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 effects of variable viscosity and thermal conductivity on a thin film flow over a shrinking/stretching sheet. (English) Zbl 1222.76014
Summary: The effects of variable viscosity and thermal conductivity on the flow and heat transfer in a laminar liquid film on a horizontal shrinking/stretching sheet are analyzed. The similarity transformation reduces the time independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The resulting five-parameter problem is solved by the homotopy perturbation method. The results are presented graphically to interpret various physical parameters appearing in the problem.
MSC:
76A20Thin fluid films (fluid mechanics)
65L99Numerical methods for ODE
References:
[1]Crane, L. J.: Flow past a stretching plate, Z. angew. Math. phys. 21, 645-647 (1970)
[2]Andersson, H. I.; Aarseth, J. B.; Dandapat, B. S.: Heat transfer in a liquid film on an unsteady stretching surface, Int. J. Heat mass transfer 43, 69-74 (2000) · Zbl 1042.76507 · doi:10.1016/S0017-9310(99)00123-4
[3]Wang, C.; Pop, I.: Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method, J. non-Newton fluid mech. 138, 161-172 (2006) · Zbl 1195.76132 · doi:10.1016/j.jnnfm.2006.05.011
[4]Liu, I. C.; Anderson, H. I.: Heat transfer in a liquid film on an unsteady stretching sheet, Int. J. Therm. sci. 47, 766-772 (2008)
[5]Mahmood, M.; Asghar, S.; Hossain, A. M.: Squeezed flow and heat transfer over a porous surface for viscous fluid, J. heat mass transfer 44, 165-173 (2007)
[6]Wang, C.: Analytic solutions for a liquid film on an unsteady stretching surface, Heat mass transfer 42, 759-766 (2006)
[7]Dandapat, B. S.; Santra, B.; Vajravelu, K.: The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet, Int. J. Heat mass transfer 50, 991-996 (2007) · Zbl 1124.80317 · doi:10.1016/j.ijheatmasstransfer.2006.08.007
[8]Anderson, H. I.; Aarseth, J. B.; Dandapat, B. S.: Heat transfer in a liquid film on an unsteady stretching surface, Int. J. Heat mass transfer 43, 69-74 (2000) · Zbl 1042.76507 · doi:10.1016/S0017-9310(99)00123-4
[9]Siddiqui, A. M.; Mahmood, R.; Ghori, Q. K.: Thin film of a third grade fluid on a moving belt by he’s homotopy perturbation method, Int. J. Nonlinear sci. Numer. simul. 7, No. 1, 7-14 (2006)
[10]Xu, L.: He’s homotopy perturbation method for a boundary layer equation in unbounded domain, Comput. math. Appl. 54, 1067-1070 (2007)
[11]Raftari, B.; Yıldırım, A.: The application of homotopy perturbation method for MHD flows of UCM fluids above porous stretching sheets, Comput. math. Appl. 59, 3328-3337 (2010) · Zbl 1198.65148 · doi:10.1016/j.camwa.2010.03.018
[12]Raftari, B.; Mohyud-Din, S. T.; Yıldırım, A.: Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method, Sci. China phys. Mech. astron. (2010)
[13]Ariel, P. D.: The three-dimensional flow past a stretching sheet and the homotopy perturbation method, Comput. math. Appl. 54, 920-925 (2007) · Zbl 1138.76029 · doi:10.1016/j.camwa.2006.12.066
[14]Ariel, P. D.: Extended homotopy perturbation method and computation of flow past a stretching sheet, Comput. math. Appl. 58, 2402-2409 (2009) · Zbl 1189.65156 · doi:10.1016/j.camwa.2009.03.013
[15]He, J. H.: Homotopy perturbation technique, Comput. math. Appl. mech. Eng. 178, 257-292 (1999)
[16]He, J. H.: Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlinear sci. Numer. simul. 6, 207-208 (2005)
[17]He, J. H.: Homotopy perturbation method for solving boundary value problems, Phys. lett. A 350, 87-88 (2006) · Zbl 1195.65207 · doi:10.1016/j.physleta.2005.10.005
[18]He, J. H.: Recent developments of the homotopy perturbation method, Topol. methods nonlinear anal. 31, 205-209 (2008) · Zbl 1159.34333
[19]Siddiqui, A. M.; Rana, M. A.; Irum, S.: Application of homotopy perturbation and numerical methods to the unsteady squeezing MHD flow of a second grade fluid between circular plates, Int. J. Nonlinear sci. Numer. simul. 10, No. 6, 699-709 (2009)
