zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
The application of homotopy analysis method to solve nonlinear differential equation governing Jeffery-Hamel flow. (English) Zbl 1221.76056
Summary: The Jeffery–Hamel flow is studied and its nonlinear ordinary differential equation is solved through the homotopy analysis method (HAM). The obtained solution in comparison with the numerical ones represents a remarkable accuracy. The results also indicate that HAM can provide us with a convenient way to control and adjust the convergence region.
MSC:
76D05Navier-Stokes equations (fluid dynamics)
76M25Other numerical methods (fluid mechanics)
References:
[1]Jeffery, G. B.: The two-dimensional steady motion of a viscous fluid, Philos mag 6, 455-465 (1915) · Zbl 45.1088.01
[2]Hamel, G.: Spiralförmige bewgungen zäher flüssigkeiten, Jahresbericht der deutschen math vereinigung 25, 34-60 (1916) · Zbl 46.1255.01
[3]Rosenhead, L.: The steady two-dimensional radial flow of viscous fluid between two inclined plane walls, Proc royal soc A 175, No. 963, 436-467 (1940) · Zbl 0025.37501 · doi:10.1098/rspa.1940.0068
[4]Batchelor, K.: An introduction to fluid dynamics, (1967) · Zbl 0152.44402
[5]Reza M. Sadri, Channel entrance flow, PhD thesis, Department of Mechanical Engineering, the University of Western Ontario, 1997.
[6]Sobeyi, J.; Drazin, P. G.: Bifurcations of two-dimensional channel flows, J fluid mech 171, 263-287 (1986) · Zbl 0609.76050 · doi:10.1017/S0022112086001441
[7]Hamadiche, M.; Scott, J.; Jeandel, D.: Temporal stability of Jeffery – Hamel flow, J fluid mech 268, 71-88 (1994) · Zbl 0809.76039 · doi:10.1017/S0022112094001266
[8]Fraenkel, L. E.: Laminar flow in symmetrical channels with slightly curved walls. I: on the Jeffery – Hamel solutions for flow between plane walls, Proc R soc lond A 267, 119-138 (1962) · Zbl 0104.42403 · doi:10.1098/rspa.1962.0087
[9]Makinde, O. D.; Mhone, P. Y.: Hermite – Padé approximation approach to MHD Jeffery – Hamel flows, Appl math comput 181, 966-972 (2006) · Zbl 1102.76049 · doi:10.1016/j.amc.2006.02.018
[10]Schlichting, Hermann: Boundary-layer theory, (2000)
[11]Rathy, R. K.: An introduction to fluid dynamics, (1976)
[12]Mcalpine, A.; Drazin, P. G.: On the spatio-temporal development of small perturbations of Jeffery – Hamel flows, Fluid dyn res 22, 123-138 (1998) · Zbl 1051.76554 · doi:10.1016/S0169-5983(97)00049-X
[13]Liao, SJ. The proposed homotopy analysis technique for the solution of nonlinear problems, PhD thesis, Shanghai Jiao Tong University, 1992.
[14]Liao, S. J.: Beyond perturbation: introduction to homotopy analysis method, (2003)
[15]Abbasbandy, S.: The application of homotopy analysis method to nonlinear equations arising in heat transfer, Phys lett A 360, 109-113 (2006)
[16]Hayat, T.; Sajid, M.: On analytic solution for thin film flow of a forth grade fluid down a vertical cylinder, Phys lett A 361, 316-322 (2007) · Zbl 1170.76307 · doi:10.1016/j.physleta.2006.09.060
[17]Sajid M, Hayat T, Asghar S. Comparison between the HAM and HPM solutions of tin film flows of non-Newtonian fluid on a moving belt, Nonlinear Dyn, in press. · Zbl 1181.76031 · doi:10.1007/s11071-006-9140-y
[18]Hayat, T.; Khan, M.; Ayub, M.: On the explicit analytical solution 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
[19]Hayat, T.; Khan, M.; Asghar, S.: Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid, Acta mech 168, 213-232 (2004) · Zbl 1063.76108 · doi:10.1007/s00707-004-0085-2
[20]Hayat, T.; Khan, M.; Asghar, S.: Magnetohydrodynamic flow of an Oldroyd 6-constant fluid, Appl math comput 155, 417-425 (2004) · Zbl 1126.76388 · doi:10.1016/S0096-3003(03)00787-2
