A reliable treatment of the homotopy analysis method for viscous flow over a non-linearly stretching sheet in presence of a chemical reaction and under influence of a magnetic field

• Authors: Saeed Dinarvand
• Languages of publication: EN

Abstracts

EN

The similarity solution for the steady two-dimensional flow of an incompressible viscous and electrically conducting fluid over a non-linearly semi-infinite stretching sheet in the presence of a chemical reaction and under the influence of a magnetic field gives a system of non-linear ordinary differential equations. These non-linear differential equations are analytically solved by applying a newly developed method, namely the Homotopy Analysis Method (HAM). The analytic solutions of the system of non-linear differential equations are constructed in the series form. The convergence of the obtained series solutions is carefully analyzed. Graphical results are presented to investigate the influence of the Schmidt number, magnetic parameter and chemical reaction parameter on the velocity and concentration fields. It is noted that the behavior of the HAM solution for concentration profiles is in good agreement with the numerical solution given in reference [A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006)].

Keywords

EN

non-linear stretching; chemical reaction; magnetic field; concentration; homotopy analysis method

Discipline

• 02.60.Lj: Ordinary and partial differential equations; boundary value problems
• 02.90.+p: Other topics in mathematical methods in physics (restricted to new topics in section 02)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2009
• Volume: 7
• Issue: 1
• Pages: 114-122

