Dual solutions in boundary layer stagnation-point flow and mass transfer with chemical reaction past a stretching/shrinking sheet

International Communications in Heat and Mass Transfer

Volumn 38, Issue 7, 2011, Pages 917-922

  Bhattacharyya, Krishnendu ^a  

^a UNIVERSITY OF BURDWAN   (India)

Author keywords

Boundary layer; Chemical reaction; Dual solutions; Mass transfer; Stagnation point flow; Stretching shrinking sheet

Indexed keywords

CONCENTRATION BOUNDARY LAYER; DUAL SOLUTIONS; FIRST ORDER CHEMICAL REACTIONS; GOVERNING EQUATIONS; SCHMIDT NUMBERS; SELF-SIMILAR; SHOOTING METHODS; SIMILARITY TRANSFORMATION; STAGNATION-POINT FLOW; VELOCITY RATIO;

CHEMICAL ANALYSIS; CHEMICAL REACTIONS; GROUNDWATER POLLUTION; MASS TRANSFER; ORDINARY DIFFERENTIAL EQUATIONS;

BOUNDARY LAYERS;

EID: 79959934401     PISSN: 07351933     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.icheatmasstransfer.2011.04.020     Document Type: Article

References (46)

1. Crane L.J. Flow past a stretching plate. ZAMP 1970, 21:645-647.
2. Pavlov K.B. Magnetohydrodynamic flow of an incompressible viscous fluid caused by the deformation of a plane surface. Magn. Gidrod. 1974, 10:146-148.
3. Gupta P.S., Gupta A.S. Heat and mass transfer on a stretching sheet with suction and blowing. Can. J. Chem. Eng. 1977, 55:744-746.
4. Rajagopal K.R., Na Y.T., Gupta A.S. Flow of a viscoelastic fluid over a stretching sheet. Rheol. Acta 1984, 23:213-215.
5. Sankara K.K., Watson L.T. Micropolar flow past a stretching sheet. ZAMP 1985, 36:845-853.
6. Chen C.K., Char M.I. Heat transfer of a continuous stretching surface with suction or blowing. J. Math. Anal. Appl. 1988, 135:568-580.
7. Vajravelu K., Rollins D. Heat transfer in electrically conducting fluid over a stretching sheet. Int. J. Nonlinear Mech. 1992, 27:265-277.
8. Chamkha A.J. Transient hydromagnetic three-dimensional natural convection from an inclined stretching permeable surface. Chem. Eng. J. 2000, 76:159-168.
9. Hiemenz K. Die Grenzschicht an einem in den gleichformingen Flussigkeits-strom einge-tauchten graden Kreiszylinder. Dingler's Poly. J. 1911, 326:321-324.
10. Chiam T.C. Stagnation-point flow towards a stretching plate. J. Phys. Soc. Jpn. 1994, 63:2443-2444.
11. Mahapatra T.R., Gupta A.S. Magnetohydrodynamic stagnation-point flow towards a stretching sheet. Acta Mech. 2001, 152:191-196.
12. Mahapatra T.R., Gupta A.S. Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Trans. 2002, 38:517-521.
13. Nazar R., Amin N., Filip D., Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. Int. J. Eng. Sci. 2004, 42:1241-1253.
14. Ishak A., Nazar R., Pop I. Mixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet. Meccanica 2006, 41:509-518.
15. Layek G.C., Mukhopadhyay S., Samad Sk.A. Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. Int. Commun. Heat Mass Trans. 2007, 34:347-356.
16. Ishak A., Jafar K., Nazar R., Pop I. MHD stagnation point flow towards a stretching sheet. Physica A 2009, 388:3377-3383.
17. Nadeem S., Hussain A., Khan M. HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. Commun. Nonlinear Sci. Numer. Simulat. 2010, 15:475-481.
18. Ishak A., Nazar R., Arifin N.M., Pop I. Dual solutions in magnetohydrodynamic mixed convection flow near a stagnation-point on a vertical surface. ASME J. Heat Trans. 2007, 129:1212-1216.
19. Ishak A., Nazar R., Arifin N.M., Pop I. Dual solutions in mixed convection flow near a stagnation point on a vertical porous plate. Int. J. Thermal Sci. 2008, 47:417-422.
20. Ishak A., Nazar R., Pop I. Dual solutions in mixed convection flow near a stagnation point on a vertical surface in a porous medium. Int. J. Heat Mass Trans. 2008, 51:1150-1155.
21. Wang C.Y. Liquid film on an unsteady stretching sheet. Q. Appl. Math. 1990, 48:601-610.
22. Miklavčič M., Wang C.Y. Viscous flow due a shrinking sheet. Q. Appl. Math. 2006, 64:283-290.
