Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid

Computers and Fluids

Volumn 47, Issue 1, 2011, Pages 16-21

  Yacob, Nor Azizah ^a   Ishak, Anuar ^b,c   Pop, Ioan ^d  

^a UNIVERSITI TEKNOLOGI MARA   (Malaysia)

^b UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

^c UNIVERSITY OF MALAYA   (Malaysia)

^d BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Boundary layer; Fluid mechanics; Melting; Micropolar fluid; Shrinking sheet; Stretching sheet

Indexed keywords

DUAL SOLUTIONS; HEAT TRANSFER CHARACTERISTICS; MELTING HEAT TRANSFER; MELTING PROCESS; MICROPOLAR FLUIDS; NONLINEAR ORDINARY DIFFERENTIAL EQUATION; RUNGE-KUTTA FEHLBERG METHOD; SHOOTING TECHNIQUE; SHRINKING SHEET; STAGNATION-POINT FLOW; STRETCHING SHEET;

BOUNDARY LAYERS; CONTACTS (FLUID MECHANICS); FLUID MECHANICS; HEAT TRANSFER; MATHEMATICAL MODELS; MELTING; ORDINARY DIFFERENTIAL EQUATIONS; RUNGE KUTTA METHODS; SHRINKAGE;

FLUIDS;

EID: 79957619935     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2011.01.040     Document Type: Article

References (53)

