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Open Physics

formerly Central European Journal of Physics


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Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet

1Department of Mathematics, Quaid-i-Azam University 45320, Islamabad, 44000, Pakistan

2Department of Mathematics, Islamia College University 25120, Peshawar, 25000, Pakistan

3Department of Mathematics, University of Sargodha, Sargodha, Pakistan

© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)

Citation Information: Open Physics. Volume 8, Issue 1, Pages 135–149, ISSN (Online) 2391-5471, DOI: 10.2478/s11534-009-0110-0, November 2009

Publication History

Published Online:
2009-11-15

Abstract

We examine the problem of flow and heat transfer in a second grade fluid over a stretching sheet [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)]. The equations considered by Vajravelu and Roper [K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999)], are found to be incorrect in the literature. In this paper, we not only corrected the equation but found a useful analytic solution to this important problem. We also extended the problem for hydromagnetic flow and heat transfer with Hall effect. The explicit analytic homotopy solution for the velocity field and heat transfer are presented. Graphs for the velocity field, skin friction coefficient, and rate of heat transfer are presented. Tables for the skin friction coefficient and rate of heat transfer are also presented. The convergence of the solution is also properly checked and discussed.

Keywords: second grade fluid; hydromagnetic flow; Hall effect; heat transfer; atretching sheet

PACS: 47.10.A-; 47.10.ad; 47.15.Cb; 47.50.Cd; 02.70.Wz

  • [1] K. Vajravelu, T. Roper, Int. J. Nonlinear Mech. 34, 1031 (1999) http://dx.doi.org/10.1016/S0020-7462(98)00073-0 [Crossref]

  • [2] L. J. Crane, Z. Angew. Math. Phys. 21, 45 (1970) http://dx.doi.org/10.1007/BF01587695 [Crossref]

  • [3] P. Carragher, L. J. Crane, Z. Angew. Math. Mech. 62, 564 (1982) http://dx.doi.org/10.1002/zamm.19820621009 [Crossref]

  • [4] B. K. Dutta, P. Roy, A. S. Gupta, Int. Commun. Heat Mass 12, 89 (1985) http://dx.doi.org/10.1016/0735-1933(85)90010-7 [Crossref]

  • [5] T. C. Chiam, J. Phys. Soc. Jpn. 63, 2443 (1994) http://dx.doi.org/10.1143/JPSJ.63.2443 [Crossref]

  • [6] T. R. Mahapatra, A. S. Gupta, Heat Mass Transfer 38, 517 (2002) http://dx.doi.org/10.1007/s002310100215 [Crossref]

  • [7] K. R. Rajagopal, T. Y. Na, A. S. Gupta, Rheol. Acta. 23, 213 (1984) http://dx.doi.org/10.1007/BF01332078 [Crossref]

  • [8] S. Bhattacharya, A. Pal, A. S. Gupta, Heat Mass Transfer 34, 41 (1998) http://dx.doi.org/10.1007/s002310050229 [Crossref]

  • [9] K. Vajravelu, D. Rollins, J. Math. Anal. Appl. 158, 241 (1991) http://dx.doi.org/10.1016/0022-247X(91)90280-D [Crossref]

  • [10] R. Nazar, N. Amin, D. Filip, I. Pop, Int. J. Eng. Sci. 42, 1241 (2004) http://dx.doi.org/10.1016/j.ijengsci.2003.12.002 [Crossref]

  • [11] J. B. McLeod, K. R. Rajagopal, Arch. Ration. Mech. An. 98, 385 (1987) http://dx.doi.org/10.1007/BF00276915 [Crossref]

  • [12] N. Afzal, I. S. Varshney, Warme Stoffubertrag. 14, 289 (1980) http://dx.doi.org/10.1007/BF01618360 [Crossref]

  • [13] W. H. H. Banks, J. Mec. Theor. Appl. 2, 375 (1983)

