Analytic solution for heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects

Communications in Nonlinear Science and Numerical Simulation

Volumn 14, Issue 11, 2009, Pages 3867-3878

  Khani, F ^a   Farmany, A ^b   Ahmadzadeh Raji, M ^c   Aziz, Abdul ^d   Samadi, F ^e  

^a Bakhtar Institute of Higher Education Iran   (Iran)

^b ISLAMIC AZAD UNIVERSITY   (Iran)

^c RAZI UNIVERSITY   (Iran)

^d GONZAGA UNIVERSITY   (United States)

^e PAYAME NOOR UNIVERSITY   (Iran)

Author keywords

Heat transfer; Homotopy analysis method; Non Darcy porous media; Non Newtonian; Viscoelastic fluid

Indexed keywords

BOUNDARY CONDITIONS; FLOW MEASUREMENT; HEAT CONVECTION; MOMENTUM; NON NEWTONIAN FLOW; NON NEWTONIAN LIQUIDS; POROUS MATERIALS; POROUS PLATES; RHEOLOGY; THERMODYNAMIC PROPERTIES; VISCOELASTICITY; VISCOUS FLOW;

ANALYSIS METHOD; CONSERVATION EQUATIONS; HEAT CONSERVATION; HOMOTOPY ANALYSE METHOD; HOMOTOPY ANALYSIS; MOMENTUM EQUATION; NON-DARCY POROUS MEDIA; NON-NEWTONIAN; VIS-COELASTIC FLUIDS; VISCO-ELASTIC FLUID;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 67349106428     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2009.01.031     Document Type: Article

References (36)

