Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium

Journal of the Taiwan Institute of Chemical Engineers

Volumn 41, Issue 1, 2010, Pages 22-28

  Ziabakhsh, Z ^a   Domairry, G ^a   Bararnia, H ^a   Babazadeh, H ^a  

^a BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Flow and diffusion of chemically reactive species; Homotopy analysis method (HAM); Nonlinearly stretching sheet; Porous medium

Indexed keywords

HOMOTOPY ANALYSIS METHODS; POROUS MEDIUM; REACTIVE SPECIES; STRETCHING SHEET;

DIFFERENTIAL EQUATIONS; DIFFUSION; NONLINEAR EQUATIONS; PAPER SHEETING; POROUS MATERIALS;

PROBLEM SOLVING;

EID: 72149120020     PISSN: 18761070     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jtice.2009.04.011     Document Type: Article

References (36)

1. Abbasbandy S. Homotopy Analysis Method for Heat Radiation Equations. Int. Commun. Heat Mass Transfer 34 (2007) 380
2. Abbasbandy S. Approximate Solution for the Nonlinear Model of Diffusion and Reaction in Porous Catalysts by Means of the Homotopy Analysis Method. Chem. Eng. J. 136 2-3 (2008) 144
3. Akyildiz F.T., Bellout H., and Vajravelu K. Diffusion of Chemically Reactive Species in a Porous Medium over a Stretching Sheet. J. Math. Anal. Appl. 320 (2006) 322
4. Ali A., Mehmood A., and Shah T. Heat Transfer Analysis of Unsteady Boundary Layer Flow by Homotopy Analysis Method. Commun. Nonlinear Sci. Numer. Simul. 13 5 (2008) 902
5. Andersson H.I., Hansen O.R., and Holmedal B. Diffusion of a Chemically Reactive Species from a Stretching Sheet. Int. J. Heat Mass Transfer 37 (1994) 659
6. Bejan A. Convection Heat Transfer (1984), Wiley-Interscience, New York, USA
7. Cortell R. MHD Flow and Mass Transfer of an Electrically Conducting Fluid of Second Grade in a Porous Medium over a Stretching Sheet with Chemically Reactive Species. Chim. Eng. Process 46 (2007) 721
8. Cortell R. Toward an Understanding of the Motion and Mass Transfer with Chemically Reactive Species for Two Classes of Viscoelastic Fluid over a Porous Stretching Sheet. Chim. Eng. Process 46 (2007) 982
9. Crane L.J. Flow Past a Stretching Plate. Z. Angew. Math. Phys. 21 (1970) 645
10. Domairry G., and Ziabakhsh Z. Solution of the Laminar Viscous Flow in a Semi-Porous Channel in the Presence of a Uniform Magnetic Field by Using the Homotopy Analysis Method. Commun. Nonlinear Sci. Numer. Simul. 14 4 (2009) 1284
11. Hayat T., and Khan M. Homotopy Solutions for a Generalized Second Grade Fluid Past a Porous Plate. Nonlinear Dyn. 24 (2005) 395
12. Hayat T., Khan M., and Asghar S. Magneto Hydrodynamic Flow of an Oldroyd 6-Constant Fluid. Appl. Math. Comput. 155 (2004) 417
13. Hayat T., Abbas Z., and Sajid M. Series Solution for the Upper-convected Maxwell Fluid over a Porous Stretching Plate. Phys. Lett. A 358 (2006) 396
14. Liao, S. J., "Proposed Homotopy Analysis Techniques for the Solution of Nonlinear Problems," Ph.D. Dissertation, Shanghai Jiao Tong University, Chna (1992).
15. Liao S.J. An Approximate Solution Technique not Depending on Small Parameters: A Special Example. Int. J. Non-Linear Mech. 303 (1995) 371
16. Liao S.J. An Explicit, Totally Analytic Approximation of Blasius's Viscous Flow Problems. Int. J. Non-Linear Mech. 34 4 (1999) 759
