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)
HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet. (English) Zbl 1221.65282
Summary: We describe the stagnation point flow of a viscous fluid towards a stretching sheet. The complete analytical solution of the boundary layer equation has been obtained by homotopy analysis method (HAM). The solutions are compared with the available numerical results obtained by {\it R. Nazar} et al. [Int. J. Eng. Sci. 42, No. 11--12, 1241--1253 (2004; Zbl 1211.76042)] and a good agreement is found. The convergence region is also computed which shows the validity of the HAM solution.

65M99Numerical methods for IVP of PDE
76D10Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids)
Full Text: DOI
[1] Sakiadis, B. C.: Boundary-layer behavior on continuous solid surfaces, Aiche J 7, 26-28 (1961)
[2] Sakiadis, B. C.: Boundary layer behavior on continuous solid surface. II. boundary layer on a continuous flat surface, Aiche J 7, 221-225 (1961)
[3] Vajravelu, K.: Viscous flow over a nonlinearly stretching sheet, Appl math comput 124, 281-288 (2001) · Zbl 1162.76335 · doi:10.1016/S0096-3003(00)00062-X
[4] Vajravelu, K.; Cannon, J. R.: Fluid flow over a nonlinearly stretching sheet, Appl math comput 181, 609-618 (2006) · Zbl 1143.76024 · doi:10.1016/j.amc.2005.08.051
[5] Cortell, R.: Viscous flow and heat transfer over a nonlinearly stretching sheet, Appl math comput 184, 864-873 (2007) · Zbl 1112.76022 · doi:10.1016/j.amc.2006.06.077
[6] Cortell, R.: Effects of dissipation and radiation on the thermal boundary layer over a non-linearly stretching sheet, Phys lett A 372, 631-636 (2008) · Zbl 1217.76028 · doi:10.1016/j.physleta.2007.08.005
[7] Chaim, T. C.: Hydromagnetic flow over a surface stretching with a power law velocity, Int J eng sci 33, 429-435 (1995) · Zbl 0899.76375 · doi:10.1016/0020-7225(94)00066-S
[8] Hayat, T.; Abbas, Z.; Javed, T.: Mixed convection flow of a micropolar fluid over a non-linearly stretching sheet, Phys lett A 372, 637-647 (2008) · Zbl 1217.76014 · doi:10.1016/j.physleta.2007.08.006
[9] Hayat, T.; Hussain, Q.; Javed, T.: The modified decomposition method and PadĂ© approximants for the MHD flow over a non-linear stretching sheet, Non-linear anal real world appl 10, 966-973 (2009) · Zbl 1167.76385 · doi:10.1016/j.nonrwa.2007.11.020
[10] Navier, M.: Memoire sur LES lois du mouvement des fluides, Mem acad sci inst France 6, 389-440 (1823)
[11] 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 42, 241-1253 (2004) · Zbl 1211.76042 · doi:10.1016/j.ijengsci.2003.12.002
[12] Yian, L. Y.; Amin, N.; Filip, D.; Pop, I.: Mixed convection flow near a non-orthogonal stagnation point towards a stretching vertical plate, Int J heat mass transfer 50, 4855-4863 (2007) · Zbl 1183.76870 · doi:10.1016/j.ijheatmasstransfer.2007.02.034
[13] Wang, C. Y.: Natural convection on a vertical radially stretching sheet, Math anal appl 332, 877-883 (2007) · Zbl 1117.35068 · doi:10.1016/j.jmaa.2006.11.006
[14] Wang, C. Y.: Stagnation flow towards a shrinking sheet, Int J non-linear mech 43, 377-382 (2008)
[15] Liao, S. J.: Beyond perturbation, (2003)
[16] Wang, J.; Chen, J. Kang; Liao, S.: An explicit solution of the large deformation of a cantilever beam under point load at the free tip, J comput appl math 212, 320-330 (2008) · Zbl 1128.74026 · doi:10.1016/j.cam.2006.12.009
[17] Xu, Hang; Liao, S. J.: Dual solutions of boundary layer flow over an upstream moving plate, Commun non-linear sci numer simul 13, 350-358 (2008) · Zbl 1131.35066 · doi:10.1016/j.cnsns.2006.04.008
[18] Liao, S. J.: An explicit totally analytic solution of laminar viscous flow over a semi-infinite flat plate, Commun non-linear sci numer simul 3, 53-57 (1998) · Zbl 0922.34012 · doi:10.1016/S1007-5704(98)90061-2
[19] Liao, S. J.: Comparison between homotopy analysis method and homotopy perturbation method, Appl math comput 169, 1186-1194 (2005) · Zbl 1082.65534 · doi:10.1016/j.amc.2004.10.058
[20] Abbasbandy, S.: The application of homotopy analysis method to nonlinear equations arising in heat transfer, Phys lett A 360, 109-113 (2006) · Zbl 1236.80010
[21] Liao, S. J.; Cheung, K. F.: Homotopy analysis of nonlinear progressive waves in deep water, J eng math 145, 105-116 (2003) · Zbl 1112.76316 · doi:10.1023/A:1022189509293
[22] Liao, S. J.: An analytic solution of unsteady boundary layer flows caused by an impulsive stretching plate, Commun non-linear sci numer simul 11, 326-339 (2006) · Zbl 1078.76022 · doi:10.1016/j.cnsns.2004.09.004
[23] Liao, S. J.: A new branch of solutions of boundary layer flows over an impermeable stretching plate, Int J heat mass transfer 48, 2529-2539 (2005) · Zbl 1189.76142 · doi:10.1016/j.ijheatmasstransfer.2005.01.005
[24] Hayat, T.; Sajid, M.; Ayub, M.: On explicit analytic solution for MHD pipe flow of a fourth grade fluid, Commun non-linear sci numer simul 13, 745-751 (2008) · Zbl 1221.76221 · doi:10.1016/j.cnsns.2006.07.009
[25] Hayat, T.; Ellahi, E.; Ariel, P. D.; Asghar, S.: Homotopy solution for the channel flow of a third grade fluid, Non-linear dyn 45, 55-64 (2006) · Zbl 1100.76005 · doi:10.1007/s11071-005-9015-7
[26] Hayat, T.; Khan, M.; Ayub, M.: On the explicit analytic solutions of an Oldroyd 6-constant fluid, Int J eng sci 42, 123-135 (2004) · Zbl 1211.76009 · doi:10.1016/S0020-7225(03)00281-7
[27] Sajid, M.; Hayat, T.; Asghar, S.: Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet, Int J heat mass transfer 50, 1723-1736 (2007) · Zbl 1140.76042 · doi:10.1016/j.ijheatmasstransfer.2006.10.011
[28] Mahapatra, T. R.; Gupta, A. S.: Heat transfer in stagnation point flow towards a stretching sheet, Int J heat mass transfer 38, 517-521 (2002)