Unsteady three-dimensional boundary layer flow due to a stretching surface in a micropolar fluid

International Journal for Numerical Methods in Fluids

Volumn 68, Issue 12, 2012, Pages 1561-1573

  Ahmad, K ^a   Nazar, R ^b   Ishak, A ^b   Pop, I ^c  

^a INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA   (Malaysia)

^b UNIVERSITI KEBANGSAAN MALAYSIA   (Malaysia)

^c BABE BOLYAI UNIVERSITY   (Romania)

Author keywords

Boundary layer; Micropolar fluid; Numerical solution; Stretching surface; Unsteady three dimensional flow

Indexed keywords

FINITE-DIFFERENCE SCHEME; GOVERNING PARAMETERS; MATERIAL PARAMETER; MICROPOLAR FLUID; MICROPOLAR FLUIDS; NUMERICAL SOLUTION; SKIN FRICTION COEFFICIENT; SMOOTH TRANSITIONS; SPATIAL REGIONS; STEADY-STATE FLOWS; STRETCHING PARAMETERS; STRETCHING SURFACE; THREE-DIMENSIONAL BOUNDARY LAYERS; UNSTEADY THREE-DIMENSIONAL FLOW; UNSTEADY-STATE FLOW;

BOUNDARY LAYER FLOW; BOUNDARY LAYERS; PARTIAL DIFFERENTIAL EQUATIONS; THREE DIMENSIONAL;

SURFACES;

EID: 84858698047     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.2543     Document Type: Article

References (45)