[20]Hesameddini, E.; Latifizadeh, H.: An optimal choice of initial solutions in the homotopy perturbation method, Int. J. Nonlinear sci. Numer. simul. 10, 1389-1398 (2009)
[21]Shadloo, M. S.; Kimiaeifar, A.: Application of HPM to find analytical solution for MHD flows of viscoelastic fluids in converging/diverging channels, J. mech. Eng. sci. 225, No. 2, 347-353 (2011)
[22]Ariel, P. D.: Homotopy perturbation method and the natural convection flow of a third grade fluid through a circular tube, Nonlinear sci. Lett. A 1, No. 2, 43-52 (2010)
[23]Gupta, Praveen Kumar; Singh, Mithilesh: Homotopy perturbation method for fractional fornberg–Whitham equation, Comput. math. Appl. 61, No. 2, 250-254 (2011) · Zbl 1211.65138 · doi:10.1016/j.camwa.2010.10.045
[24]Chun, Changbum; Sakthivel, Rathinasamy: Homotopy perturbation technique for solving two-point boundary value problems-comparison with other methods, Comput. phys. Commun. 181, 1021-1024 (2010) · Zbl 1216.65094 · doi:10.1016/j.cpc.2010.02.007
[25]Khan, Y.; Faraz, N.; Yıldırım, A.; Wu, Q.: A series solution of the long porous slider, Tribol. trans. 54, 187-191 (2011)
[26]Jalaal, M.; Nejad, M. G.; Jalili, P.; Esmaeilpour, M.; Bararnia, H.; Ghasemi, E.; Soleimani, Soheil; Ganji, D. D.; Moghimi, S. M.: Homotopy perturbation method for motion of a spherical solid particle in plane Couette fluid flow, Comput. math. Appl. 61, 2267-2270 (2011) · Zbl 1219.76036 · doi:10.1016/j.camwa.2010.09.042
[27]Moghimi, S. M.; Ganji, D. D.; Bararnia, H.; Hosseini, M.; Jalaal, M.: Homotopy perturbation method for nonlinear MHD Jeffery–Hamel problem, Comput. math. Appl. 61, 2213-2216 (2011) · Zbl 1219.76038 · doi:10.1016/j.camwa.2010.09.018
[28]Khan, Najeeb Alam; Khan, Nasir-Uddin; Ayaz, Muhammad; Mahmood, Amir: Analytical methods for solving the time-fractional Swift–Hohenberg (S–H) equation, Comput. math. Appl. 61, 2182-2185 (2011) · Zbl 1219.65144 · doi:10.1016/j.camwa.2010.09.009
[29]Khan, Y.: An effective modification of the Laplace decomposition method for nonlinear equations, Int. J. Nonlinear sci. Numer. simul. 10, No. 11–12, 1373-1376 (2009)
[30]Khan, Y.; Faraz, N.: Application of modified Laplace decomposition method for solving boundary layer equation, J. King saud univ. Sci. 23, 115-119 (2011)
[31]Khan, Y.; Faraz, N.: A new approach to differential difference equations, J. adv. Res. differ. Equ. 2, No. 2, 1-12 (2010)
[32]Khan, Y.; Austin, F.: Application of the Laplace decomposition method to nonlinear homogeneous and non-homogenous advection equations, Z. naturforsch. 65a, 849-853 (2010)
[33]Khan, Y.; Wu, Q.: Homotopy perturbation transform method for nonlinear equations using he’s polynomials, Comput. math. Appl. 61, 1963-1967 (2011) · Zbl 1219.65119 · doi:10.1016/j.camwa.2010.08.022
[34]Faraz, N.; Khan, Y.; Yildirim, A.: Analytical approach to two-dimensional viscous flow with a shrinking sheet via variational iteration algorithm-II, J. King saud univ. Sci. 23, No. 1, 77-81 (2011)
[35]He, J. H.; Wu, G. C.; Austin, F.: The variational iteration method which should be followed, Nonlinear sci. Lett. A 1, No. 1, 1-30 (2010)
[36]Faraz, N.: Study of the effects of the Reynolds number on circular porous slider via variational iteration algorithm-II, Comput. math. Appl. 61, 1991-1994 (2011)
[37]Ma, W. X.; Fuchssteiner, B.: Explicit and exact solutions to a Kolmogorov–petrovskii–piskunov equation, Int. J. Nonlinear mech. 31, 329-338 (1996) · Zbl 0863.35106 · doi:10.1016/0020-7462(95)00064-X
[38]Ma, W. X.; Lee, J. H.: A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation, Chaos solitons fractals 42, 1356-1363 (2009) · Zbl 1198.35231 · doi:10.1016/j.chaos.2009.03.043
[39]Ma, W. X.; Fan, E.: Linear superposition principle applying to Hirota bilinear equations, Comput. math. Appl. 61, 950-959 (2011) · Zbl 1217.35164 · doi:10.1016/j.camwa.2010.12.043