Similarity Solutions for Heat and Mass Transfer of MHD Flow Over a Permeable Stretching Wedge with Variable Fluid Properties and Heat Generation/Absorption
(*) Corresponding author
DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)
Abstract
The problem of steady boundary layer flow for Newtonian fluid with variable viscosity and thermal conductivity over stretching wedge in the presence of magnetic field and heat generation (absorption) is studied. The system of governing partial differential equations with the boundary conditions is reduced to a system of ordinary differential equations with appropriate boundary conditions using Lie group. The reduced ordinary differential equations along with the boundary conditions are solved numerically using the fourth order Runge-Kutta method algorithm with the shooting technique. The effects of various parameters on the velocity, the temperature and the concentration profiles are discussed. Finally, the numerical values of the physical quantities, such as local skin-friction coefficient, the local Nusselt number and the local Sherwood number are illustrated graphically.
Copyright © 2014 Praise Worthy Prize - All rights reserved.
Keywords
Full Text:
PDFReferences
L. J. Crane, Flow past a stretching sheet, ZAMP 21(1970), 645-617.
http://dx.doi.org/10.1007/bf01587695
P. S. Gupte and A. S. Gupta, Heat and mass transfer on a stretching sheet with suction or blowing, Can. J. Chem. Eng. 55 (1977), 744-746.
http://dx.doi.org/10.1002/cjce.5450550619
R. Cortell , A note on flow and heat transfer of a viscoelastic liquid over a stretching sheet, Int. J. Non-linear Mech. 41(2006) , 78-85.
http://dx.doi.org/10.1016/j.ijnonlinmec.2005.04.008
T. Y. Na and I. Pop, Boundary-layer flow of a micropolar fluid due to a stretching wall, Archive of Applied Mech. 67(1997) , 229-236.
http://dx.doi.org/10.1007/s004190050113
M. A. A. Mahmoud, Hydromagnetic stagnation point flow towards a porous stretching sheet with variable surface heat flux in the presence of heat generation, Chem. Eng. Comm 198(2011), 837-846.
http://dx.doi.org/10.1080/00986445.2011.545292
M.S. Abel, J.V. Tawade and M.M. Nandeppanavar, MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet, Meccanica 47 (2012), 385-393.
http://dx.doi.org/10.1007/s11012-011-9448-7
B. S. Dandapat, S. A. Singh, and R. P. Singh, Heat transfer due to permeable stretching. Wall in presence of transverse magnetic field, Arch. Mech. 56(2004), 87-101.
R. Cortell , Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet, Phys. Letter A 372(2008) ,631-636.
http://dx.doi.org/10.1016/j.physleta.2007.08.005
N. Afzal and I. S. Varshney, The cooling of a low heat resistance stretching sheet moving through a fluid, Wärme-und Stofübertr 14(1980) ,289-293.
T. Fang, Flow and heat transfer characteristics of the boundary layers over a stretching surface with a uniform-shear free stream, Int. J. Heat Mass Transfer 51(2008) ,2199-2213.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.11.013
W. H. H. Banks and M. B. Zaturska, Eigensolutions in boundary layer flow adjacent to a stretching wall, IMA J. Appl. Math. 49(1986), 263-273.
http://dx.doi.org/10.1093/imamat/36.3.263
M. A. A. Mahmoud and S. E. Waheed, MHD flow and heat transfer of a micropolar fluid over a nonlinear stretching surface with variable surface heat flux and heat generation, Can. J. Chem Eng. 89(2011), 1408-1415.
http://dx.doi.org/10.1002/cjce.20495
M. A. A. Mahmoud and A. M. Megahed, Non-uniform heat generation effect on heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching sheet, Meccanica 47(2012), 1331-1339.
http://dx.doi.org/10.1007/s11012-011-9499-9
C. H. Chen, Mixed convection cooling of a heated, continuously stretching surface, Heat Mass Transfer 36(2000) , 79-89.
http://dx.doi.org/10.1007/s002310050367
R. C. Bataller, Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface, J. Mater. Process. Techno. 203 (2008), 176-183.
http://dx.doi.org/10.1016/j.jmatprotec.2007.09.055
M. A. A. Mahmoud and A. M. Megahed, MHD flow and heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet with variable fluid properties, Can. J. Phys. 87(2009), 1065-1071.
http://dx.doi.org/10.1139/p09-066
B.S. Dandapat and S. Chakraborty, Effects of variable fluid properties on unsteady thin-film flow over a non-linear stretching sheet, Inter. J. Heat Mass Trans. 53 (2010), 5757–5763.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.08.007
M. M. Rahman, A. Aziz and M. A. Al-Lawatia, Heat transfer in micropolar fluid along an inclined permeable plate with variable fluid properties, Inter. J. Therm. Sci. 49 (2010), 9931002.
http://dx.doi.org/10.1016/j.ijthermalsci.2010.01.002
K.V. Prasad, K. Vajravelu and P.S. Datti, The effects of variable fluid properties on the hydromagnetic flow and heat transfer over a non-linearly stretching sheet, Inter. J. Therm. Sci. 49 (2010) , 603–610.
http://dx.doi.org/10.1016/j.ijthermalsci.2009.08.005
M.M.M. Abdou, Effect of radiation with temperature dependent viscosity and thermal conductivity on unsteady a stretching sheet through porous media, Nonlinear Analysis: Modelling and Control 15 (2010), 257–270.
M. A. A. Mahmoud, Hydromagnetic stagnation point flow towards a porous stretching sheet with variable surface heat flux in the presence of heat generation, Chem. Eng. Comm. 198(2011), 837-846.
http://dx.doi.org/10.1080/00986445.2011.545292
K. Das, Influence of thermophoresis and chemical reaction on MHD micropolar fluid flow with variable fluid properties, Inter. J. Heat Mass Trans. 55 (2012), 7166–7174.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.07.033
V. M. Falkner and S. W. Skan, Solutions of the boundary-layer equations, Philos. Magazine,7 (1931), 865-896.
http://dx.doi.org/10.1080/14786443109461870
K. R. Rajagopal, A. S. Gupta and T.Y. Na, A note on the Falkner-Skan flows of a nonNewtonian fluid, Int. J. Non-linear Mech. 18 (1983), 313-320.
http://dx.doi.org/10.1016/0020-7462(83)90028-8
H. T. Lin and L. K. Lin, Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number, Int. J. Heat Mass Trans. 30(1987) ,1111-1118.
http://dx.doi.org/10.1016/0017-9310(87)90041-x
T. Watanabe, Thermal boundary layers over a wedge with uniform suction or injection in forced flow, Acta Mech. 83 (1990), 119-126.
http://dx.doi.org/10.1007/bf01172973
M. Kumari, H.S. Takhar and G. Nath, Mixed convection flow over a vertical wedge embedded in a highly porous medium, Heat Mass Trans. 37(2001), 139-146.
http://dx.doi.org/10.1007/s002310000154
B. L. Kuo, Heat transfer analysis for the Falkner–Skan wedge flow by the differential transformation method, Int. J. Heat Mass Transf. 48(2005), 5036-5046.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2003.10.046
A. Isak, R. Nazar and I. Pop, Falkner-Skan equation for flow past a moving wedge with suction or injection, J. Appl. Math & Computing 25 (2007), 67-83.
http://dx.doi.org/10.1007/bf02832339
M. M. Rahman and I. A. Eltayeb, Convective slip flow of rarefied fluids over a wedge with thermal jump and variable transport properties, Int. J. Thermal Sci. 50(2011), 468-479.
http://dx.doi.org/10.1016/j.ijthermalsci.2010.10.020
R.G. Abdel-Rahman, Group classification of the dispersion equation of gaseous pollutants in presence of a temperature inversion, J. Quantitative Spectroscopy & Radiative Trans. 98(2006), 1-17.
http://dx.doi.org/10.1016/j.jqsrt.2005.05.068
P. J. Olver, Applications of Lie Groups to Differential Equations, (vol. 107 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1986).
http://dx.doi.org/10.1007/978-1-4684-0274-2
G. W. Bluman and S. Kumei, Symmetries and Differential Equations, (vol. 81 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1989).
http://dx.doi.org/10.1007/978-1-4757-4307-4
N. H. Ibragimov and et al., CRC Handbook of Lie Group Analysis of Differential Equations, (Vol. I, II, and III, CRC Press, Boca Raton, 1994-1996).
M.B. Abd-el-malek and H.S. Hassan, Symmetry analysis for steady boundary-layer stagnation-point flow of Rivlin–Ericksen fluid of second grade subject to suction, Nonlinear Analysis: Modelling and Control 15 (2010), 379-396.
M.A.A. Hamad, M.J. Uddin and A.I.M. Ismail, Investigation of combined heat and mass transfer by Lie group analysis with variable diffusivity taking into account hydrodynamic slip and thermal convective boundary conditions, Int. J. Heat Mass Trans. 55(2012) , 1355–1362.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2011.08.043
KH. S. Mekheimer, S. Z. A. Husseny, A. T. Ali and R. E. Abo–Elkhair, , Similarity solution for flow of a micro-polar fluid through a porous medium, A.A.M. 6 (2011), 2082-2093.
M.A.A. Hamad and M. Ferdows, Similarity solutions of boundary layer stagnation-point flow towards a heated porous stretching sheet saturated with a nanofluid with heat absorption/generation and suction/blowing: A Lie group analysis, Commun. Nonlinear. Sci. Numer. Simulat. 17 (2012) , 132-140.
http://dx.doi.org/10.1016/j.cnsns.2011.02.024
I.A. Hassanien, H.M. El-Hawary, R. G. Abdel-Rahman and A.S. Elfeshawey, Corrigendum of ‘‘Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate’’[International Journal of Non-Linear Mechanics 38 (2003), 513–520 ], Inter. J. Non-Linear Mech. 47(2012), 719-725.
http://dx.doi.org/10.1016/j.ijnonlinmec.2011.11.003
M. Jalil and S. Asghar, Flow of power-law fluid over a stretching surface: A Lie group analysis, Inter. J. Non-Linear Mech. 48 (2013) , 65 –71.
http://dx.doi.org/10.1016/j.ijnonlinmec.2012.07.004
K.A. Yih, Uniform suction blowing effect on forced-convection about a wedge - uniform heat-flux, Acta Mech. 128 (1998), 173–181.
http://dx.doi.org/10.1007/bf01251888
A. Posteinicu, and I. Pop, Falkner–Skan boundary layer flow of a power-law fluid past a stretching wedge, Appl. Math. Comput. 217(2011) , 4359-4368.
http://dx.doi.org/10.1016/j.amc.2010.09.037
Refbacks
- There are currently no refbacks.
Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2024 Praise Worthy Prize