Numerical Solutions of Boundary Layer Flow over an Exponentially Stretching/Shrinking Sheet with Generalized Slip Velocity
In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1100531Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2000
 B.C. Sakiadis, “Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow,” AIChE J., vol. 7, 1961, pp. 26–28.
 F.K. Tsou, E.M. Sparrow, and R.J. Goldstein, “Flow and heat transfer in the boundary layer on a continuous moving surfaces,” Int. J. Heat Mass Transf.,vol. 10, 1967, pp. 219–235.
 L.J. Crane, “Flow past a stretching plate,” ZeitschriftFürAngew. Math. Und Phys.,vol. 21, 1970, pp. 645–647.
 C.Y. Wang, “Liquid film on an unsteady stretching sheet,” Quart. Appl. Math.,vol. 48, 1990, pp. 601–610.
 M. Miklavcic, and C.Y. Wang, “Viscous flow due to a shrinking sheet,” Quart. Appl. Math.,vol. 64, 2006, pp. 283–290.
 E. Magyari, and B. Keller, “Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface,” J. Phys. D Appl. Phys.,vol. 32, 1999, pp. 577–585.
 E.M.A. Elbashbeshy, “Heat transfer over an exponentially stretching continuous surface with suction,” Arch. Mech.,vol. 53, 2001, pp. 643–651.
 K. Bhattacharyya, “Boundary layer flow and heat transfer over an exponentially shrinking sheet,” Chinese Phys. Lett.,vol. 28, 2011, pp. 074701.
 N. Najib, N. Bachok, N.M. Arifin, and A. Ishak, “Boundary layer stagnation point flow and heat transfer past a permeable exponentially shrinking cylinder,” Int. J. Math. Model. Methods Appl. Sci.,vol. 8, 2014, pp. 121–126.
 G.S. Beavers, and D.D. Joseph, “Boundary conditions at a naturally permeable wall,” J. Fluid Mech.,vol. 30, 1967, pp. 197–207.
 C.Y. Wang, “Stagnation flow with slip: Exact solutions of the Navier-Stokes equations,” Z. Angew. Math. Phys.,vol. 54, 2003, pp. 184–189.
 P.D. Ariel, “Axisymmetric flow due to a stretching sheet with partial slip,” Comput. Math. with Appl.,vol. 54, 2007, pp. 1169–1183.
 K. Bhattacharyya, S. Mukhopadhyay, and G.C. Layek, “Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet,” Int. J. Heat Mass Transf.,vol. 54, 2011, pp. 308–313.
 F. Aman, A. Ishak, and I. Pop, “Magnetohydrodynamic stagnation-point flow towards a stretching/shrinking sheet with slip effects,” Int. Commun. Heat Mass Transf.,vol. 47, 2013,pp. 68–72.
 P.A. Thompson, and S. M. Troian, “A general boundary conditon for liquid flow at solid surfaces,” Nature,vol. 389, 1997, pp. 360–362.
 M. Sajid, K. Mahmood, and Z. Abbas, “Axisymmetric stagnation-point flow with a general slip boundary condition over a lubricated surface,” Chinese Phys. Lett.vol. 29, 2012, pp. 24702.
 A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Commun. Nonlinear Sci. Numer. Simul.,vol. 14, 2009, pp. 1064–1068.
 J. Kierzenka, and L.F. Shampine, “A BVP solver based on residual control and the Maltab PSE,” C. Trans. Math. Softw.,vol. 27,2001, pp. 299–316.
 L.F. Shampine, I. Gladwell, and S. Thompson, Solving ODEs with MATLAB, Cambridge University Press, 2003.
 J.H. Merkin, “On dual solutions occurring in mixed convection in a porous medium,” J. Eng. Math.,vol. 20, 1986, pp. 171–179.
 P.D. Weidman, D.G. Kubitschek, and A.M.J. Davis, “The effect of transpiration on self-similar boundary layer flow over moving surfaces,” Int. J. Eng. Sci.,vol. 44, 2006, pp. 730–737.
 A.V. Roşca, and I. Pop, “Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip,” Int. J. Heat Mass Transf.,vol. 60, 2013, pp. 355–364.