Study of a third grade non-Newtonian fluid flow between two parallel plates using the multi-step differential transform method

Computers and Mathematics with Applications

Volumn 62, Issue 8, 2011, Pages 2871-2891

  Keimanesh, M ^a   Rashidi, M M ^a   Chamkha, Ali J ^b   Jafari, R ^c  

^a BU ALI SINA UNIVERSITY   (Iran)

^b KUWAIT UNIVERSITY   (Kuwait)

^c UNIVERSITÉ DE SHERBROOKE   (Canada)

Author keywords

Couette flow; CouettePoiseuille flow; Multi step differential transform method (MDTM); Non Newtonian fluid; Poiseuille flow; Third grade fluid

Indexed keywords

COUETTE FLOWS; COUETTE-POISEUILLE FLOW; MULTI-STEP; NON-NEWTONIAN FLUIDS; POISEUILLE FLOW; THIRD GRADE FLUIDS;

DIFFERENTIAL EQUATIONS; FLOW MEASUREMENT; FLOW STRUCTURE; FLUIDS; NON NEWTONIAN LIQUIDS; NONLINEAR EQUATIONS; NUMERICAL METHODS; PROBLEM SOLVING; RHEOLOGY; VELOCITY MEASUREMENT; VISCOUS FLOW;

NON NEWTONIAN FLOW;

EID: 80053341138     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.07.054     Document Type: Article

References (20)

1. Zaid M. Odibat, Cyrille Bertelle, M.A. Aziz-Alaoui, and Gérard H.E. Duchamp A multi-step differential transform method and application to non-chaotic or chaotic systems Computers and Mathematics with Applications 59 2010 1462 1472
2. A.K. Alomari A new analytic solution for fractional chaotic dynamical systems using the differential transform method Computers and Mathematics with Applications 61 2011 2528 2534
3. R.P. Chhabra, and J.F. Richardson Non-Newtonian Fluid Behaviour second ed. Non-Newtonian Flow and Applied Rheology 2008 1 55
4. K.R. Rajagopal On the stability of third-grade fluids Architect Mechanical 32 6 1980 867
5. R.L. Fosdick, and K.R. Rajagopal Thermodynamics and stability of fluids of third grade Proceedings of the Royal Society of LondonSeries A 77 1980 339 351
6. J.K. Zhou Differential Transformation and its Applications for Electrical Circuits 1986 Huazhong Univ. Press Wuhan, China (in Chinese)
7. M.M. Rashidi, M. Keimanesh, Using differential transform method and the Padé approximant for solving MHD flow in a laminar liquid film from a horizontal stretching surface, Mathematical Problem in Engineering (2010) doi:10.1155/2010/491319.
8. M.M. Rashidi, M. Keimanesh, O. Anwar Bég, and T.K. Hung Magnetohydrodynamic biorheological transport phenomena in a porous medium: a simulation of magnetic blood flow control and filtration International Journal for Numerical Methods in Biomedical Engineering 2010 10.1002/cnm.1420
9. M.M. Rashidi The modified differential transform method for solving MHD boundary-layer equations Computer Physics Communications 180 2009 2210 2217
10. A.M. Siddiqui, M. Hameed, B.M. Siddiqui, and Q.K. Ghori Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid Communications in Nonlinear Science and Numerical Simulation 15 2010 2388 2399
11. I.H. Abdel-Halim Hassan Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems Chaos Solitons and Fractals 36 2008 53 65 (Pubitemid 47576633)
12. D.W. Zingg, and T.T. Chisholm RungeKutta methods for linear ordinary differential equations Applied Numerical Mathematics 31 1999 227 238 (Pubitemid 30507856)
13. I. Hashim, and M.S.H. Chowdhury Adaptation of homotopy-perturbation method for numericanalytic solution of system of ODEs Physics Letters A 372 2008 470 481
14. S.J. Liao Beyond Perturbation: Introduction to the Homotopy Analysis Method 2003 Chapman and Hall/CRC Press Boca Raton
15. M.M. Rashidi, and S. Dinarvand Purely analytic approximate solutions for steady three-dimensional problem of condensation film on inclined rotating disk by homotopy analysis method Nonlinear Analysis. Real World Applications 10 2009 2346 2356
16. M.M. Rashidi, S.A. Mohimanian pour, and S. Abbasbandy Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation Communications in Nonlinear Science and Numerical Simulation 16 2011 1874 1889
17. H. Jafari, A. Golbabai, S. Seifi, and K. Sayevand Homotopy analysis method for solving multi-term linear and nonlinear diffusion-wave equations of fractional order Computers and Mathematics with Applications 59 2010 1337 1344
18. M.M. Rashidi, and H. Shahmohamadi Analytical solution of three-dimensional NavierStokes equations for the flow near an infinite rotating disk Communications in Nonlinear Science and Numerical Simulation 14 7 2009 2999 3006
19. Shuiping Yang, Aiguo Xiao, and Hong Su Convergence of the variational iteration method for solving multi-order fractional differential equations Computers and Mathematics with Applications 60 2010 2871 2879
20. A.S.V. Ravi Kanth, and K. Aruna He's variational iteration method for treating nonlinear singular boundary value problems Computers and Mathematics with Applications 60 2010 821 829