23. Hayat T., Abbas Z., Sajid M. On the analytic solution of magnetohydrodynamic flow of a second grade fluid over a shrinking sheet. ASME J. Appl. Mech. 2007, 74:1165-1171.
24. Hayat T., Javed T., Sajid M. Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface. Phys. Lett. A 2008, 372:3264-3273.
25. Fang T., Zhang J. Closed-form exact solution of MHD viscous flow over a shrinking sheet. Commun. Nonlinear Sci. Numer. Simulat. 2009, 14:2853-2857.
26. Noor N.F.M., Kechil S.A., Hashim I. Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet. Commun. Nonlinear Sci. Numer. Simulat. 2010, 15:144-148.
27. Fang T., Yao S., Zhang J., Aziz A. Viscous flow over a shrinking sheet with a second order slip flow model. Commun. Nonlinear Sci. Numer. Simulat. 2010, 15:1831-1842.
28. Fang T. Boundary layer flow over a shrinking sheet with power law velocity. Int. J. Heat Mass Trans. 2008, 51:5838-5843.
29. Fang T., Liang W., Lee C.F. A new solution branch for the Blasius equation-a shrinking sheet problem. Comput. Math. Appl. 2008, 56:3088-3095.
30. Fang T., Zhang J., Yao S. Viscous flow over an unsteady shrinking sheet with mass transfer. Chin. Phys. Lett. 2009, 26:014703.
31. Fang T., Zhang J., Yao S. Slip magnetohydrodynamic viscous flow over a permeable shrinking sheet. Chin. Phys. Lett. 2010, 27:124702.
32. Fang T., Zhang J. Thermal boundary layers over a shrinking sheet: an analytical solution. Acta Mech. 2010, 209:325-343.
33. Yao S., Fang T., Zhong Y. Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Commun. Nonlinear Sci. Numer. Simulat. 2011, 16:752-760.
34. Wang C.Y. Stagnation flow towards a shrinking sheet. Int. J. Nonlinear Mech. 2008, 43:377-382.
35. Ishak A., Lok Y.Y., Pop I. Stagnation-point flow over a shrinking sheet in a micropolar fluid. Chem. Eng. Commun. 2010, 197:1417-1427.
36. Bhattacharyya K., Layek G.C. Effects of suction/blowing on steady boundary layer stagnation-point flow and heat transfer towards a shrinking sheet with thermal radiation. Int. J. Heat Mass Trans. 2011, 54:302-307.
37. Bhattacharyya K., Mukhopadhyay S., Layek G.C. Slip effects on boundary layer stagnation-point flow and heat transfer towards a shrinking sheet. Int. J. Heat Mass Trans. 2011, 54:308-313.
38. Lok Y.Y., Ishak A., Pop I. MHD stagnation-point flow towards a shrinking sheet. Int. J. Numer. Meth. Heat Fluid Flow 2011, 21:61-72.
39. Chambre P.L., Young J.D. On diffusion of a chemically reactive species in a laminar boundary layer flow. Phys. Fluids 1958, 1:48-54.
40. Andersson H.I., Hansen O.R., Holmedal B. Diffusion of a chemically reactive species from a stretching sheet. Int. J. Heat Mass Trans. 1994, 37:659-664.
41. Afify A. MHD free convective flow and mass transfer over a stretching sheet with chemical reaction. Heat Mass Trans. 2004, 40:495-500.
42. Akyildiz F.T., Bellout H., Vajravelu K. Diffusion of chemically reactive species in a porous medium over a stretching sheet. J. Math. Anal. Appl. 2006, 320:322-339.
43. Cortell R. Toward an understanding of the motion and mass transfer with chemically reactive species for two classes of viscoelastic fluid over a porous stretching sheet. Chem. Eng. Process. 2007, 46:982-989.
44. Mansour M.A., El-Anssary N.F., Aly A.M. Effects of chemical reaction and thermal stratification on MHD free convective heat and mass transfer over a vertical stretching surface embedded in a porous media considering Soret and Dufour numbers. Chem. Eng. J. 2008, 145:340-345.
45. Hayat T., Abbas Z., Ali N. MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species. Phys. Lett. A 2008, 372:4698-4704.
46. Bhattacharyya K., Layek G.C. Chemically reactive solute distribution in MHD boundary layer flow over a permeable stretching sheet with suction or blowing. Chem. Eng. Commun. 2010, 197:1527-1540.