Dates

published

1 - 3 - 2009

online

8 - 1 - 2009

Contributors

author

Saeed Dinarvand

• Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran

References

• [1] B.C. Sakiadis, AICHE J. 7, 26 (1961) http://dx.doi.org/10.1002/aic.690070108[Crossref]
• [2] F.K. Tsou, E.M. Sparrow, R.J. Glodstein, Int. J. Heat Mass Tran. 10, 219 (1967) http://dx.doi.org/10.1016/0017-9310(67)90100-7[Crossref]
• [3] L.E. Erickson, L.T. Fan, V.G. Fox, Ind. Eng. Chem. 5, 19 (1966) http://dx.doi.org/10.1021/i160017a004[Crossref]
• [4] T.S. Chen, F.A. Strobel, J. Heat Trans.-T. ASME 102, 170 (1980) http://dx.doi.org/10.1115/1.3244232[Crossref]
• [5] A. Chakrabarti, A.S. Gupta, Q. Appl. Math. 37, 73 (1979)
• [6] K. Vajravelu, A. Hadjinicolaou, Int. J. Eng. Sci. 35, 1237 (1997) http://dx.doi.org/10.1016/S0020-7225(97)00031-1[Crossref]
• [7] S.P. Anjalidevi, R. Kandasamy, Heat Mass Transfer 35, 465 (1999) http://dx.doi.org/10.1007/s002310050349[Crossref]
• [8] H.I. Andersson, O.R. Hansen, B. Holmedal, Int. J. Heat Mass Transfer 37, 659 (1994) http://dx.doi.org/10.1016/0017-9310(94)90137-6[Crossref]
• [9] R. Muthucumaraswamy, P. Ganesan, Forsch. Ingenieurwes. 66, 17 (2000) http://dx.doi.org/10.1007/s100100000026[Crossref]
• [10] U.N. Das, R.K. Deka, V.M. Soundalgekar, Forsch. Ingenieurwes. 60, 284 (1994) http://dx.doi.org/10.1007/BF02601318[Crossref]
• [11] R. Muthucumaraswamy, P. Ganesan, Acta Mech. 147, 45 (2001) http://dx.doi.org/10.1007/BF01182351[Crossref]
• [12] R. Muthucumaraswamy, Forsch. Ingenieurwes. 67, 129 (2002) http://dx.doi.org/10.1007/s10010-002-0083-2[Crossref]
• [13] S.P. Anjalidevi, R. Kandasamy, Z. Angew. Math. Mech. 80, 697 (2000) http://dx.doi.org/10.1002/1521-4001(200010)80:10<697::AID-ZAMM697>3.0.CO;2-F[Crossref]
• [14] A. Raptis, C. Perdikis, Int. J. Nonlinear Mech. 41, 527 (2006) http://dx.doi.org/10.1016/j.ijnonlinmec.2005.12.003[Crossref]
• [15] S.J. Liao, Ph.D. Thesis, Shanghai Jiao Tong University (Shanghai, China, 1992)
• [16] S.J. Liao, J. Fluid Mech. 385, 101 (1999) http://dx.doi.org/10.1017/S0022112099004292[Crossref]
• [17] S.J. Liao, Int. J. Nonlinear Mech. 34, 759 (1999) http://dx.doi.org/10.1016/S0020-7462(98)00056-0[Crossref]
• [18] S.J. Liao, J. Fluid Mech. 488, 189 (2003) http://dx.doi.org/10.1017/S0022112003004865[Crossref]
• [19] S.J. Liao, Beyond Perturbation: Introduction to the Homotopy Analysis Method (Chapman and Hall/CRC Press, Boca Raton US, 2003)
• [20] S.J. Liao, Appl. Math. Comput. 147, 499 (2004) http://dx.doi.org/10.1016/S0096-3003(02)00790-7[Crossref]
• [21] S.J. Liao, Appl. Math. Comput. 169, 1186 (2005) http://dx.doi.org/10.1016/j.amc.2004.10.058[Crossref]
• [22] M. Sajid, T. Hayat, S. Asghar, Nonlinear Dynam. 50, 27 (2007) http://dx.doi.org/10.1007/s11071-006-9140-y[Crossref]
• [23] F.M. Allan, Appl. Math. Comput. 190, 6 (2007) http://dx.doi.org/10.1016/j.amc.2006.12.074[Crossref]
• [24] S. Abbasbandy, Phys. Lett. A 360, 109 (2006) http://dx.doi.org/10.1016/j.physleta.2006.07.065[Crossref]
• [25] S. Abbasbandy, Chem. Eng. J. (in press)
• [26] F.M. Allan, Chaos Soliton. Fract. (in press)
• [27] F.M. Allan, M.I. Syam, J. Comput. Appl. Math. 182, 362 (2005) http://dx.doi.org/10.1016/j.cam.2004.12.017[Crossref]
• [28] T. Hayat, T. Javed, Phys. Lett. A 370, 243 (2007) http://dx.doi.org/10.1016/j.physleta.2007.05.108[Crossref]
• [29] M. Sajid, A.M. Siddiqui, T. Hayat, Int. J. Eng. Sci. 45, 381 (2007) http://dx.doi.org/10.1016/j.ijengsci.2007.04.010[Crossref]
• [30] T. Hayat, M. Sajid, Int. J. Heat Mass Tran. 50, 75 (2007) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.06.045[Crossref]
• [31] T. Hayat, Naveed Ahmed, M. Sajid, S. Asghar, Comput. Math. Appl. 54, 407 (2007) http://dx.doi.org/10.1016/j.camwa.2006.12.036[Crossref]
• [32] T. Hayat, M. Sajid, M. Ayub, Communications in Nonlinear Science and Numerical Simulation 12, 1481 (2007) http://dx.doi.org/10.1016/j.cnsns.2006.02.009[Crossref]
• [33] Yann Bouremel, Communications in Nonlinear Science and Numerical Simulation 12, 714 (2007) http://dx.doi.org/10.1016/j.cnsns.2005.07.001[Crossref]
• [34] M. M. Rashidi, G. Domairry, S. Dinarvand, Communications in Nonlinear Science and Numerical Simulation (in press)
• [35] Z. Ziabakhsh, G. Domairry, Communications in Nonlinear Science and Numerical Simulation (in press)
• [36] J. Cheng, S.J. Liao, R.N. Mohapatra, K. Vajravelu, J. Math. Anal. Appl. 343, 233 (2008) http://dx.doi.org/10.1016/j.jmaa.2008.01.050[Crossref]
• [37] T.T. Zhang, L. Jia, Z.C. Wang, X. Li, Phys. Lett. A 372, 3223 (2008) http://dx.doi.org/10.1016/j.physleta.2008.01.077[Crossref]
• [38] M. M. Rashidi, S. Dinarvand, Nonlinear Anal.-Real (in press)
• [39] S. Abbasbandy, Z. Angew. Math. Phys. 59, 51 (2008) http://dx.doi.org/10.1007/s00033-007-6115-x[Crossref]
• [40] S. Abbasbandy, F. Samadian Zakaria, Nonlinear Dynam. 51, 83 (2008) http://dx.doi.org/10.1007/s11071-006-9193-y[Crossref]
• [41] S. Abbasbandy, M. Yürüsoyb, M. Pakdemirlic, Z. Naturforsch. A 63, 564 (2008)
• [42] J.H. He, Int. J. Nonlinear. Mech. 35, 37 (2000) http://dx.doi.org/10.1016/S0020-7462(98)00085-7[Crossref]
• [43] J.H. He, Phys. Lett. A 350, 87 (2006) http://dx.doi.org/10.1016/j.physleta.2005.10.005[Crossref]
• [44] F.T. Akyildiz, H. Bellout, K. Vajravelu, J. Math. Anal. Appl. 320, 322 (2006) http://dx.doi.org/10.1016/j.jmaa.2005.06.095[Crossref]
• [45] L.J. Crane, Z. Angew. Math. Phys. 21, 645 (1970) http://dx.doi.org/10.1007/BF01587695[Crossref]

Identifiers

DOI

10.2478/s11534-008-0145-7