A novel analytical solution of mixed convection about an inclined flat plate embedded in a porous medium using the DTM-Padé

International Journal of Thermal Sciences

Volumn 49, Issue 12, 2010, Pages 2405-2412

  Rashidi, Mohammad Mehdi ^a   Laraqi, Najib ^b   Sadri, Seyed Majid ^a  

^a BU ALI SINA UNIVERSITY   (Iran)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Differential transform method; Mixed convection flow; Nonlinear differential equations; Pad approximant; Porous medium

Indexed keywords

APPROXIMANTS; DIFFERENTIAL TRANSFORM METHOD; MIXED CONVECTION FLOW; NONLINEAR DIFFERENTIAL EQUATION; POROUS MEDIUM;

FLOW MEASUREMENT; MATHEMATICAL TRANSFORMATIONS; MIXED CONVECTION; ORDINARY DIFFERENTIAL EQUATIONS; POROUS MATERIALS; PROBLEM SOLVING; RUNGE KUTTA METHODS;

NONLINEAR EQUATIONS;

EID: 77957848016     PISSN: 12900729     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijthermalsci.2010.07.005     Document Type: Article

References (43)

1. A.H. Nayfeh Introduction to Perturbation Techniques 1979 Wiley
2. R.H. Rand, and D. Armbruster Perturbation Methods, Bifurcation Theory and Computer Algebraic 1987 Springer
3. J. Biazar, E. Babolian, and R. Islam Solution of a system of Volterra integral equations of the first kind by Adomian method Journal of Applied Mathematics and Computation 139 2003 249 258
4. H. Sadeghi Goghary, Sh Javadi, and E. Babolian Restarted Adomian method for system of nonlinear Volterra integral equations Journal of Applied Mathematics and Computation 161 2005 745 751 (Pubitemid 41663484)
5. J. Biazar, H. Ghazvini, and M. Eslami He's homotopy perturbation method for systems of integro-differential equations Chaos Solitons & Fractals 39 2007 1253 1258
6. E. Yusufoglu (Agadjanov) An efficient algorithm for solving integro-differential equations system Journal of Applied Mathematics and Computation 192 2007 51 55 (Pubitemid 47362293)
7. M.M. Rashidi, G. Domairry, and S. Dinarvand Approximate solutions for the Burger and regularized long wave equations by means of the Homotopy analysis method Communications in Nonlinear and Numerical Simulation 14 2009 708 717
8. 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
9. S. Dinarvand, A. Doosthoseini, E. Doosthoseini, and M.M. Rashidi Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces Nonlinear Analysis: Real World Applications 11 2009 1159 1169
10. S. Dinarvand, and M.M. Rashidi A reliable treatment of homotopy analysis method for two-dimensional viscous flow in a rectangular domain bounded by two moving porous walls Nonlinear Analysis: Real World Applications 11 2010 1502 1512
11. S.Q. Wang, and J.H. He Variational iteration method for solving integro-differential equations Journal of Physics 367 2007 188 191
12. M.M. Rashidi, and H. Shahmohamadi Analytical solution of three-dimensional Navier-Stokes equations for the flow near an infinite rotating disk Communications in Nonlinear and Numerical Simulation 14 2009 2999 3006
13. J.H. He Homotopy perturbation technique Journal of Applied Mathematics and Computation 178 1999 257 262
14. J.H. He A coupling method of a homotopy technique and a perturbation technique for non-linear problems International Journal of Non-Linear Mechanics 35 2000 37 43
15. J.H. He Homotopy perturbation method: a new nonlinear analytical technique Journal of Applied Mathematics and Computation 135 2003 73 79
16. J.H. He Comparison of homotopy perturbation method and homotopy analysis method Journal of Applied Mathematics and Computation 156 2004 527 539
17. S.J. Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, PhD thesis, Shanghai Jiao Tong University (1992).
18. S.J. Liao Beyond Perturbation: Introduction to the Homotopy Analysis Method 2003 Chapman & Hall/CRC Press Boca Raton
19. J.K. Zhou Differential Transformation and Its Applications for Electrical Circuits 1986 Huazhong University Press Wuhan, China (in Chinese)
20. C.K. Chen, and S.H. Ho Solving partial differential equations by two dimensional differential transform method Applied Mathematics and Computation 106 1999 171 179
