Unsteady Stagnation-Point Flow towards a Shrinking Sheet with Radiation Effect

Authors: F. M. Ali, R. Nazar, N. M. Arifin, I. Pop

Abstract:

In this paper, the problem of unsteady stagnation-point flow and heat transfer induced by a shrinking sheet in the presence of radiation effect is studied. The transformed boundary layer equations are solved numerically by the shooting method. The influence of radiation, unsteadiness and shrinking parameters, and the Prandtl number on the reduced skin friction coefficient and the heat transfer coefficient, as well as the velocity and temperature profiles are presented and discussed in detail. It is found that dual solutions exist and the temperature distribution becomes less significant with radiation parameter.

Keywords: Heat transfer, Radiation effect, Shrinking sheet Unsteady flow.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1092447

References:

[1] C. Y. Wang, "Liquid film on an unsteady stretching sheet,” Quarterly of Applied Mathematics, vol. 48, pp 601–610, 1990.
[2] M. Miklavcic and C. Y. Wang "Viscous flow due to a shrinking sheet,” Quarterly of Applied Mathematics, vol. 64, pp. 283–290, 2006.
[3] C. Y. Wang, "Stagnation flow towards a shrinking sheet,” International Journal of Non-Linear Mechanics, vol. 43, pp. 377–382, 2008.
[4] T. Fang, "Boundary layer flow over a shrinking sheet with power-law velocity,” International Journal of Heat and MassTransfer, vol. 51, pp. 5838–5843, 2008.
[5] T. Fang and J. Zhang, "Thermal boundary layers over a shrinking sheet: an analytical solution,” Acta Mechanica, vol. 209, pp. 325–343, 2010.
[6] M. Sajid and T. Hayat, "The application of homotopy analysis method for method for MHD viscous flow due to a shrinking sheet,” Chaos,Solitons and Fractals, vol. 39, pp. 1317–1323, 2009.
[7] T. Hayat, Z. Abbas, T. Javed and M. Sajid, "Three-dimensional rotating flow induced by a shrinking sheet for suction,"Chaos, Solitons and Fractals, vol. 39, pp. 1615–1626, 2009.
[8] C. D. Surma Devi, H. S. Takhar and G. Nath, "Unsteady, three-dimensional, boundary-layer flow due to a stretching surface,” International Journal of Heat and Mass Transfer, vol. 29, pp. 1996–1999, 1986.
[9] K. N. Lakshmisha, S. Venkateswaran and G. Nath, "Three-dimensional unsteady flow with heat and mass transfer over a continuous stretching surface,” Journal of Heat Transfer, vol. 110, pp. 590–595, 1988.
[10] F. M. Ali, R. Nazar, N. M. Arifin and I. Pop, "Unsteady flow across a stretching surface,” International Communications in Heat and Mass Transfer, vol. 37, pp. 476–479, 2010.
[11] M. Abd El-Aziz, "Radiation effect on the flow and heat transfer over an unsteady stretching sheet,” International Communications in Heat and Mass Transfer, vol. 36, pp. 521–524, 2009.
[12] T-G. Fang, J. Zhang and S-S Yao, "Viscous flow over an unsteady shrinking sheet with mass transfer,” Chinese Physics Letters, vol. 26, pp. 014703-1–014703-4, 2009.
[13] F. M. Ali, R. Nazar, N. M. Arifin and I. Pop, "Unsteady shrinking sheet with mass transfer in a rotating fluid,” International Journal for Numerical Methods in Fluids, vol. 66, pp. 1465–1474, 2011.
[14] F. M. Ali, R. Nazar, N. M. Arifin and I. Pop, "Unsteady flow and heat transfer past an axisymmetric permeable shrinking sheet with radiation effect,” International Journal for Numerical Methods in Fluids, vol. 67, pp. 1310–1320, 2011.
[15] C. Midya, "Heat transfer in MHD boundary layer flow over a shrinking sheet with radiation and heat sink,” Journal of Global Research in Mathematical Archives, vol. 1(2), pp 63–70, 2013.
[16] A. Raptis, C. Perdikis and H. S. Takhar, "Effect of thermal radiation on MHD flow,” Journal of Applied Mathematics and Computing, vol. 153, pp. 645–649, 2004.
[17] R. C. Bataller, "Radiation effects in the Blasius flow,” Journal of Applied Mathematics and Computing, vol. 198, pp. 333–338, 2008.
[18] R. Cortell, "Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface,” Journal of Materials Processing Technology, vol. 203, pp. 176–183, 2008.
[19] D. B. Meade, B. S. Haran and R. E. White, "The shooting technique for the solution of two-point boundary value problems,” Maple Tech., vol. 3, pp. 85–93, 1996.
[20] C. Y. Wang, "Impinging stagnation flows,” Physics of Fluids, vol. 30(3), pp. 915–917, 1987.
[21] J. H. Merkin, "On dual solutions occuring in mixed convection in a porous medium,” Journal of Engineering Mathematics, vol. 20, pp. 171–179, 1987.
[22] P. D. Weidman, D. 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, vol. 44, pp. 730–737, 2006.