  • [14] W. H. H. Banks, M. B. Zaturska, IMA J. Appl. Math. 36, 263 (1986) http://dx.doi.org/10.1093/imamat/36.3.263 [Crossref]

  • [15] N. Afzal, Int. J. Heat Mass Tran. 36, 1128 (1993) http://dx.doi.org/10.1016/S0017-9310(05)80296-0 [Crossref]

  • [16] A. Chakrabarti, A. S. Gupta, Q. Appl. Math. 37, 73 (1979)

  • [17] K. Cramer, S, Pai, Magnetofluid Dynamics for Engineers and Applied Physicists (McGraw — Hill, New York, 1973)

  • [18] M. Katagiri, J. Phys. Soc. Jpn. 27, 1051 (1969) http://dx.doi.org/10.1143/JPSJ.27.1051 [Crossref]

  • [19] A. S. Gupta, Acta Mech. 22, 281 (1975) http://dx.doi.org/10.1007/BF01170681 [Crossref]

  • [20] I. Pop, V. M. Soundalgekar, Acta Mech. 20, 315 (1974) http://dx.doi.org/10.1007/BF01175933 [Crossref]

  • [21] L. Debnath, S. C. Ray, A. K. Chatterjee, Z. Angew. Math. Mech. 59, 469 (1979) http://dx.doi.org/10.1002/zamm.19790590910 [Crossref]

  • [22] T. Hayat, R. Naz, S. Asghar, Appl. Math. Comput 157, 103 (2004) http://dx.doi.org/10.1016/j.amc.2003.08.069 [Crossref]

  • [23] H. Sato, J. Phys. Soc. Jpn. 16, 1427 (1961) http://dx.doi.org/10.1143/JPSJ.16.1427 [Crossref]

  • [24] M. A. Hossain, J. Phys. Soc. Jpn. 55, 2183 (1986) http://dx.doi.org/10.1143/JPSJ.55.2183 [Crossref]

  • [25] M. A. Hossain, K. Mohammad, J. Phys. Soc. Jpn. 27, 1531 (1988) http://dx.doi.org/10.1143/JJAP.27.1531 [Crossref]

  • [26] M. A. Hossain, R. I. M. A. Rashid, J. Phys. Soc. Jpn. 56, 97 (1987) http://dx.doi.org/10.1143/JPSJ.56.97 [Crossref]

  • [27] A. Raptis, P. C. Ram, Astrophys. Space Sci. 106, 257 (1984) http://dx.doi.org/10.1007/BF00650353 [Crossref]

  • [28] P. C. Ram, Warme Stoffubertrag. 22, 223 (1988) http://dx.doi.org/10.1007/BF01052991 [Crossref]

  • [29] S. Asghar, M. R. Mohyuddin, T. Hayat, Int. J. Heat Mass Tran. 48, 599 (2005) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2004.08.023 [Crossref]

  • [30] E. M. Abo-Eldahab, M. E. Elbarbary, Int. J. Eng. Sci. 39, 1641 (2001) http://dx.doi.org/10.1016/S0020-7225(01)00020-9 [Crossref]

  • [31] E. M. Abo-Eldahab, M. Abd El Aziz, Int. Commun. Heat Mass 31, 751 (2004) http://dx.doi.org/10.1016/S0735-1933(04)00062-4 [Crossref]

  • [32] E. M. Abo-Eldahab, A. M. Salem, Int. Commun. Heat Mass 31, 343 (2004) http://dx.doi.org/10.1016/j.icheatmasstransfer.2004.02.005 [Crossref]

  • [33] E. M. Abo-Eldahab, M. Abd El Aziz, Appl. Math. Comput. 162, 881 (2005) http://dx.doi.org/10.1016/j.amc.2003.12.129 [Crossref]

  • [34] S. J. Liao, PhD thesis, Shanghai Jiao Tong University (Shanghai, China, 1992)

  • [35] S. J. Liao, Int. J. Nonlinear Mech. 34, 759 (1999) http://dx.doi.org/10.1016/S0020-7462(98)00056-0 [Crossref]

