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Conjugate-MHD mixed convection from a vertical flat plate in presence of viscous dissipation

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Abstract

The present article investigates MHD-mixed convection heat transfer about a thin vertical plate in the presence of viscous dissipation and wall conduction (i.e. conjugate) heat transfer effects. The fluid is assumed to be incompressible and dense. The Keller box method, an implicit finite difference method, is used in the solution of the nonlinear boundary layer equations, following their transformation into the non-similar ordinary equations. Comprehensive parametric tests are conducted to determine the effects of the mixed convection parameter Ri, the magnetic parameter Mn and viscous dissipation parameter Ec on the local skin friction and local heat transfer are presented graphically and analyzed.

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Abbreviations

B0 :

Magnetic field strength

c p :

Specific heat of the convective fluid

Ec:

Eccert number

f :

Dimensionless stream function

Gr:

Grashof number

Ha:

Hartman number

k :

Thermal conductivity

L:

Characteristic plate length of plate, \( L = \left( {{{U_{\infty } } \mathord{\left/ {\vphantom {{U_{\infty } } v}} \right. \kern-0pt} v}} \right)\left( {{{bk_{f} } \mathord{\left/ {\vphantom {{bk_{f} } {k_{s} }}} \right. \kern-0pt} {k_{s} }}} \right)^{2} \)

Mn:

Magnetic parameter, \( M = {{Ha} \mathord{\left/ {\vphantom {{Ha} {\text{Re} }}} \right. \kern-0pt} {\text{Re} }} \)

Re :

Reynolds number

u, υ :

Velocities in x and y directions, respectively

x, y :

Coordinates in horizontal and vertical directions, respectively

σ :

Magnetic permeability

β :

Coefficient of thermal expansion,

η :

Pseudo similarity variable, \( y\text{Re}_{x}^{1/2} /x \)

ξ :

Non-similarity variable, x/L

ρ :

Fluid density

υ :

Kinematic viscosity

θ :

Dimensionless temperature profile

s :

Solid

w :

Wall

∞ :

Free stream

References

  1. Azim MA, Mamun AA, Rahman AA (2010) Viscous joule heating MHD–conjugate heat transfer for a vertical flat plate in the presence of heat generation. Int Commun Heat Mass Transf 37:666–674

    Article  Google Scholar 

  2. Jafar K, Nazar R, Ishak A, Pop I (2012) MHD flow and heat transfer over stretching/shrinking sheets with external magnetic field, viscous dissipation and joule effects. Can J Chem Eng 90:1336–1346

    Article  Google Scholar 

  3. Prasad KV, Sujatha A, Vajravelu K, Pop I (2012) MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermo physical properties. Meccanica 47:1425–1439

    Article  MATH  MathSciNet  Google Scholar 

  4. Guedda M, Ouahsine A (2012) Similarity solutions of mhd flows in a saturated porous medium. Eur J Mech B Fluid 33:87–94

    Article  MATH  MathSciNet  Google Scholar 

  5. Kumar H (2013) Heat transfer in MHD boundary-layer flow through a porous medium, due to a non-isothermal stretching sheet, with suction, radiation, and heat annihilation. Chem Eng Commun 200:895–906

    Article  Google Scholar 

  6. Pal D, Mondal H (2012) Soret and Dufour effects on MHD non-Darcian mixed convection heat and mass transfer over a stretching sheet with non-uniform heat source/sink. Phys B Condens Matter 407:642–651

    Article  ADS  Google Scholar 

  7. Hsiao KL, Hsu CH (2009) Conjugate heat transfer of mixed convection for viscoelastic fluid past a horizontal flat-plate fin. Appl Therm Eng 29:28–36

    Article  Google Scholar 

  8. Miyamoto M, Sumikawa J, Akiyohi T, Nakamura T (1980) Effects of axial heat conduction in a vertical flat plate on free convection heat transfer. Int J Heat Mass Transf 23:1545–1553

    Article  ADS  Google Scholar 

  9. Sparrow EM, Chyu MK (1982) Conjugated forced convection–conduction analysis of heat transfer in a plate fin. J Heat Transf 104:204–206

    Article  Google Scholar 

  10. Char MI, Chen CK, Cleaver JW (1990) Conjugate forced convection heat transfer from a continuous, moving flat sheet. Int J Heat Fluid Flow 11(3):257–261