17. Liao S.J. Beyond Perturbation: Introduction to Homotopy Analysis Method (2003), Chapman & Hall/CRC Press, Boca Raton
18. Liao S.J. On the Homotopy Analysis Method for Nonlinear Problems. Appl. Math. Comput. 47 2 (2004) 499
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
20. Liao S.J., and Cheung K.F. Homotopy Analysis of Nonlinear Progressive Waves in Deep Water. J. Eng. Math. 45 2 (2003) 103
21. Liao S.J., and Magyari E. Exponentially Decaying Boundary-Layers as Limiting Cases of Families of Algebraically Decaying Ones. Z. Angew. Math. Phys. 57 (2006) 777
22. Mehmood A., and Ali A. Unsteady Boundary Layer Flow due to an Impulsively Started Moving Plate. IMechE Part G: J. Aerospace Eng. 221 (2007) 385
23. Mehmood A., and Ali A. Analytic Solution of Three-dimensional Viscous Flow and Heat Transfer over a Stretching Flat Surface by Homotopy Analysis Method. Trans. ASME J. Heat Transfer 130 121701 (2008) 1
24. Mehmood A., and Ali A. An Explicit Analytic Solution of Steady Three-Dimensional Stagnation Point Flow of Second Grade Fluid toward a Heated Plate. Trans. ASME J. Appl. Mech. 75 061003 (2008) 1
25. Mehmood A., Ali A., and Shah T. Unsteady Boundary-Layer Viscous Flow due to an Impulsively Started Porous Plate. Can. J. Phys. 86 (2008) 1079
26. Mehmood A., Ali A., Takhar H.S., and Shah T. Corrigendum: Unsteady Three-Dimensional MHD Boundary Layer Flow due to the Impulsive Motion of the Stretching Sheet. Acta Mech. 199 (2008) 241
27. Prasad K.V., Abel S., Khan S.K., and Datti P.S. Non-Darcy Forced Convective Heat Transfer in a Viscoelastic Fluid Flow Over a Non-Isothermal Stretching Sheet. J. Porous Media 5 (2002) 41
28. Prasad K.V., Abel S., and Datti P.S. Diffusion of Chemically Reactive Species of a Non-Newtonian Fluid Immersed in a Porous Medium over a Stretching Sheet. Int. J. Non-Linear Mech. 38 (2003) 651
29. Rajagopal K., Veena P.H., and Pravin V.K. Nonsimilar Solutions for Heat and Mass Transfer Flow in an Electrically Conducting Viscoelastic Fluid over a Stretching Sheet Saturated in a Porous Medium with Suction/Blowing. J. Porous Media 11 (2008) 219
30. Raptis A., and Perdikis C. Viscous Flow over a Nonlinearly Stretching Sheet in the Presence of a Chemical Reaction and Magnetic Field. Int. J. Non-Linear Mech. 41 (2006) 527
31. Sakiadis B.C. Boundary-Layer Behaviour on Continuous Solid Surfaces: I. Boundary-Layer Equations for Two-dimensional and Axisymmetric Flow. AIChE J. 7 (1961) 26
32. Sakiadis B.C. Boundary-Layer Behaviour on Continuous Solid Surfaces: II. The Boundary Layer on a Continuous Flat Surface. AIChE J. 7 (1961) 221
33. Thakar H.S., Chamkha A.J., and Nath G. Flow and Mass Transfer on a Stretching Sheet with a Magnetic Filed and Chemically Reactive Species. Int. J. Eng. Sci. 38 (2000) 1303
34. Vafai K., and Tien C.L. Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media. Int. J. Heat Mass Transfer 24 (1981) 195
35. Ziabakhsh Z., and Domairry G. Analytic Solution of Natural Convection Flow of a Non Newtonian Fluid between Two Vertical Flat Plates Using Homotopy Analysis Method. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 1868
36. Ziabakhsh Z., Domairry G., and Ghazizadeh H.R. Analytical Solution of the Stagnation-Point Flow in a Porous Medium by Using the Homotopy Analysis Method. J. Taiwan Inst. Chem. Engrs. 40 (2009) 91