1. Akyildiz F.T. A note on the flow of a third-grade between heated parallel plates. Int J Nonlinear Mech 36 (2001) 349-352
2. Shenoy A.V. Non-Newtonian fluid heat transfer in porous media. Adv Heat Transfer 24 (1994) 101-190
3. Chen T., and Chen C.K. Free convection of non-Newtonian fluids along a vertical plate embedded in a porous medium. ASME J Heat Transfer 110 (1988) 257-260
4. Victor T. The flow of a viscoelastic fluid between two parallel plates with heat transfer. Int J Eng Sci 29 (1991) 1545-1556
5. Hayat T., Ahmed N., and Sajid M. Analytic solution for MHD flow of a third order fluid in a porous channel. J Comput Appl Math 214 2 (2008) 572-582
6. Sajid M., and Hayat T. The application of homotopy analysis method to thin film flows of a third order fluid. Chaos Solitons Fract 38 2 (2008) 506-515
7. Tigoiu V. The flow of a third grade fluid between two coaxial rotating discs with heat transfer. Rev Roumaine Math Pures Appl 40 (1995) 541-558
8. Massoudi M., and Christie I. Effects of variable viscosity and viscous dissipation on the flow of a 3rd grade fluid in a pipe. Int J Nonlinear Mech 30 (1995) 687-699
9. Passerini A., and Videman J.H. Decay in time of kinetic energy of second- and third-grade fluids in unbounded domains. In: Marques M.M., and Rodrigues J.F. (Eds). Trends in applications of mathematics to mechanics (Pitman monographs and surveys in pure and applied mathematics) (1995), Longman, Harlow, UK 195-208
10. Sequeira A., and Videman J.H. Global existence of classical solutions for the equations of third grade fluids. J Math Phys Sci 29 (1995) 47-69
11. Busuioc V., and Iftmie D. Global existence and uniqueness of solutions for the equations of third grade fluids. Int J Nonlinear Mech 39 (2004) 1-12
12. Takhar SH., Bhargava R., Rawat S., Bg T.A., and Bg O.A. Finite element modeling of laminar flow of a third grade fluid in a Darcy Forchheimer porous medium suction effects. Int J Appl Mech Eng 12 (2007) 215-233
13. Bég O.A., Takhar H.S., Bhargava R., Rawat S., and Prasad V.R. Numerical study of heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects. Phys Scr 77 (2008) 10.1088/0031-8949/77/06/065402
14. Liao SJ. The proposed homotopy analysis technique for the solution of nonlinear problems. PhD thesis. Shanghai Jiao Tong University; 1992.
15. Liao S.J. An explicit, totally analytic approximate solution for Blasius viscous flow problems. Int J Nonlinear Mech 34 (1999) 759-778
16. Liao S.J. Beyond perturbation: introduction to the homotopy analysis method (2003), Chapman & Hall/CRC Press, Boca Raton
17. Liao S.J. A general approach to get series solution of non-similarity boundary-layer flows. Commun Nonlinear Sci Numer Simul 14 5 (2009) 2144-2159
18. Liao S.J. On the homotopy analysis method for nonlinear problems. Appl Math Comput 147 (2004) 499-513
19. Liao S.J. A new branch of solutions of boundary-layer flows over an impermeable stretched plate. Int J Heat Mass Transfer 48 (2005) 2529-2539
20. Tan Y., and Abbasbandy S. Homotopy analysis method for quadratic Riccati differential equation. Commun Nonlinear Sci Numer Simul 13 3 (2008) 539-546
21. Molabahrami A., and Khani F. The homotopy analysis method to solve the Burgers-Huxley equation. Nonlinear Anal Real World Appl 10 2 (2009) 589-600
22. Sajid M., Ahmad I., Hayat T., and Ayub M. Unsteady flow and heat transfer of a second grade fluid over a stretching sheet. Commun Nonlinear Sci Numer Simul 14 1 (2009) 96-108
23. Khani F., Ahmadzadeh Raji M., and Hamedi Nejad H. Analytical solutions and efficiency of the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient. Commun Nonlinear Sci Numer Simul 14 (2009) 3327-3338
24. Song L., and Zhang H.Q. Application of homotopy analysis method to fractional KdV Burgers Kuramoto equation. Phys Lett A 367 (2007) 88-94
25. Khani F., Ahmadzadeh Raji M., and Hamedi-Nezhad S. A series solution of the fin problem with a temperature-dependent thermal conductivity. Commun Nonlinear Sci Numer Simul 14 7 (2009) 3007-3017
26. Liao S.J. Notes on the homotopy analysis method: some definitions and theorems. Commun Nonlinear Sci Numer Simul 14 4 (2009) 983-997
27. Hayat T., Abbas Z., and Pop I. Mixed convection in the stagnation point flow adjacent to a vertical surface in a viscoelastic fluid. Int J Heat Mass Transfer 51 (2008) 3200-3206
28. Hayat T., and Abbas Z. Heat transfer analysis on the MHD flow of a second grade fluid in a channel with porous medium. Chaos Solitons Fract 38 2 (2008) 556-567
29. Hayat T., Saif S., and Abbas Z. The influence of heat transfer in an MHD second grade fluid film over an unsteady stretching sheet. Phys Lett A 372 30 (2008) 5037-5045
30. Fosdick R.L., and Rajagopal K.R. Thermodynamics and stability of fluids of third grade. Proc R Soc A 369 (1980) 351-377
31. Hayat T., Ellahi R., and Asghar S. The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: an analytical solution. Commun Nonlinear Sci Numer Simul 12 (2007) 300-313
32. Asghar S., Mohyuddin M.R., Ariel P.D., and Hayat T. On Stokes' problem for the flow of a third-grade fluid induced by a variable shear stress. Can J Phys 84 (2006) 945-958
33. Hayat T., and Ali N. Peristaltically induced motion of a MHD third grade fluid in a deformable tube. Physica A 370 (2006) 225-239
34. Hayat T., and Kara A.H. Couette flow of a third-grade fluid with variable magnetic field. Math Comput Model 43 (2006) 132-137
35. Hayat T., Khan M., Siddiqui A.M., and Asghar S. Transient flows of a second grade fluid. Int J Nonlinear Mech 39 (2004) 1621-1633
36. Liao S.J. Comparison between the homotopy analysis method and homotopy perturbation method. Appl Math Comput 169 (2005) 1186-1194