    Article  Google Scholar 

  11. Tewari SS, Jaluria Y (1990) Mixed convection heat transfer from thermal sources mounted on horizontal and vertical sources. J Heat Transf 112:975–987

    Article  Google Scholar 

  12. Pop I, Ingham B, Yuan Y (1996) Mixed convective conjugate heat transfer from a vertical flat plate, Zeithschrift für Angwandte Mathematik und Mechanik76 (5): 281 -289

  13. Wang TY (1998) The coupling of conduction with mixed convection of micro polar fluids past a vertical flat plate. Int Commun Heat Mass Transf 25(8):1075–1084

    Article  Google Scholar 

  14. Rao CG, Balaji C, Venkateshan SP (2001) Conjugate mixed convection with surface radiation from a vertical plate with a discrete heat source. J Heat Transf 123(4):698–702

    Article  Google Scholar 

  15. Rao CG, Balaji C, Venkateshan SP (2004) Effect of surface radiation on conjugate mixed convection in a vertical channel with a discrete heat source in each wall. Int J Heat Mass Transf 47(3):3331–3347

    Google Scholar 

  16. Chang CL (2006) Numerical simulation of micro polar fluid flow along a flat plate with wall conduction and buoyancy effects. J Phys D Appl Phys 39:1132–1140

    Article  ADS  Google Scholar 

  17. Mamun AA, Chowdhury ZR, Azim MA, Maleque MA (2008) Conjugate heat transfer for a vertical flat plate with heat generation effect. Nonlinear Anal Modell Control 13(2):213–223

    MATH  Google Scholar 

  18. Sawant SM, Rao CG (2010) Combined conduction-mixed convection-surface radiation from a uniformly heated vertical plate. Chem Eng Commun 97(6):881–899

    Article  Google Scholar 

  19. Kaya A (2011) Effects of buoyancy and conjugate heat transfer on non-darcy mixed convection about a vertical slender hollow cylinder embedded in a porous medium with high porosity. Int J Heat Mass Transf 54:818–825

    Article  MATH  Google Scholar 

  20. Kumar GG, Rao CG (2011) Interaction of surface radiation with conjugate mixed convection from a vertical plate with multiple non identical discrete heat sources. Chem Eng Commun 198(5):692–710

    Article  Google Scholar 

  21. Kumar GG, Rao CG (2012) Parametric studies sand correlations for combined conduction-mixed convection–radiation from a non-identically and discretely heated vertical plate. Heat Mass Transf 48:505–517

    Article  ADS  Google Scholar 

  22. Damseh RA, Duwairi HM, Al-Odat M (2006) Similarity analysis of magnetic field and thermal radiation effects on forced convection flow. Turk J Eng Environ Sci 30:83–89

    Google Scholar 

  23. Cebeci T (1984) Convective heat transfer, 2nd edn. Horizons Publishing Inc., Long Beach, California

    MATH  Google Scholar 

  24. Takhar HS, Beg OA (1997) Effects of transverse magnetic field, Prandtl number and Reynolds number on non-Darcy mixed convective flow of an incompressible viscous fluid past a porous vertical flat plate in a saturated porous medium. Int J Energy Resour 21:87–100

    Article  Google Scholar 

  25. Lloyd JR, Sparrow M (1970) Combined force and free convection flow on vertical surfaces. Int J Heat Mass Transf 13:434–438

    Article  Google Scholar 

  26. Aydin O, Kaya A (2009) MHD mixed convection of a viscous dissipating fluid about a permeable vertical flat plate. Appl Math Model 33:4086–4096

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanical Engineering, Kahramanmaras Sutcu Imam University, 46100, Kahramanmaras, Turkey

    Ahmet Kaya

  2. Department of Mechanical Engineering, Karadeniz Technical University, 61080, Trabzon, Turkey

    Orhan Aydin

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  1. Ahmet Kaya
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  2. Orhan Aydin
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Correspondence to Orhan Aydin.

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Kaya, A., Aydin, O. Conjugate-MHD mixed convection from a vertical flat plate in presence of viscous dissipation. Meccanica 50, 2919–2926 (2015). https://doi.org/10.1007/s11012-015-0178-0

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