Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip

International Journal of Heat and Mass Transfer - Tập 60 - Trang 355-364 - 2013
Alin V. Roşca1, Ioan Pop2
1Faculty of Economics and Business Administration, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania
2Department of Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

Tài liệu tham khảo

Crane, 1970, Flow past a stretching plate, J. Appl. Math. Phys. (ZAMP), 21, 645, 10.1007/BF01587695 Banks, 1983, Similarity solutions of the boundary-layer equations for a stretching wall, J. Mech. Theor. Appl., 2, 375 Grubka, 1985, Heat transfer characteristics of a continuous stretching surface with variable temperature, ASME J. Heat Transfer, 107, 248, 10.1115/1.3247387 Magyari, 2000, Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls, Eur. J. Mech. B/Fluids, 19, 109, 10.1016/S0997-7546(00)00104-7 Liao, 2004, On explicit analytic solutions of boundary-layer equations about flows in a porous medium or for a stretching wall, Int. J. Heat Mass Transfer, 47, 5, 10.1016/S0017-9310(03)00405-8 Fisher, 1976 Goldstein, 1965, On backward boundary layers and flow in converging passage, J. Fluid Mech., 21, 33, 10.1017/S0022112065000034 Miklavčič, 2008, Viscous flow due to a shrinking sheet, Q. Appl. Math., 64, 283, 10.1090/S0033-569X-06-01002-5 Fang, 2008, Boundary layer flow over a shrinking sheet with power-law velocity, Int. J. Heat Mass Transfer, 51, 5838, 10.1016/j.ijheatmasstransfer.2008.04.067 Fang, 2008, A new solution branch for the Blasius equation – a shrinking sheet problem, Comput. Math. Appl., 56, 3088, 10.1016/j.camwa.2008.07.027 Fang, 2010, Viscous flow over a shrinking sheet with a second order slip flow model, Commun. Nonlinear Sci. Numer. Simul., 15, 1831, 10.1016/j.cnsns.2009.07.017 Fang, 2011, Flow and heat transfer over a generalized stretching/shrinking wall problem – exact solutions of the Navier–Stokes equations, Int. J. Non-Linear Mech., 46, 1116, 10.1016/j.ijnonlinmec.2011.04.014 Fang, 2009, Closed-form exact solutions of MHD viscous flow over a shrinking sheet, Commun. Nonlinear Sci. Numer. Simul., 14, 2853, 10.1016/j.cnsns.2008.10.005 Fang, 2010, Thermal boundary layers over a shrinking sheet: an analytical solution, Acta Mech., 209, 325, 10.1007/s00707-009-0183-2 Sajid, 2009, The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet, Chaos Solitons Fractals, 39, 1317, 10.1016/j.chaos.2007.06.019 Fang, 2010, Viscous flow with second-order slip velocity over a stretching sheet, Z. Naturforsch. A – Phys. Sci., 65a, 1087, 10.1515/zna-2010-1212 Wang, 2011, Review of similarity stretching exact solutions of the Navier–Stokes equations, Eur. J. Mech. B/Fluids, 30, 475, 10.1016/j.euromechflu.2011.05.006 Ramachandran, 1987, Mixed convection from vertical and inclined moving sheets in a parallel free stream, J. Thermophys. Heat Transfer, 1, 274, 10.2514/3.39 Ingham, 1986, Singular and non-unique solutions of the boundarylayer equations for the flow due to free convection near a continuously moving vertical plate, J. Appl. Math. Phys. (ZAMP), 37, 559, 10.1007/BF00945430 Daskalakis, 1993, Free convection effects in the boundary layer along a vertical stretching flat surface, Can. J. Phys., 70, 1253, 10.1139/p92-204 Chen, 1998, Laminar mixed convection adjacent to vertical, continuously stretching surface, Heat Mass Transfer, 33, 471, 10.1007/s002310050217 Chen, 2000, Mixed convection cooling of heated continuously stretching surface, Heat Mass Transfer, 36, 79, 10.1007/s002310050367 Chamkha, 1999, Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption, Int. J. Heat Fluid Flow, 20, 84, 10.1016/S0142-727X(98)10032-2 Ali, 2004, The buoyancy effects on the boundary layers induced by continuous surfaces stretched with rapidly decreasing velocities, Heat Mass Transfer, 40, 285, 10.1007/s00231-002-0405-9 Ishak, 2010, Stagnation-point flow over a shrinking sheet in a micropolar fluid, Chem. Eng. Commun., 197, 1417, 10.1080/00986441003626169 Karwe, 1988, Fluid flow and mixed convection transport from a moving plate in rolling and extrusion processes, ASME J. Heat Transfer, 110, 655, 10.1115/1.3250542 Bejan, 1995 Pop, 2001 Wu, 2008, A slip model for rarefied gas flows at arbitrary Knudsen number, Appl. Phys. Lett., 93, 253103, 10.1063/1.3052923 Vajravelu, 2004, Hydromagnetic flow of a second grade fluid over a stretching sheet, Appl. Math. Comput., 148, 783 Cortell, 2006, Flow and heat transfer of an electrically conducting fluid of second grade over a stretching sheet subject to suction and to a transverse magnetic field, Int. J. Heat Mass Transfer, 49, 1851, 10.1016/j.ijheatmasstransfer.2005.11.013 Fang, 2011, Note on the heat transfer of flows over a stretching wall in porous media: exact solutions, Transp. Porous Media, 86, 579, 10.1007/s11242-010-9640-6 Weidman, 2006, The effect of transpiration on self-similar boundary layer flow over moving surfaces, Int. J. Eng. Sci., 44, 730, 10.1016/j.ijengsci.2006.04.005 Postelnicu, 2011, Falkner–Skan boundary layer flow of a power-law fluid past a stretching wedge, Appl. Math. Comput., 217, 4359 Harris, 2009, Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip, Transp. Porous Media, 77, 267, 10.1007/s11242-008-9309-6 L.F. Shampine, M.W. Reichelt, J. Kierzenka, Solving boundary value problems for ordinary differential equations in Matlab with bvp4c, 2010. <http://www.mathworks.com/bvp_tutorial>. Lok, 2009, Mixed convection flow of a micropolar fluid near a non-orthogonal stagnation-point on a stretching vertical sheet, Int. J. Numer. Methods Heat Fluid Flow, 19, 459, 10.1108/09615530910938380