Flow and heat transfer over a generalized stretching/shrinking wall problem - Exact solutions of the NavierStokes equations

International Journal of Non-Linear Mechanics

Volumn 46, Issue 9, 2011, Pages 1116-1127

  Fang, Tiegang ^a   Yao, Shanshan ^a   Pop, Ioan ^b  

^a North Carolina State University   (United States)

^b BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Analytical solution; Exact solution; Heat transfer; NavierStokes equation; Shrinking sheet; Similarity equation; Stretching surface

Indexed keywords

ANALYTICAL SOLUTIONS; EXACT SOLUTION; SHRINKING SHEET; SIMILARITY EQUATION; STRETCHING SURFACE;

HEAT FLUX; SHRINKAGE; VISCOUS FLOW;

HEAT TRANSFER;

EID: 80051548371     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2011.04.014     Document Type: Article

References (35)

1. M.V. Karwe, and Y. Jaluria Numerical simulation of thermal transport associated with a continuous moving flat sheet in materials processing ASME J. Heat Transfer 113 1991 612 619 (Pubitemid 21697241)
2. L.J. Crane Flow past a stretching plane J. Appl. Math. Phys. (ZAMP) 21 1970 645 647
3. W.H.H. Banks Similarity solutions of the boundary layer equations for a stretching wall J. Mécan. Theoret. Appl. 2 1983 375 392 (Pubitemid 14483527)
4. E. Magyari, and B. Keller Exact solutions for self-similar boundary-layer flows induced by permeable stretching surfaces Eur. J. Mech. B-Fluids 19 2000 109 122
5. S.J. Liao, and I. Pop Explicit analytic solution for similarity boundary layer equations Int. J. Heat Mass Transfer 47 2004 75 85 (Pubitemid 37250100)
6. P. Carragher, and L.J. Crane Heat transfer on a continuous stretching sheet J. Appl. Math. Mech. (ZAMM) 62 1982 564 565
7. J.L. Grubka, and K.M. Bobba Heat transfer characteristics of a continuous stretching surface with variable temperature ASME J. Heat Transfer 107 1985 248 250 (Pubitemid 15475815)
8. B.K. Dutta, P. Roy, and A.S. Gupta Temperature field in flow over a stretching sheet with uniform heat flux Int. Commun. Heat Mass Transfer 12 1985 89 94 (Pubitemid 16456605)
9. P.S. Gupta, and A.S. Gupta Heat and mass transfer on a stretching sheet with suction or blowing Canad. J. Chem. Eng. 55 1977 744 746
10. R.C. Bataller Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface J. Mater. Process. Technol. 203 2008 176 183 (Pubitemid 351697687)
11. E. Magyari, and P.D. Weidman Heat transfer on a plate beneath an external uniform shear flow Int. J. Therm. Sci. 45 2006 110 115 (Pubitemid 41705331)
12. G.E. Cossali Similarity solutions of energy and momentum boundary layer equations for a powerlaw shear driven flow over a semi-infinite flat plate Eur. J. Mech. B/Fluids 25 2006 18 32 (Pubitemid 41501484)
13. T. Fang Flow and heat transfer characteristics of the boundary layers over a stretching surface with a uniform-shear free stream Int. J. Heat Mass Transfer 51 2008 2199 2213
14. E. Magyari, and B. Keller Heat transfer characteristics of boundary-layer flows induced by continuous surfaces stretched with prescribed skin friction Heat Mass Transfer 42 2006 679 687
15. H.I. Andersson Slip flow past a stretching surface Acta Mech. 158 2002 121 125 (Pubitemid 35297922)
16. A. Chakrabarti, and A.S. Gupta Hydromagnetic flow and heat transfer over a stretching sheet Q. Appl. Math 37 1979 73 78 (Pubitemid 9452219)
17. I. Pop, and T.Y. Na A note on MHD flow over a stretching permeable surface Mech. Res. Commun. 25 1998 263 269 (Pubitemid 128636900)
18. H.I. Andersson, K.H. Bach, and B.S. Dandapat Magnetohydrodynamic flow of a powerlaw fluid over a stretching sheet Int. J. Non-Linear Mech. 29 1992 929 936
19. A. Pantokratoras Flow adjacent to a stretching permeable sheet in a DarcyBrinkman porous medium Transp. Porous Media 80 2009 223 227
20. C.Y. Wang The three-dimensional flow due to a stretching flat surface Phys. Fluids 27 1984 1915 1917 (Pubitemid 14623872)
21. N. Afzal, A. Badaruddin, and A.A. Elgarvi Momentum and transport on a continuous flat surface moving in a parallel stream Int. J. Heat Mass Transfer 36 1993 3399 3403 (Pubitemid 23711527)
22. N. Afzal Momentum transfer on power law stretching plate with free stream pressure gradient Int. J. Eng. Sci. 41 2003 1197 1207
23. 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. 44 2006 730 737
24. A. Ishak, R. Nazar, and I. Pop Flow and heat transfer characteristics on a moving flat plate in a parallel stream with constant surface heat flux Heat Mass Transfer 45 2009 563 567
25. M. Miklavčič, and C.Y. Wang Viscous flow due to a shrinking sheet Q. Appl. Math 46 2006 283 290 (Pubitemid 44295911)
26. S. Goldstein On backward boundary layers and flow in converging passages J. Fluid Mech. 21 1965 33 45
27. T. Fang Boundary layer flow over a shrinking sheet with powerlaw velocity Int. J. Heat Mass Transfer 51 2008 5838 5843
28. T. Fang, W. Liang, and C.F. Lee A new solution branch for the Blasius equation - a shrinking sheet problem Comput. Math. Appl. 56 2008 3088 3095
29. T. Fang, and J. Zhang Closed-form exact solutions of MHD viscous flow over a shrinking sheet Commun. Nonlinear Sci. Numer. Simul. 14 2009 2853 2857
30. T. Fang, J. Zhang, and S. Yao Viscous flow over an unsteady shrinking sheet with mass transfer Chin. Phys. Lett. 26 2009 014703
31. T. Fang, J. Zhang, and S. Yao Slip MHD viscous flow over a stretching sheet - an exact solution Commun. Nonlinear Sci. Numer. Simulat. 14 2009 3731 3737
32. C.Y. Wang Stagnation flow towards a shrinking sheet Int. J. Non-Linear Mech. 43 2008 377 382
33. T. Hayat, Z. Abbas, T. Javed, and M. Sajud Three-dimensional rotating flow induced by a shrinking sheet for suction Chaos Solitons Fractals 39 2009 1615 1626
34. Y.Y. Lok, A. Ishak, and I. Pop MHD stagnation-point flow towards a shrinking sheet Int. J. Numer. Methods Heat Fluid Flow 21 2011 61 72
35. T. Fang, and J. Zhang Heat transfer over a shrinking sheet - an analytical solution Acta Mechanica 209 2010 325 343