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PLOS ONE  2013 

Mixed Convection Boundary Layer Flow over a Moving Vertical Flat Plate in an External Fluid Flow with Viscous Dissipation Effect

DOI: 10.1371/journal.pone.0060766

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Abstract:

The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.

References

[1]  Tadmor Z, Klein I (1970) Engineering Principles of Plasticating Extrusion, Polymer Science and Engineering Series. Van Norstrand Reinhold, New York.
[2]  Bejan A (1995) Convection Heat Transfer (2nd ed.). Wiley, New York.
[3]  Kays WM, Crawford ME (2005) Convective Heat and Mass Transfer (4th ed.). McGraw Hill, New York, 2005.
[4]  Bergman TL, Lavine AS, Incropera FP, Dewitt DP (2011) Fundamentals of Heat and Mass Transfer (7th ed.). Wiley, New York.
[5]  Abraham JP, Sparrow EM (2005) Friction drag resulting from the simultaneous imposed motions of a freestream and its bounding surface. Int. J. Heat Fluid Flow 26: 289–295.
[6]  Sparrow EM, Abraham JP (2005) Universal solutions for the streamwise variation of the temperature of a moving sheet in the presence of a moving fluid. Int. J. Heat Mass Transfer 48: 3047–3056.
[7]  Jaluria Y (1992) Transport from continuously moving materials undergoing thermal processing. Ann. Rev. Heat Transfer 4: 187–245.
[8]  Karwe MV, Jaluria Y (1998) Fluid flow and mixed convection transport from a moving plate in rolling and extrusion processes. ASME J. Heat Transfer 11: 655–661.
[9]  Afzal N, Badaruddin A, Elgarvi AA (1993) Momentum and heat transport on a continuous flat surface moving in a parallel stream. Int. J. Heat Mass Transfer 36: 3399–3403.
[10]  Afzal N (1993) Heat transfer from a stretching surface. Int. J. Heat Mass Transfer 36: 1128–1131.
[11]  Afzal N (2003) Momentum transfer on power law stretching plate with free stream pressure gradient. Int. J. Engng. Sci. 41: 1197–1207.
[12]  Fang F (2003) Further study on a moving-wall boundary-layer problem with mass transfer. Acta Mech. 163: 183–188.
[13]  Fang T, Lee–fon F (2005) A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate. Appl. Math. Letters 18: 487–495.
[14]  Weidman PD, Kubitschek DG, Davis AMJ (2006) The effect of transpiration on self-similar boundary layer flow over moving surfaces. Int. J. Engng. Sci. 44: 730–737.
[15]  Ishak A, Nazar R, Pop I (2007) Bounadry layer on a moving wall with suction or injection. Chin Phys Letter 8: 2274–2276.
[16]  Dey J, Nath G (1981) Mixed convection flow on vertical surface. W?rme- und Stoffübertr 15: 279–283.
[17]  Hieber CA (1973) Mixed convection above a heated horizontal surface. Int. J. Heat Mass Transfer 16: 769–785.
[18]  Schneider W (1979) A similarity solution for combined forced and free convection flow over a horizontal plate. Int. J. Heat Mass Transfer 22: 1401–1406.
[19]  Afzal N, Hussain T (1984) Mixed convection over a horizontal plate. J. Heat Trans-T ASME 106: 240–241.
[20]  Ishak A (2009) Mixed convection boundary layer flow over a horizontal plate with thermal radiation. Heat Mass Transfer 46: 147–151.
[21]  Ishak A, Nazar R, Pop I (2006) The Schneider problem for a micropolar fluid. Fluid Dyn. Res. 38: 489–502.
[22]  Ingham DB (1986) Singular and non-unique solutions of the boundary-layer equations for the flow due to free convection near a continuously moving vertical plate. Z. Angew. Math. Phys. 37: 559–572.
[23]  Merkin JH (1985) On dual solutions occuring in mixed convection in a porous medium. J. Eng. Math. 20: 171–179.
[24]  Xu H, Liao S-J (2008) Dual solutions of boundary layer flow over an upstream moving plate. Commun. Nonlinear Sci. Numer. Simulat. 13: 350–358.
[25]  Ishak A, Nazar R, Pop I (2007) Boundary layer on a moving wall with suction and injection. Chin. Phys. Lett. 24: 2274–2276.
[26]  Ishak A, Nazar R, Pop I (2009) Flow and heat transfer characteristics on a moving flat plate in a parallel stream with constant surface heat flux. Heat Mass Transfer 45: 563–567.
[27]  Bachok N, Ishak A (2010) The effects of suction and injection on a moving flat plate in a parallel stream with prescribed surface heat flux. WSEAS Trans. Heat Mass Transfer 5: 73–82.
[28]  Chen C-H (2003) Convection cooling of a continuously moving surface in manufacturing processes. J. Mater. Process. Tech. 138: 332–338.
[29]  Bataller RC (2008) Similarity solutions for flow and heat transfer of a quiescent fluid over a nonlinearly stretching surface. J. Mater. Process. Tech. 203: 176–183.
[30]  Bachok N, Ishak A, Pop I (2010) Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. Int. J. Thermal Sci. 49: 1663–1668.
[31]  Ishak A, Nazar R, Pop I (2006) Flow of a micropolar fluid on a continuous moving surface. Arch. Mech. 58: 529–541.
[32]  Ishak A, Nazar R, Pop I (2006) Moving wedge and flat plate in a micropolar fluid. Int. J. Eng. Sci. 44: 1225–1236.
[33]  Ishak A, Nazar R, Pop I (2006) Unsteady mixed convection boundary layer flow due to a stretching vertical surface. Arabian J. Sci. Eng. 31: 165–182.
[34]  Aman F, Ishak A (2012) Mixed convection boundary layer flow towards a vertical plate with a convective surface boundary condition. Math. Prob. Eng 2012: Article ID 453457.
[35]  Postelnicu A, Pop I (2011) Falkner-Skan boundary layer flow of a power-law fluid past a stretching wedge. Appl. Math. Comp. 217: 4359–4368.
[36]  Rosca AV, Pop I (2013) Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. Int. J. Heat Mass Transfer 60: 355–364.
[37]  Fang T-G, Zhang J, Yao S-S (2009) Viscous flow over an unsteady shrinking sheet with mass transfer. Chin. Phys. Lett. 26: 014703–1–014703-4.

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