1. Sparrow E.M., Abraham J.P. Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid. Int J Heat Mass Transf 2005, 48:3047-3056.
2. Sakiadis B.C. Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J 1961, 7:26-28.
3. Tsou F.K., Sparrow E.M., Goldstein R.J. Flow and heat transfer in the boundary layer on a continuous moving surface. Int J Heat Mass Transf 1967, 10:219-235.
4. Crane L.J. Flow past a stretching plate. Z Angew Math Phys 1970, 21:645-647.
5. Dutta B.K., Roy P., Gupta A.S. Temperature field in flow over a stretching sheet with uniform heat flux. Int Commun Heat Mass Transf 1985, 12:89-94.
6. Grubka L.J., Bobba K.M. Heat transfer characteristics of a continuous, stretching surface with variable temperature. ASME J Heat Transf 1985, 107:248-250.
7. 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.
8. Ishak A., Nazar R., Pop I. Boundary layer on a moving wall with suction and injection. Chin Phys Lett 2007, 24:2274-2276.
9. Ishak A., Nazar R., Pop I. Boundary-layer flow of a micropolar fluid on a continuous moving or fixed surface. Can J Phys 2006, 84:399-410.
10. Ishak A., Nazar R., Pop I. Heat transfer over a stretching surface with variable heat flux in micropolar fluids. Phys Lett A 2008, 372:559-561.
11. Ishak A., Nazar R., Pop I. Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat Mass Transf 2008, 44:921-927.
12. Ishak A., Nazar R., Pop I. Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature. Nonlinear Anal Real World Appl 2009, 10:2909-2913.
13. Xu H., Liao S.J. Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet. Comp Math Appl 2009, 57:1425-1431.
14. Miklavčič M., Wang C.Y. Viscous flow due to a shrinking sheet. Quart Appl Math 2006, 64:283-290.
15. Fang T., Liang W., Lee C.F. A new solution branch for the Blasius equation - a shrinking sheet problem. Comp Math Appl 2008, 56:3088-3095.
16. Fang T., Zhang J., Yao S. Viscous flow over an unsteady shrinking sheet with mass transfer. Chin Phys Lett 2009, 26:014703.
17. 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.
18. Yao B., Chen J. A new analytical solution branch for the Blasius equation with a shrinking sheet. Appl Math Comp 2009, 215:1146-1153.
19. Wang C.Y. Stagnation flow towards a shrinking sheet. Int J Non-Linear Mech 2008, 43:377-382.
20. 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.
21. 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.
22. Hayat T., Abbas Z., Javed T., Sajid M. Three-dimensional rotating flow induced by a shrinking sheet for suction. Chaos Solitons Fract 2009, 39:1615-1626.
23. 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.
24. Bachok N., Ishak A., Pop I. Unsteady three-dimensional boundary layer flow due to a permeable shrinking sheet. Appl Math Mech - Engl Ed 2010, 31:1421-1428.
25. Goldstein S. On backward boundary layers and flow in converging passages. J Fluid Mech 1965, 21:33-45.
26. Eringen A.C. Theory of micropolar fluids. J Math Mech 1966, 16:1-18.
27. Eringen A.C. Theory of thermomicrofluids. J Math Anal Appl 1972, 38:480-496.
28. Kolpashchikov V.L., Migun N.P., Prokhorenko P.P. Experimental determination of material micropolar fluid constants. Int J Eng Sci 1983, 21:405-411.
29. Łukaszewicz G. Micropolar fluids: theory and application 1999, Birkhäuser, Basel.
30. Eringen A.C. Microcontinuum field theories. II: fluent media 2001, Springer, New York.
31. Heruska M.W., Watson L.T., Sankara K.K. Micropolar flow past a porous stretching sheet. Comput Fluids 1986, 14:117-129.
32. Ashraf M., Kamal M.A., Syed K.S. Numerical study of asymmetric laminar flow of micropolar fluids in a porous channel. Comput Fluids 2009, 38:1895-1902.
33. Ishak A., Nazar R., Pop I. Stagnation flow of a micropolar fluid towards a vertical permeable surface. Int Commun Heat Mass Transf 2008, 35:276-281.
34. Magyari E., Pop I., Valkó P.P. Stokes' first problem for micropolar fluids. Fluid Dyn Res 2010, 42:025503.
35. Cheng W.T., Lin C.H. Melting effect on mixed convective heat transfer with aiding and opposing external flows from the vertical plate in a liquid-saturated porous medium. Int J Heat Mass Transf 2007, 50:3026-3034.
36. Tien C., Yen Y.C. The effect of melting on forced convection heat transfer. J Appl Meteorol 1965, 4:523-527.
37. Epstein M., Cho D.H. Melting heat transfer in steady laminar flow over a flat plate. J Heat Transf 1976, 98:531-533.
38. Cheng W.T., Lin C.H. Transient mixed convective heat transfer with melting effect from the vertical plate in a liquid saturated porous medium. Int J Eng Sci 2006, 44:1023-1036.
39. Ishak A., Nazar R., Bachok N., Pop I. Melting heat transfer in steady laminar flow over a moving surface. Heat Mass Transf 2010, 46:463-468.
40. Guram G.S., Smith A.C. Stagnation flows of micropolar fluids with strong and weak interactions. Comp Math Appl 1980, 6:213-233.
41. Jena S.K., Mathur M.N. Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a non-isothermal vertical flat plate. Int J Eng Sci 1981, 19:1431-1439.
42. Ahmadi G. Self-similar solution of imcompressible micropolar boundary layer flow over a semi-infinite plate. Int J Eng Sci 1976, 14:639-646.
43. Peddieson J. An application of the micropolar fluid model to the calculation of turbulent shear flow. Int J Eng Sci 1972, 10:23-32.
44. Yücel A. Mixed convection in micropolar fluid flow over a horizontal plate with surface mass transfer. Int J Eng Sci 1989, 27:1593-1602.
45. Rosenhead L. Laminar boundary layers 1963, Oxford University Press.
46. Yih K.A. Uniform suction/blowing effect on forced convection about a wedge: uniform heat flux. Acta Mech 1998, 128:173-181.
47. Ishak A., Nazar R., Pop I. Falkner-Skan equation for flow past a moving wedge with suction or injection. J Appl Math Computing 2007, 25:67-83.
48. Merkin J.H. On dual solutions occurring in mixed convection in a porous medium. J Eng Math 1985, 20:171-179.
49. Weidman P.D., Kubitschek D.G., Davis A.M.J. The effect of transpiration on self-similar boundary layer flow over moving surfaces. Int J Eng Sci 2006, 44:730-737.
50. Merrill K., Beauchesne M., Previte J., Paullet J., Weidman P. Final steady flow near a stagnation point on a vertical surface in a porous medium. Int J Heat Mass Transf 2006, 49:4681-4686.
51. Paullet J., Weidman P. Analysis of stagnation point flow toward a stretching sheet. Int J Non-Linear Mech 2007, 42:1084-1091.
52. Harris S.D., Ingham D.B., Pop I. Mixed convection boundary-layer flow near the stagnation point on a vertical surface in a porous medium: Brinkman model with slip. Transp Porous Med 2009, 77:267-285.
53. Postelnicu A., Pop I. Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge. Appl Math Comp 2011, 217:4359-4368.