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Boundary Layer Stagnation-Point Slip Flow and Heat Transfer towards a Shrinking/Stretching Cylinder over a Permeable Surface

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DOI: 10.4236/am.2015.63044    3,023 Downloads   3,432 Views   Citations

ABSTRACT

In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/a<0) are non-unique with dual solutions, which is different from a stretching cylinder (c/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Mat, N. , Arifin, N. , Nazar, R. and Bachok, N. (2015) Boundary Layer Stagnation-Point Slip Flow and Heat Transfer towards a Shrinking/Stretching Cylinder over a Permeable Surface. Applied Mathematics, 6, 466-475. doi: 10.4236/am.2015.63044.

References

[1] Crane, L.J. (1970) Flow Past a Stretching Plate. ZAMP, 21, 645-647.
http://dx.doi.org/10.1007/BF01587695
[2] Chiam, T.C. (1994) Stagnation-Point Flow towards a Stretching Plate. Journal of Physical Society of Japan, 63, 2443-2444.
http://dx.doi.org/10.1143/JPSJ.63.2443
[3] Wang, C.Y. (2008) Stagnation Flow towards a Shrinking Sheet. International Journal of Non-Linear Mechanics, 43, 377-382.
http://dx.doi.org/10.1016/j.ijnonlinmec.2007.12.021
[4] Fan, T., Xu, H. and Pop, I. (2010) Unsteady Stagnation Flow and Heat Transfer towards a Shrinking Sheet. International Communications in Heat and Mass Transfer, 37, 1440-1446.
http://dx.doi.org/10.1016/j.icheatmasstransfer.2010.08.002
[5] Bachok, N., Ishak, A. and Pop, I. (2010) Melting Heat Transfer in Boundary Layer Stagnation-Point Flow towards a Stretching/Shrinking Sheet. Physics Letters A, 374, 4075-4079.
http://dx.doi.org/10.1016/j.physleta.2010.08.032
[6] Ahmad, K., Nazar, R. and Pop, I. (2011) Boundary Layer Flow and Heat Transfer of a Micropolar Fluid near The Stagnation Point on a Stretching Vertical Surface with Presribed Skin Friction. International Journal of Minerals, Metallurgy and Materials, 18, 502-507.
http://dx.doi.org/10.1007/s12613-011-0469-y
[7] Lok, Y.Y., Ishak, A. and Pop, I. (2011) MHD Stagnation Point Flow with Suction towards a Shrinking Sheet. Sains Malaysiana, 40, 1179-1186.
[8] Bhattacharyya, K., Mukhopadhyay, S. and Layek, G.C. (2011) Slip Effects on Boundary Layer Stagnation-Point Flow and Heat Transfer towards a Shrinking Sheet. International Journal of Heat and Mass Transfer, 54, 308-331.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.09.041
[9] Bhattacharyya, K. and Vajravelu, K. (2012) Stagnation-Point Flow and Heat Transfer over an Exponentially Shrinking Sheet. Communications in Nonlinear Science and Numerical Simulation, 17, 2728-2734.

  
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