[21]Ayub, M.; Rasheed, A.; Hayat, T.: Exact flow of a third grade fluid past a porous plate using homotopy analysis method, Int J eng sci 41, 2091-2103 (2003) · Zbl 1211.76076 · doi:10.1016/S0020-7225(03)00207-6
[22]Hayat, T.; Khan, M.; Ayub, M.: Couette and Poiseuille flows of an Oldroyd 6-constant fluid with magnetic field, J math anal appl 298, 225-244 (2004) · Zbl 1067.35074 · doi:10.1016/j.jmaa.2004.05.011
[23]Hayat, T.; Abbas, Z.; Sajid, M.: Series solution for the upper-convected Maxwell fluid over a porous stretching plate, Phys lett A 358, 396-403 (2006) · Zbl 1142.76511 · doi:10.1016/j.physleta.2006.04.117
[24]Sajid, M.; Hayat, T.; Asghar, S.: On the analytic solution of the steady flow of a fourth grade fluid, Phys lett A 355, 18-26 (2006)
[25]Hayat, T.; Masood, Khan; Sajid, M.; Ayub, M.: Steady flow of an Oldroyd 8-constant fluid between coaxial cylinders in a porous medium, J porous media 9, 709-722 (2006)
[26]Hayat, T.; Abbas, Z.; Sajid, M.; Asghar, S.: The influence of radiation on MHD flow of second grade fluid, Int J heat mass transfer 50, 931-941 (2007) · Zbl 1124.80325 · doi:10.1016/j.ijheatmasstransfer.2006.08.014
[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]Sajid, M.; Hayat, T.; Asghar, S.: Non-similar solution for the axisymmetric flow of a third-grade fluid over a radially stretching sheet, Acta mech 189, 193-205 (2007) · Zbl 1117.76006 · doi:10.1007/s00707-006-0430-8
[29]Abbas, Z.; Sajid, M.; Hayat, T.: MHD boundary-layer flow of an upper-convected Maxwell fluid in a porous channel, Theoret comput fluid dyn 20, 229-238 (2006) · Zbl 1109.76065 · doi:10.1007/s00162-006-0025-y
[30]Liao, S. J.: On the homotopy analysis method for nonlinear problems, Appl math comput 147, 499-513 (2004) · Zbl 1086.35005 · doi:10.1016/S0096-3003(02)00790-7
[31]Hang, Xu; Liao, S. J.: Dual solutions of boundary layer flow over an upstream moving plate, J commun nonlin sci numer simul 13, 350-358 (2008) · Zbl 1131.35066 · doi:10.1016/j.cnsns.2006.04.008
[32]Cheng, Yang; Liao, S. J.: On the explicit, purely analytic solution of von Kármán swirling viscous flow, J commun nonlin sci numer simul 11, 83-93 (2006) · Zbl 1075.35059 · doi:10.1016/j.cnsns.2004.05.006
[33]Chun, Wang; Ioan, Pop: Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method, J non-Newtonian fluid mech 138, 161-172 (2006) · Zbl 1195.76132 · doi:10.1016/j.jnnfm.2006.05.011
[34]Liao, S. J.; Campo, A.: Analytic solutions of the temperature distribution in Blasius viscous flow problems, J fluid mech 453, 411-425 (2002) · Zbl 1007.76014 · doi:10.1017/S0022112001007169
[35]Liao, S. J.: On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluid over a stretching sheet, J fluid mech 488, 189-212 (2003) · Zbl 1063.76671 · doi:10.1017/S0022112003004865
[36]Liao, S. J.: An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude, Int J non-linear mech 38, 1173-1183 (2003)
[37]Liao, S. J.; Pop, I.: Explicit analytic solution for similarity boundary layer equations, Int J heat mass transfer, 47-75 (2004) · Zbl 1045.76008 · doi:10.1016/S0017-9310(03)00405-8
[38]Liao, S. J.: An analytical approximation of the drag coefficient for the viscous flow past a sphere, Int J non-linear mech 37, 1-18 (2002) · Zbl 1116.76335 · doi:10.1016/S0020-7462(00)00092-5
[39]Liao, S. J.: An explicit analytic solution to the Thomas – Fermi equation, Appl math comput 144, 495-506 (2003) · Zbl 1034.34005 · doi:10.1016/S0096-3003(02)00423-X
[40]Liao, S. J.; Cheung, K. F.: Homotopy analysis of nonlinear progressive waves in deep water, J eng math 45, 105-116 (2003) · Zbl 1112.76316 · doi:10.1023/A:1022189509293
[41]Liao, S. J.; Chwang, A. T.: Application of homotopy analysis method in non-linear oscillations, Trans ASME J appl mech 65, 914-922 (1998)
[42]MATLAB®nbsp; 6 – The Language of Technical Computing, 2006.