MHD FREE CONVECTION BOUNDARY LAYER FLOW OF A NANO FLUID OVER A PERMEABLE SHRINKING SHEET WITH NTH ORDER CHEMICAL REACTION
An analysis is presented to study the free convective unsteady magnatohydrodynamic boundary layer flow of a Nano fluid over a permeable shrinking sheet in the presence of nth order chemical reaction. Magnetic field of varying strength is applied normal to the sheet. The Nano fluid model under consideration includes Brownian motion, thermophoresis effects and nth order chemical reaction. The governing partial differential equations are transformed into a set of ordinary differential equations by applying the local similarity transformations and then the highly coupled nonlinear differential equations are solved by the method of lines. The effect of various controlling flow parameters on the dimensionless velocity, temperature and nanoparticle volume fraction profiles are analyzed.
Bhattacharyya S.N and Gupta, A.S, 1985,”On the stability of viscous Flow over a stretching sheet”, Quarterly Applied Mathematics, 43, pp. 359-367. DOI: https://doi.org/10.1090/qam/814233
Gupta, P.S and Gupta, A.S, 1977, “Heat and mass transfer on a stretching sheet with suction and blowing”, Canadian Journal of Chemical Engineering, 55, pp. 744-746. DOI: https://doi.org/10.1002/cjce.5450550619
Cheng, W.T and Lin, H.T, 2002, “Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge”, International journal of Engineering Science, 40, pp. 531 - 539. DOI: https://doi.org/10.1016/S0020-7225(01)00081-7
Crane, L.J. ‘‘Flow past a stretching plate’’, ZAMP, 21, pp. 645–655 (1970). DOI: https://doi.org/10.1007/BF01587695
Carragher, P. and Carane, L.J. ‘‘Heat transfer on a continuous stretching sheet’’, Z.Angew. Math. Mech., 62, pp. 564–565 (1982). DOI: https://doi.org/10.1002/zamm.19820621009
Ariel, P.D., Hayat, T. and Ashgar, S. ‘‘the flow of an elasto-viscous fluid past a stretching sheet with partial slip’’, Acta Mech., 187, pp. 29–35 (2006). DOI: https://doi.org/10.1007/s00707-006-0370-3
Nadeem, S., Hussain, A., Malik, M.Y. and Hayat, T. ‘‘Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet’’, Appl. Math. Mech., 30(10), pp. 1255–1262 (2009). DOI: https://doi.org/10.1007/s10483-009-1005-6
Nadeem, S., Hussain, A. and Khan, M. ‘‘Stagnation flow of a Jeffrey fluid over a shrinking sheet’’, Z. Naturforsch., 65a, pp. 540–548 (2010). DOI: https://doi.org/10.1515/zna-2010-6-709
Hayat, T. and Qasim, M. ‘‘Radiation and magnetic field effects on the unsteady mixed convection flow of a second grade fluid over a vertical stretching sheet’’, Int. J. Numer. Methods Fluids, 66(7), pp. 820–832 (2010). DOI: https://doi.org/10.1002/fld.2285
Nadeem, S. and Faraz, N. ‘‘Thin film flow of a second grade fluid over a stretching/shrinking sheet with variable temperature-dependent viscosity’’, Chin. Phys. Lett., 27(3), p. 034704 (2010). DOI: https://doi.org/10.1088/0256-307X/27/3/034704
Ishak, A., Nazar, R. and Pop, I. ‘‘Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature’’, Nonlinear Anal.RWA, 10, pp. 2909–2913 (2009). DOI: https://doi.org/10.1016/j.nonrwa.2008.09.010
Hayat, T., Shehzad, S.A., Qasim, M. and Obaidat, S. ‘‘Steady flow of Maxwell fluid with convective boundary conditions’’, Z. Naturforsch., 66a, pp. 417–422 (2011). DOI: https://doi.org/10.1515/zna-2011-6-706
Wang, C. and Pop, I. ‘‘Analysis of the flow of a power-law fluid film on an unsteady stretching surface by means of homotopy analysis method’’,J. Non-Newtonian Fluid Mech., 138, pp. 161– 172 (2006). DOI: https://doi.org/10.1016/j.jnnfm.2006.05.011
Magyari, E. and Keller, B. ‘‘Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface’’, J. Phys. Appl. Phys., 32, pp. 577–585 (1999). DOI: https://doi.org/10.1088/0022-3727/32/5/012
Partha, M.K., Murthy, P.V. and Rajasekhar, G.P. ‘‘Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface’’, Heat Mass Transf., 41, pp. 360–366 (2005). DOI: https://doi.org/10.1007/s00231-004-0552-2
Elbashbeshy, E.M.A. ‘‘Heat transfer over an exponentially stretching continuous surface with suction’’, Arch. Mech., 53, pp. 643–651 (2001).