  • [36] S. J. Liao, A. Campo, J. Fluid Mech. 453, 411 (2002) http://dx.doi.org/10.1017/S0022112001007169 [Crossref]

  • [37] S. J. Liao, Int. J. Nonlinear Mech. 7, 1 (2002) http://dx.doi.org/10.1016/S0020-7462(00)00092-5 [Crossref]

  • [38] S. J. Liao, Int. J. Nonlinear Mech. 38, 1173 (2003) http://dx.doi.org/10.1016/S0020-7462(02)00062-8 [Crossref]

  • [39] M. Ayub, A. Rashid, T. Hayat, Int. J. Eng. Sci. 41, 2091 (2003) http://dx.doi.org/10.1016/S0020-7225(03)00207-6 [Crossref]

  • [40] T. Hayat, M. Khan, M. Ayub, Int. J. Eng. Sci. 42, 123 (2004) http://dx.doi.org/10.1016/S0020-7225(03)00281-7 [Crossref]

  • [41] T. Hayat, M. Khan, S. Asghar, Acta Mech. 168, 213 (2004) http://dx.doi.org/10.1007/s00707-004-0085-2 [Crossref]

  • [42] T. Hayat, M. Khan, M. Ayub, Z. Angew. Math. Phys. 56, 1012 (2005) http://dx.doi.org/10.1007/s00033-005-4006-6 [Crossref]

  • [43] T. Hayat, M. Khan, Nonlinear Dynam. 42, 395 (2005) http://dx.doi.org/10.1007/s11071-005-7346-z [Crossref]

  • [44] T. Hayat, M. Khan, M. Sajid, M. Ayub, J. Porous Media 9, 709 (2006) http://dx.doi.org/10.1615/JPorMedia.v9.i8.10 [Crossref]

  • [45] S. Abbasbandy, Int. Commun. Heat Mass 34, 380 (2007) http://dx.doi.org/10.1016/j.icheatmasstransfer.2006.12.001 [Crossref]

  • [46] S. Abbasbandy, Phys. Lett. A 361, 478 (2007) http://dx.doi.org/10.1016/j.physleta.2006.09.105 [Crossref]

  • [47] S. Abbasbandy, Phys. Lett. A 360, 109 (2006) http://dx.doi.org/10.1016/j.physleta.2006.07.065 [Crossref]

  • [48] P. D. Ariel, T. Hayat, S. Asghar, Int. J. Nonlin. Sci. Num. 7, 399 (2006)

  • [49] T. Hayat, Z. Abbas, M. Sajid, S. Asghar, Int. J. Heat Mass Tran. 50, 931 (2007) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.08.014 [Crossref]

  • [50] T. Hayat, M. Sajid, Int. J. Heat Mass Tran. 50, 75 (2007) http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.06.045 [Crossref]

  • [51] T. Hayat, M. Sajid, Int. J. Eng. Sci. 45, 393 (2007) http://dx.doi.org/10.1016/j.ijengsci.2007.04.009 [Crossref]

  • [52] L. Song, HQ. Zhang, Phys. Lett. A 367, 88 (2007) http://dx.doi.org/10.1016/j.physleta.2007.02.083 [Crossref]

  • [53] M. Sajid, T. Hayat, S. Asghar, Phys. Lett. A 355, 18 (2006) http://dx.doi.org/10.1016/j.physleta.2006.01.092 [Crossref]

  • [54] S. J. Liao, Commun Nonlinear Sci. 11, 326 (2006) http://dx.doi.org/10.1016/j.cnsns.2004.09.004 [Crossref]

  • [55] S. J. Liao, Commun Nonlinear Sci. 14, 983 (2009) http://dx.doi.org/10.1016/j.cnsns.2008.04.013 [Crossref]

  • [56] T. Hayat, M. Sajid, Phys. Lett A. 361, 316 (2007) http://dx.doi.org/10.1016/j.physleta.2006.09.060 [Crossref]

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