Advanced Search
Article Contents
Article Contents

Stability analysis of stagnation point flow in nanofluid over stretching/shrinking sheet with slip effect using buongiorno's model

The reviewing process of the paper is handled by Gafurjan Ibragimov, Siti Hasana Sapar and Siti Nur Iqmal Ibrahim

The first author is supported by Putra grant of Universiti Putra Malaysia.
Abstract Full Text(HTML) Figure(4) / Table(1) Related Papers Cited by
  • The study on stagnation boundary layer flow in nanofluid over stretching/shrinking sheet with the effect of slip at the boundary was considered by applying the Buongiorno's model. The partial differential equations of the governing equations were transformed into ordinary differential equations by using appropriate similarity transformation in order to obtain the similarity equations. The equations then were substituted into bvp4c code in Matlab software to get the numerical results. The results of skin friction coefficient, heat transfer coefficient as well as mass transfer coefficient on the governing parameters such as slip parameter, Brownian motion parameter, and thermophoresis parameter are shown graphically. The presence of slip parameter is significantly affected the skin friction, heat and mass transfer coefficient. The smallest number of Brownian motion is sufficient to increase the heat transfer coefficient while largest number of thermophoresis parameter is required to increase mass transfer coefficient. The stability analysis results expressed that the first solution is stable and physically realizable whereas the second solution is not.

    Mathematics Subject Classification: 76D10.


    \begin{equation} \\ \end{equation}
  • 加载中
  • Figure 1.  Skin friction coefficient $ f''(0) $, heat transfer coefficient $ -\theta'(0) $ and mass transfer coefficient $ -\phi'(0) $ vs $ \varepsilon $ for different $ \sigma $

    Figure 2.  Heat transfer coefficient $ -\theta'(0) $ and mass transfer coefficient $ -\phi'(0) $ vs $ \varepsilon $ for different $ Nb $

    Figure 3.  Heat transfer coefficient $ -\theta'(0) $ and mass transfer coefficient $ -\phi'(0) $ vs $ \varepsilon $ for different $ Nt $

    Figure 4.  Velocity profile $ f'(\eta) $, temperature profile $ \theta(\eta) $ and concentration profile $ \phi(\eta) $ for different $ \varepsilon $

    Table 1.  Smallest eigenvalues $ \gamma $ for selected values of $ \varepsilon $ with different $ \sigma $

