp. 171-179
  10. Weidman, P. D., et al., The Effects of Transpiration on Self-Similar Boundary Layer Flow over Moving Surfaces. International Journal of Engineering Sciences, 44 (2006), pp. 730-737
  11. Merill, K., et al., Final steady flow near a stagnation point on a vertical surface in a porous medium, International Journal of Heat and Mass Transfer, 49 (2006), pp. 4681-4686
  12. Ishak, A., Flow and heat transfer over a shrinking sheet: a stability analysis. International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, 8 (2014), 5, pp. 905-909
  13. Noor, A., et al., Stability analysis of stagnation-point flow past a shrinking sheet in a nanofluid, Journal of Quality Measurement and Analysis,10 (2014), 2, pp. 51-63
  14. Nazar, R., et al., Stability analysis of three-dimensional flow and heat transfer over a permeable shrinking surface in a Cu-water nanofluid, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 8 (2014), 5, pp. 782-788
  15. Noor, A., et al., Stability analysis of flow and heat transfer on a permeable moving plate in a Co-flowing nanofluid, Proceedings, The 2014 UKM FST Postgraduate Colloquium, Selangor, Malaysia, 2014, Vol. 1614, pp. 898-905
  16. Hafidzuddin, E. H., et al., Stability analysis of unsteady three-dimensional viscous flow over a permeable stretching/shrinking surface, Journal of Quality Measurement and Analysis, 11 (2015), 1, pp. 19-31
  17. Yasin, M. H. M., et al., MHD stagnation-point flow and heat transfer with effects of viscous dissipation, Joule heating and partial velocity slip, Scientific Reports, 5 (2015), pp. 1-8, ID 17848
  18. Klemp, J. P., Acrivos, A., A moving-wall boundary layer with reverse flow, Journal of Fluid Mechanics, 53 (1972), 1, pp. 177-191
  19. Husaini, M. Y., et al., On similarity solution of a boundary layer problem with upstream moving wall, SIAM Journal of Applied Mathematics, 7 (1987), 4, pp 699-709
  20. Fang, T., Similarity solutions for a moving-flat plate thermal boundary layer, Acta Mechanica, 163 (2003), 3-4, pp. 161-172
  21. Fang T., Further study on a moving-wall boundary layer problem with mass transfer, Acta Mechanica, 163 (2003), 3-4, pp 183-188
  22. Fang, T., Lee, C. F., A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate, Applied Mathematics Letters, 18 (2005), 5, pp. 487-495
  23. Bachok, N., et al., Boundary-layer flow of nanofluids over a moving surface in a flowing fluid, International Journal of Thermal Sciences, 49 (2010), 9, pp. 1663-1668
  24. Kuznetsov, A.V., Nield, D. A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, 49 (2010), 2, pp. 243-247
  25. Kuznetsov, A. V., Nield, D. A., The Cheng-Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid: A revised model, International Journal of Heat and Mass Transfer, 65 (2013), pp. 682-685.
  26. Mukhopadhyay, S., Andersson, H. I., Effects of slip and heat transfer analysis of flow over an unsteady stretching surface, Heat Mass Transfer, 45 (2009), pp. 1447-1452
  27. Dzulkifli, N. F., et al., Soret and Dufour effects on unsteady boundary layer flow and heat transfer of nanofluid over a stretching/shrinking sheet: A stability analysis, Journal of Chemical Engineering & Process Technology, 8 (2017), 3, pp. 1-9, ID 1000336
  28. Bakar, S. A., et al., A Stability Analysis on Mixed Convection Boundary Layer Flow along a Permeable Vertical Cylinder in a Porous Medium Filled with a Nanofluid and Thermal Radiation, Applied Sciences, 8 (2018), pp. 1-13, ID 483
  29. Najib, N., et al., Stability Analysis of Stagnation-Point Flow in a Nanofluid over a Stretching/Shrinking Sheet with Second-Order Slip, Soret and Dufour Effects: A Revised Model, Applied Sciences, 8 (2018), pp. 1-13, ID 642
  30. Bakar, N. A. A., et al., Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect, Results in Physics, 9 (2018), pp. 1335-1344
  31. Harris, S. D., et al., Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip, Transport Porous Media, 77 (2009), pp. 267-285
  32. Buongiorno, J., Convective transport in nanofluids. ASME J. Heat Transfer, 128 (2006), pp. 240-250

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