zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Unsteady boundary layer flow in the region of the stagnation point on a stretching sheet. (English) Zbl 1211.76042
Summary: Unsteady two-dimensional stagnation point flow of an incompressible viscous fluid over a flat deformable sheet is studied when the flow is started impulsively from rest and the sheet is suddenly stretched in its own plane with a velocity proportional to the distance from the stagnation point. After a similarity transformation, the unsteady boundary layer equation is solved numerically using the Keller-box method for the whole transient from $\tau =0$ to the steady state $\tau \rightarrow \infty $. Also, a complete analysis is made of the governing equation at $\tau =0$, the initial unsteady flow, at large times $\tau =\infty $, the steady state flow, and a series solution valid at small times $\tau\ll 1$). It is found that there is a smooth transition from the initial unsteady state flow (small time solution) to the final steady state flow (large time solution).

76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
Full Text: DOI
[1] Vleggaar, I.: Laminar boundary-layer behaviour on continuous accelerating surfaces. Chem. engng. Sci. 32, 1517-1525 (1977)
[2] Wang, C. Y.: Exact solutions of the unsteady Navier--Stokes equations. Appl. mech. Rev. 42, 9269-9282 (1989)
[3] Wang, C. Y.: Exact solutions of the steady-state Navier--Stokes equations. Ann. rev. Fluid mech. 23, 159-177 (1991)
[4] Crane, L. I.: Flow past a stretching plate. J. appl. Mech. phys. (ZAMP) 21, 645-657 (1970)
[5] Brady, J. F.; Acrivos, A.: Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier--Stokes equations with reverse flow. J. fluid mech. 112, 127-150 (1981) · Zbl 0491.76037
[6] Kuiken, H. K.: On boundary layers in fluid mechanics that decay algebraically along stretches of wall that are not vanishingly small. IMA J. Appl. math. 27, 387-405 (1981) · Zbl 0472.76045
[7] Banks, W. H. H.: Similarity solutions of the boundary-layer equations for a stretching wall. J. méc. Théoret. appl. 2, 375-392 (1983) · Zbl 0538.76039
[8] Banks, W. H. H.; Zaturska, M. B.: Eigen solutions in boundary-layer flow adjacent to a stretching wall. IMA J. Appl. math. 36, 263-273 (1986) · Zbl 0619.76011
[9] Magyari, E.; Keller, B.: Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls. Eur. J. Mech. B-fluids 19, 109-122 (2000) · Zbl 0976.76021
[10] Chiam, T. C.: Stagnation-point flow towards a stretching plate. J. phys. Soc. jpn. 63, 2443-2444 (1994)
[11] Mahapatra, T. R.; Gupta, A. S.: Heat transfer in stagnation point flow towards a stretching sheet. Heat mass transfer 38, 517-521 (2002)
[12] Klemp, J. B.; Acrivos, A. A.: A method for integrating the boundary-layer equations through a region of reverse flow. J. fluid mech. 53, 177-199 (1972) · Zbl 0242.76019
[13] Klemp, J. B.; Acrivos, A. A.: A moving-wall boundary layer with reverse flow. J. fluid mech. 76, 363-381 (1976) · Zbl 0344.76026
[14] Hussaini, M. Y.; Lakin, W. D.; Nachman, A.: On similarity solutions of a boundary layer problem with an upstream moving wall. SIAM J. Appl. math. 47, 699-709 (1987) · Zbl 0634.76034
[15] Mcleod, J. B.; Rajagopal, K. R.: On the uniqueness of flow of a Navier--Stokes fluid due to a stretching boundary. Arch. ratl. Mech. anal. 98, 385-393 (1987) · Zbl 0631.76021
[16] Riley, N.; Weidman, P. D.: Multiple solutions of the Falkner--Skan equation for flow past a stretching boundary. SIAM J. Appl. math. 49, 1350-1358 (1989) · Zbl 0682.76026
[17] Troy, W. C.; Overman, W. A.; Ermentrout, G. B.: Uniqueness of flow of a second-order fluid past a stretching sheet. Quart. appl. Math. 45, 753-755 (1987) · Zbl 0613.76006
[18] Pop, I.; Na, T. -Y.: Unsteady flow past a stretching sheet. Mech. res. Comm. 23, 413-422 (1996) · Zbl 0893.76017
[19] Wang, C. Y.; Du, G.; Miklavi, M.; Chang, C. C.: Impulsive stretching of a surface in a viscous fluid. SIAM J. Appl. math. 57, 1-14 (1997) · Zbl 0869.76013
[20] Lakshmisha, K. N.; Venkateswaran, S.; Nath, G.: Three-dimensional unsteady flow with heat and mass transfer over a continuous stretching surface. J. heat transfer 110, 590-595 (1988)
[21] Nazar, R.; Amin, N.; Pop, I.: Unsteady boundary layer flow due to a stretching surface in a rotating fluid. Mech. res. Comm. 31, 121-128 (2004) · Zbl 1053.76017
[22] Williams, J. C.; Rhyne, T. H.: Boundary layer development on a wedge impulsively set into motion. SIAM J. Appl. math. 38, 215-224 (1980) · Zbl 0443.76039
[23] Seshadri, R.; Sreeshylan, N.; Nath, G.: Unsteady mixed convection flow in the stagnation region of a heated vertical plate due to impulsive motion. Int. J. Heat mass transfer 45, 1345-1352 (2002) · Zbl 1121.76394
[24] Cebeci, T.; Bradshaw, P.: Physical and computational aspects of convective heat transfer. (1988) · Zbl 0702.76003
[25] Hiemenz, K.: Die grenzschicht an einem in den gleichenformigen flüssigkeitsstrom eingetauchten geraden kreiszilinder. Dingles polytech. J. 326, 321-324 (1911)
[26] Lok, Y. Y.; Phang, P.; Amin, N.; Pop, I.: Unsteady boundary layer flow of a micropolar fluid near the forward stagnation point of a plane surface. Int. J. Engng. sci. 41, 173-186 (2003) · Zbl 1211.76041