    $ \sigma $ $ \varepsilon $ First solution Second solution
    0 -1.246 0.0622 -0.0614
    -1.24 0.2121 -0.2036
    -1.2 0.5780 -0.5172
    0.2 -1.388 0.0802 -0.0791
    -1.38 0.2390 -0.2300
    -1.3 0.7707 -0.6783
    0.4 -1.582 0.0719 -0.0712
    -1.58 0.1273 -0.1251
    -1.5 0.6936 -0.6301
     | Show Table
    DownLoad: CSV
  • [1] N. BachokN. NajibN. M. Arifin and N. Senu, Stability of dual solutions in boundary layer flow and heat transfer on a moving plate in a copper-water nanofluid with slip effect, WSEAS Transactions on Fluid Mechanics, 11 (2016), 151-158. 
    [2] J. Buongiorno, Convective transport in nanofluids, Journal of Heat Transfer, 128 (2006), 240-250. 
    [3] S. K. Das, S. U. S. Choi, W. Yu and T. Pradeep, Nanofluids Science and Technology, John Wiley & Sons, New York, 2007.
    [4] N. F. DzulkifliN. BachokI. PopN. A. YacobN. M. Arifin and H. Rosali, 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), 1-9. 
    [5] R. Hamid, R. Nazar and I. Pop, Non-alignment stagnationpoint flow of a nanofluid past a permeable stretching$/$shrinking sheet: Buongiorno's model, , Scientific Reports, 5 (2015), 14640.
    [6] S. D. HarrisD. B. Ingham and I. Pop, 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), 267-285. 
    [7] W. IbrahimB. Shankar and M. M. Nandeppanavar, MHD stagnation point flow and heat transfer due to nanofluid towards a stretching sheet, International Journal of Heat and Mass Transfer, 56 (2013), 1-9. 
    [8] A. Ishak, Flow and heat transfer over a shrinking sheet: A stability analysis, International Journal of Mechanical, Aerospace, Industrial and Mechatronics Engineering, 8 (2014), 905-909. 
    [9] R. Jusoh and R. Nazar, Stagnation point flow and heat transfer of a nanofluid over a stretching$/$shrinking sheet with convective boundary conditions and suction, AIP Proceeding, 1830 (2017), 020043.
    [10] M. I. KhanM. TamoorT. Hayat and A. Alsaedi, MHD boundary layer thermal slip flow by nonlinearly stretching cylinder with suction/blowing and radiation, Results in Physics, 7 (2017), 1207-1211. 
    [11] S. MansurA. Ishak and I. Pop, Stagnation-point flow towards a stretching$/$shrinking sheet in a nanofluid using Buongiorno's model, Journal of Process Mechanical Engineering, 4 (2015), 1-9. 
    [12] S. Mansur and A. Ishak, The magnetohydrodynamic boundary layer flow of a nanofluid past a stretching/shrinking sheet with slip boundary conditions, Journal of Applied Mathematics, 90752 (2014), 1-7.  doi: 10.1155/2013/350647.
    [13] S. MansurA. Ishak and I. Pop, The magnetohydrodynamic stagnation point flow of a nanofluid over a stretching/shrinking sheet with suction, Plos One, 11 (2015), 1-14.  doi: 10.1155/2013/350647.
    [14] A. Mehmood and A. Ali, The effect of slip condition on unsteady MHD oscillatory ow of a viscous uid in a planer channel, Romanian Journal of Physics, 52 (2007), 85-91. 
    [15] K. MerillM. BeauchesneJ. PreviteJ. Paullet and P. Weidman, Final steady flow near a stagnation point on a vertical surface in a porous medium, International Journal of Heat and Mass Transfer, 49 (2006), 4681-4686. 
    [16] J. H. Merkin, On dual solutions occurring in mixed convection in a porous medium, Journal of Engineering Mathematics, 20 (1985), 171-179. 
    [17] M. K. A. Mohamed, N. A. Z. Noar, M. Z. Salleh and A. Ishak, Slip flow on stagnation point over a stretching sheet in a viscoelastic nanofluid, , AIP Proceedings, 1830 (2017), 020015.
    [18] S. Mukhopadhyay, MHD boundary layer slip flow along a stretching cylinder, Ain Shams Engineering Journal, 4 (2013), 317-324. 
    [19] N. NajibN. Bachok and N. M. Arifin, Stability of dual solutions in boundary layer flow and heat transfer over an exponentially shrinking cylinder, Indian Journal of Science and Technology, 9 (2016), 1-6. 
    [20] N. NajibN. BachokN. M. Arifin and N. Senu, Boundary layer flow and heat transfer of nanofluids over a moving plate with partial slip and thermal convective boundary condition: Stability analysis, International Journal of Mechanics, 11 (2017), 19-24. 
    [21] A. V. Rosca and I. Pop, Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip, International Journal of Heat and Mass Transfer, 6 (2013), 355-364. 
    [22] R. Sharma and A. Ishak, Stagnation point flow of a micropolar fluid over a stretching/ shrinking sheet with second-order velocity slip, Journal of Aerospace Engineering, 04016025 (2016), 1-8. 
    [23] P. D. WeidmanD. G. Kubitschek and A. M. J. Davis, The effect of transpiration on self-similar boundary layer flow over moving surfaces, International Journal of Engineering Science, 44 (2006), 730-737. 
    [24] K. Zaimi and A. Ishak, Stagnation-point flow towards a stretching vertical sheet with slip effects, Mathematics, 4 (2016), 1-8. 
  • 加载中




Article Metrics

HTML views(1859) PDF downloads(348) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint