| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Viscous Slip MHD Flow over a Moving Sheet with an Arbitrary Surface Velocity |
| Tiegang Fang**, Fujun Wang |
Mechanical and Aerospace Engineering Department, North Carolina State University, Raleigh 27695, USA
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| Cite this article: |
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Tiegang Fang, Fujun Wang 2018 Chin. Phys. Lett. 35 104701 |
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Abstract The magnetohydrodynamic (MHD) flow induced by a stretching or shrinking sheet under slip conditions is studied. Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.
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Received: 17 June 2018
Published: 15 September 2018
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| PACS: |
47.10.ad
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(Navier-Stokes equations)
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47.15.Cb
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(Laminar boundary layers)
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52.30.Cv
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(Magnetohydrodynamics (including electron magnetohydrodynamics))
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| [1] | Fisher E G 1976 Extrusion of Plastics (New York: Wiley) | | [2] | Altan T, Oh S and Gegel H 1979 Metal Forming: Fundamentals and Applications (Metals Park, OH: American Society of Metals) | | [3] | Jaluria Y 2018 Continuous Materials Processing. In Advanced Materials Processing and Manufacturing (Cham: Springer) p 107 | | [4] | Sakiadis B C 1961 AIChE J. 7 26 | | [5] | Tsou F K, Sparrow E M and Goldstain R J 1967 Int. J. Heat Mass Transfer 10 219 | | [6] | Crane L J 1970 Z. Angew. Math. Phys. 21 645 | | [7] | Chen C K and Char M I 1988 J. Math. Anal. Appl. 135 568 | | [8] | Fang T 2008 Int. J. Heat Mass Transfer 51 2199 | | [9] | Magyari E and Keller B 2000 Eur. J. Mech. B 19 109 | | [10] | Liao S J 2005 Int. J. Heat Mass Transfer 48 2529 | | [11] | Wang C Y 1991 Annu. Rev. Fluid Mech. 23 159 | | [12] | Fang T, Zhang J and Yao S 2009 Chin. Phys. Lett. 26 014703 | | [13] | Asghar S, Afzal S and Ahmad A 2017 Chin. Phys. B 26 014704 | | [14] | Nadeem S and Hayat T 2016 Chin. Phys. B 25 114701 | | [15] | Bhattacharyya K, Hayat T and Alsaedi A 2014 Chin. Phys. B 23 124701 | | [16] | Ahmad A, Asghar S and Alsaedi A 2014 Chin. Phys. B 23 074401 | | [17] | Gal-el-Hak M 1999 J. Fluids Eng. Trans. ASME 121 5 | | [18] | Yoshimura A and Prudhomme R K 1988 J. Rheol. 32 53 | | [19] | Andersson H I 1995 Acta Mech. 113 241 | | [20] | Pop I and Na T Y 1998 Mech. Res. Commun. 25 263 | | [21] | Liao S J 2003 J. Fluid Mech. 488 189 | | [22] | Sajid M, Hayat T and Javed T 2007 Nonlinear Dyn. 51 259 | | [23] | Fang T G, Zhang J and Yao S S 2009 Commun. Nonlinear Sci. Numer. Simul. 14 3731 | | [24] | Fang T G, Zhang J and Yao S S 2010 Chin. Phys. Lett. 27 124702 | | [25] | Fang T G and Aziz A 2010 Z. Naturforsch. A 65 1087 | | [26] | Weidman P D and Magyari E 2010 Acta Mechanica 209 353 | | [27] | Fang T G ang Zhong Y F 2010 Commun. Nonlinear Sci. Numer. Simul. 15 3768 | | [28] | Ahmad A and Asghar S 2011 Appl. Math. Lett. 24 1905 | | [29] | Magyari E and Kumaran V 2010 Commun. Nonlinear Sci. Numer. Simul. 15 3237 | | [30] | Vleggaar J 1977 Chem. Eng. Sci. 32 1517 | | [31] | Ali M E 1995 Int. J. Heat Fluid Flow 16 280 | | [32] | Dean M M 1980 Annu. Rev. Fluid Mech. 12 365 | | [33] | Lage J L and Bejan A 1990 ASME J. Heat Transfer 112 92 | | [34] | Galtier S 2016 Introduction to Modern Magnetohydrodynamics (Cambridge: Cambridge University Press) |
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