MachaMadhu and Naikoti Kishan, “Magnetohydrodynamic Mixed Convection Stagnation-Point Flow of a Power-Law Non-Newtonian Nanofluid towards a Stretching Surface with Radiation and Heat Source/Sink”. Journal of Fluids .Volume 2015, Article ID 634186, 14 pages .http://dx.doi.org/10.1155/2015/634186. DOI: https://doi.org/10.1155/2015/634186
Wang CY (1990). “Liquid film on an unsteady stretching sheet”. Quarterly of Applied Mathematics 48, pp. 601-610. DOI: https://doi.org/10.1090/qam/1079908
Miklavcic M, Wang CY (2006). “Viscous flow due to a shrinking sheet”. Quarterly of Applied Mathematics 64(2), pp. 283-290. DOI: https://doi.org/10.1090/S0033-569X-06-01002-5
Hayat T, Abbas Z, Ali N (2008). “MHD flow and mass transfer of a upper convected Maxwell fluid past a porous shrinking sheet with chemical reaction species”. Physics Letters A 372(26), pp. 4698-4704. DOI: https://doi.org/10.1016/j.physleta.2008.05.006
Hayat T, Abbas Z, Sajid M (2007).” On the analytic solution of magnetohydrodynamic flow of a econd grade fluid over a shrinking sheet”. Journal of Applied Mechanics, Trans. ASME 74(6), pp. 1165-1171. DOI: https://doi.org/10.1115/1.2723820
D. A. Nield, and A. V. Kuznetsov, “The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid”, International Journal of Heat and Mass Transfer, vol. 52, pp. 5792-5795, 2009a. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.024
D. A. Nield, and A. V. Kuznetsov, “Thermal instability in a porous medium layer saturated by a nanofluid”, International Journal of Heat and Mass Transfer, vol. 52, pp. 5796–5801, 2009b. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.023
A. J. Chamkha, R. S. R. Gorla, and K. Ghodeswar, “Non-similar solution for natural convective boundary layer flow over a sphere Transport in Porous Media, vol. 86, pp. 13-22, 2011. DOI: https://doi.org/10.1007/s11242-010-9601-0
D. A. Nield, and A. V. Kuznetsov, “The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid”, International Journal of Heat and Mass Transfer, vol. 54, pp. 374-378, 2011. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2010.09.034
R. S. R. Gorla, and A. J. Chamkha, “Natural convective boundary layer flow over a horizontal plate embedded in a porous medium saturated with a nanofluid”, Journal of Modern Physics, vol. 2, pp.62-71, 2011. DOI: https://doi.org/10.4236/jmp.2011.22011
Hunegnaw Dessie, Naikoti Kishan, “Unsteady MHD Flow of Heat and Mass Transfer of Nanofluids over Stretching Sheet with a Non-Uniform Heat/Source/Sink Considering Viscous Dissipation and Chemical Reaction”, International Journal of Engineering Research in Africa, Vol.14,pp. 1-12. 2015. DOI: https://doi.org/10.4028/www.scientific.net/JERA.14.1
Pavlov, KB: “Magnetohydromagnetic flow of an incompressible viscous fluid caused by deformation of a surface” .Magn. Gidrodin. 4, 146-147 (1974).
Jafar, K, Nazar, R, Ishak, a, Pop, I: “MHD flow and heat transfer over stretching/shrinking sheets with external magnetic field, viscous dissipation and Joule effects”. Can. J. Chem. Eng. 99, 1-11 (2011).
Samir kumarNandy,Sumanta Sidui,Tapas Ray Mahapatra: “Unsteady MHD boundary layer flow and heat transfer of nanofluid over a permeable shrinking sheet in the presence of thermal radiation.” Alxendria eng.journal (2014) 53,929-937. DOI: https://doi.org/10.1016/j.aej.2014.09.001
Brewster M.Q, “Thermal Radiative Transfer Properties”, Wiley, Newyork, 1972.
Vajravelu K., Prasad K.V, Datti P.S, Raju B.T, “MHD flow and heat transfer of an Ostwald-de Waele fluid over an unsteady stretching surface.” Ain Shams Eng.J.5 (1) (2014) 157-167. DOI: https://doi.org/10.1016/j.asej.2013.07.009
Anuradha S, Priyadharshini P, “MHD Free Convection Boundary Layer Flow of a Nanofluid overa Permeable Shrinking Sheet in the Presence of Thermal Radiation and Chemical Reaction” Chemical and Process Engineering Research , Vol.46 (2016)
Copyright (c) 2017 S. Anuradha, M Yegammai
This work is licensed under a Creative Commons Attribution 4.0 International License.
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal.
- That it is not under consideration for publication elsewhere.
- That its release has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Authors who publish with International Journal of Engineering Technologies and Management Research agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors can enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or edit it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) before and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
For More info, please visit CopyRight Section