21. F. Ayaz Solutions of the systems of differential equations by differential transform method Applied Mathematics and Computation 147 2004 547 567
22. I.H. Abdel-Halim Hassan Comparison differential transformation technique with Adomian decomposition method for linear and nonlinear initial value problems Chaos Solitons & Fractals 36 2008 53 65
23. M.J. Jang, C.L. Chen, and Y.C. Liu Analysis of the response of a strongly nonlinear damped system using a differential transformation technique Applied Mathematics and Computation 88 2-3 1997 137 151
24. C.L. Chen, Y.C. Liu, and J. Optim Solution of two-boundary-value problems using the differential transformation method Theory Applications 99 1998 23 35 (Pubitemid 128355906)
25. M.J. Jang, C.L. Chen, and Y.C. Liu On solving the initial-value problems using the differential transformation method Applied Mathematics and Computation 115 2-3 2000 145 160
26. S. Momani, and Z. Odibat Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation Physics Letters A 370 5-6 2007 379 387
27. Z. Odibat, and S. Momani Approximate solutions for boundary value problems of time-fractional wave equation Applied Mathematics and Computation 181 2006 1351 1358 (Pubitemid 44528059)
28. Z. Odibat, and S. Momani Numerical methods for nonlinear partial differential equations of fractional order Applied Mathematical Modelling 32 1 2008 28 39 (Pubitemid 47355246)
29. B.L. Kuo Heat transfer analysis for the Falkner-Skan wedge flow by the differential transformation method International Journal of Heat and Mass Transfer 48 23-24 2005 5036 5046 (Pubitemid 41360550)
30. B.L. Kuo Application of the differential transformation method to the solutions of the free convection problem Applied Mathematics and Computation 165 1 2005 63 79 (Pubitemid 40537170)
31. Y. Keskin, A. Kurnaz, M.E. Kiris, and G. Oturanc Approximate solutions of generalized pantograph equations by the differential transform method International Journal of Nonlinear Sciences and Numerical Simulation 8 2007 159 164
32. Y. Keskin, and G. Oturanc The reduced differential transform method: a new approach to fractional partial differential equations Nonlinear Science Letters A 1 2010 207 217
33. M.M. Rashidi, Differential Transform Method for Solving Two Dimensional Viscous Flow, in: International Conference on Applied Physics and Mathematics (2009).
34. M.M. Rashidi, Differential Transform Method for MHD Boundary-Layer Equations: Combination of the DTM and the Padé Approximant, in: International Conference on Applied Physics and Mathematics (2009).
35. M.M. Rashidi, E. Erfani, A Novel Analytical Solution of the Thermal Boundary-Layer Over a Flat Plate with a Convective Surface Boundary Condition Using DTM-Padé, in: International Conference on Applied Physics and Mathematics (2009).
36. A.S. Furumoto, A systematic program for geothermal exploration on the island of Hawaii, in: Presented at the 45th Annual International Meeting of Society of Exploration and Geophysics, Denver, 12-16 October (1975).
37. R.A. Wooding Convection in a saturated porous medium at large Rayleigh number or Peclet number Journal of Fluid Mechanics 15 1963 527 544
38. D.A. Nield Onset of thermohaline convection in a porous medium Water Resource 4 1968 553 560
39. R.A. Wooding Rayleigh instability of a thermal boundary layer in flow through a porous medium Journal of Fluid Mechanics 9 1960 183 192
40. P. Cheng Free convection about a vertical flat plate embedded in a porous medium with application to heat transfer from aq dike Journal of Geophysics 82 1977 2040 2044
41. D.A. Nield, and A. Bejan Convection in Porous Media 2006 Springer
42. G.A. Baker, Peter Graves-Morris, and Peter A. Carruthers Padé Approximants Part I: Basic Theory 1981 Addison-Wesley Publishing Company
43. M.M. Rashidi The modified differential transform method for solving MHD boundary-layer equations Computer Physics Communications 180 2009 2210 2217