1. Stokes GG. On the effect of the inertial friction of fluids on the motion of pendulums. Transactions of the Cambridge Philosophical Society 1851; 9:8-106.
2. Rayleigh L. On the motion of solid bodies through viscous liquid. Philosophical Magazine 1911; 21:697-711.
3. Stuart JT. Recent Research on Unsteady Boundary Layers. Laval University Press: Quebec, 1972; 1-59.
4. Riley N. Unsteady laminar boundary layers. SIAM Review 1975; 17:274-297.
5. Riley N. Unsteady viscous flows. Science Progress (Oxford) 1990; 74:361-377.
6. Tani I. History of boundary layer theory. Annual Review of Fluid Mechanics 1977; 9:87-111.
7. McCroskey WJ. Some current research in unsteady fluid dynamics-the 1976 Freeman scholar lecture. ASME Journal of Fluids Engineering 1977; 99:8-38.
8. Telionis DP. Review-unsteady boundary layers, separated and attached. ASME Journal of Fluids Engineering 1979; 101:29-43.
9. Telionis DP. Unsteady Viscous Flows. Springer: Berlin, 1981.
10. Gersten K, Herwig H. Stromungsmechanik. Vieweg: Wisbaden, 1992.
11. Schlichting H, Gersten K. Boundary Layer Theory (9th edn). Springer: Berlin, 2000.
12. Eringen AC. Theory of micropolar fluids. Journal of Mathematics and Mechanics 1966; 16:1-18.
13. Eringen AC. Theory of thermomicropolar fluids. Journal of Mathematical Analysis and Applications 1972; 38:480-496.
14. Ariman T, Turk MA, Sylvester ND. Microcontinuum fluid mechanics-a review. International Journal of Engineering Science 1973; 11:905-930.
15. Ariman T, Turk MA, Sylvester ND. Application of microcontinuum fluid mechanics. International Journal of Engineering Science 1974; 12:273-293.
16. Peddieson J, McNitt RP. Boundary layer theory for a micropolar fluid. Recent Advances in Engineering Science, vol. 5. Gordon and Breach: London, 1970; 405-476.
17. Lukaszewicz G. Micropolar Fluids: Theory and Application. Basel: Birkhäser, 1999.
18. Eringen AC. Microcontinuum Field Theories II: Fluent Media. Springer: New York, 2001.
19. Crane LJ. Flow past a stretching plate. Zeitschrift fur Angewandte Mathematik und Physik 1970; 21:645-647.
20. Wang CY. The three-dimensional flow due to a stretching flat surface. Physics of Fluids 1984; 27:1915-1917.
21. Wang CY. Flow across a stretching surface. Journal of Applied Mechanics 1991; 58:579-580.
22. Lakshmisha KN, Venkateswaran S, Nath G. Three-dimensional unsteady flow with heat and mass transfer over a continous stretching surface. Journal of Heat Transfer 1988; 110:590-595.
23. Rajeswari V, Kumari M, Nath G. Unsteady three-dimensional boundary layer flow due to a stretching surface. Acta Mechanica 1993; 98:123-141.
24. Pop I, Na TY. Unsteady flow past a stretching sheet. Mechanics Research Communications 1996; 23:413-422.
25. Takhar HS, Nath G. Unsteady flow over a stretching surface with a magnetic field in a rotating fluid. Zeitschrift für Angewandte Mathematik und Physik 1998; 49:989-1001.
26. Nazar R, Amin N, Filip D, Pop I. Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. International Journal of Engineering Science 2004; 42:1241-1253.
27. Ishak A, Nazar R, Pop I. Unsteady mixed convection boundary layer flow due to a stretching vertical surface. Arabian Journal for Science and Engineering 2006; 31:165-182.
28. Wang CY, Du Q, Miklavcic M, Chang CC. Impulsive stretching of a surface in a viscous fluid. SIAM Journal on Applied Mathematics 1997; 57:1-14.
29. Ishak A, Nazar R, Pop I. Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature. Nonlinear Analysis: Real World Applications 2009; 10:2909-2913.
30. Ali FM, Nazar R, Arifin NM, Ishak A, Pop I. Unsteady flow across a stretching surface. International Communications in Heat and Mass Transfer 2010; 37:476-479.
31. Chamkha AJ, Jaradat M, Pop I. Three-dimensional micropolar flow due to a stretching flat surface. International Journal of Fluid Mechanics Research 2003; 30:357-366.
32. Surma Devi CD, Takhar HS, Nath G. Unsteady three-dimensional boundary layer flow due to a stretching surface. International Journal of Heat and Mass Transfer 1986; 29:1996-1999.
33. Takhar HS, Chamkha AJ, Nath G. Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface. Acta Mechanica 2001; 146:59-71.
34. Mizukami A. Nonsteady shear flow of micropolar fluids. International Journal of Engineering Science 1981; 19:75-82.
35. Khonsari MM, Brewe DE. On the performance of finite journal bearings lubricated with micropolar fluids. Tribology Transactions 1989; 32:155-160.
36. Papautsky I, Brazzle J, Ameel T, Frazier AB. Laminar fluid behavior in microchannels using micropolar fluid theory. Sensors and Actuators 1999; 73:101-108.
37. Rees DAS, Bassom AP. The Blasius boundary-layer flow of a micropolar fluid. International Journal of Engineering Science 1996; 34:113-124.
38. Guram GS, Smith C. Stagnation flows of micropolar fluids with strong and weak interactions. Computers and Mathematics with Applications 1980; 6:213-233.
39. Jena SK, Mathur MN. Similarity solutions for laminar free convection flow of a thermomicropolar fluid past a nonisothermal flat plate. International Journal of Engineering Science 1981; 19:1431-1439.
40. Ahmadi G. Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate. International Journal of Engineering Science 1976; 14:639-646.
41. Peddieson J. An application of the micropolar fluid model to the calculation of turbulent shear flow. International Journal of Engineering Science 1972; 10:23-32.
42. Rees DAS, Pop I. Free convection boundary-layer flow of a micropolar fluid from a vertical flat plate. IMA Journal of Applied Mathematics 1998; 61:179-197.
43. Hassanien IA, Gorla RSR. Combined forced and free convection in stagnation flows of micropolar fluids over vertical non-isothermal surfaces. International Journal of Engineering Science 1990; 28:783-792.
44. Kelson NA, Desseaux A. Effect of surface conditions on flow of a micropolar fluid driven by a porous stretching sheet. International Journal of Engineering Science 2001; 39:1881-1897.
45. Cebeci T, Bradshaw P. Physical and Computational Aspects of Convective Heat Transfer. Springer: New York, 1984.