PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2010 | 8 | 1 | 135-149
Article title

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

Content
Title variants
Languages of publication
EN
Abstracts
EN
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.
Publisher
Journal
Year
Volume
8
Issue
1
Pages
135-149
Physical description
Dates
published
1 - 2 - 2010
online
15 - 11 - 2009
References
  • [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]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-009-0110-0
Identifiers
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.