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Magnetohydrodynamic natural convection heat transfer from radiate vertical porous surfaces

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Abstract.

Magnetohydrodynamic natural convection heat transfer from radiate vertical surfaces with fluid suction or injection is considered. The nonsimilarity parameter is found to be the conductive fluid injection or suction along the streamwise coordinate ξ = V{4x/υ2 gβ(T w – T ∞)}1/4. Three dimensionless parameters had been found to describe the problem: the magnetic influence number N = σB 2 y υ/ρV 2, the radiation-conduction parameter R d = kα R /4aT 3 ∞, and the Gebhart number Ge x = gβx/cp to represent the effect of the viscous dissipation. It is found that increasing the magnetic field strength causes the velocity and the heat transfer rates inside the boundary layer to decrease. Its apparent that increasing the radiation-conduction parameter decreases the velocity and enhances the heat transfer rates. The Gebhart number, i.e, the viscous dissipation had no effect on the present problem.

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Abbreviations

a :

Stefan-Boltzmann constant

B y :

Magnetic field flux density Wb/m2

Cf x :

Local skin friction factor

c p :

Specific heat capacity

f :

Dimensionless stream function

Ge x :

Gebhart number, gβx/cp

g :

Gravitational acceleration

k :

Thermal Conductivity

L :

Length of the plate

N :

Magnetic influence number, σB 2 y υ/ρV 2

p :

Pressure

Pr :

Prandtl number

q r :

Radiative heat flux

q w (x):

Local surface heat flux

Q w (x):

Dimensionless Local surface heat flux

R d :

Planck number (Radiation-Conduction parameter), kα R /4aT 3 ∞

T :

Temperature

T ∞ :

Free stream temperature

T w :

Wall temperature

u, v :

Velocity components in x- and y-directions

V :

Porous wall suction or injection velocity

V w :

Porous wall suction or injection velocity

x, y :

Axial and normal coordinates

α:

Thermal diffusivity

α R :

Roseland mean absorption coefficient, 4/3R d

β:

Coefficient of thermal expansion

ξ:

Nonsimilarity parameter, V{4x/υ2 gβ(T w – T ∞)}1/4

η:

Peseudo-similarity variable

θ:

Dimensionless temperature

θ w :

Ratio of surface temperature to the ambient temperature, T w /T ∞

μ:

Dynamice viscosity

υ:

Kinemtic viscosity

ρ:

Fluid density

σ:

Electrical conductivity

τ w :

Local wall shear stress

ψ:

Dimensional stream function

References

  1. Sparrow EM; Cess RD (1961) Effect of magnetic field on free convection heat transfer. Int J Heat Mass Transfer 3: 267–274

    Article  Google Scholar 

  2. Romig M (1964) The influence of electric and magnetic field on heat transfer to electrically conducting fluids. Adv Heat Transfer 1: 268–352

    Google Scholar 

  3. Riley N (1964) Magnetohydrodynamics free convection. J Fluid Mech 18: 577–586

    Google Scholar 

  4. Garandet JP; Alboussiere T; Moreau R (1992) Buoyancy driven convection in a rectangular enclosure with a transverse magnetic field. Int J Heat Mass Transfer 35: 741–749

    Article  CAS  Google Scholar 

  5. Sacheti NC; Chamdran P; Singh AK (1994) An exact solution for unsteady magnetohydrodynamic free convection flow with constant heat flux. Int Commun Heat Mass Transfer 21: 131–142

    Article  Google Scholar 

  6. Soundalgekar VM; Takhar HS; and Vighnesam NV (1960) The combined free and forced convection flow past a semi-infinite plate with variable surface temperature. Nuclear Eng Design 110: 95–98

    Article  Google Scholar 

  7. Hossain MA; Takhar HS (1996) Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Heat Mass Transfer 31: 243–248

    Article  CAS  Google Scholar 

  8. Hossain MA; Alim MA; Rees DA (1999) The effect of radiation on free convection from a porous vertical plate. Int J Heat Mass Transfer 42: 181–191

    Article  CAS  Google Scholar 

  9. Eckert ER (1958) Mass transfer cooling of a laminar boundary by injection of a light weight foreign gas. Jet Propulsion 28: 34–39

    Google Scholar 

  10. Sparrow EM; Cess RD (1961) Free convection with blowing or suction. J Heat Transfer 83: 387–396

    Google Scholar 

  11. Merkin HJ (1975) The effects of blowing and suction on free convection boundary layers. Int J Heat Mass Transfer 18: 237–244

    Article  Google Scholar 

  12. Clarke JF (1973) Transipiration and natural convection, the vertical flat plate problem. J Fluid Mech 57: 45–61

    Google Scholar 

  13. Lin HT; Yu WS (1976) Free convection on a horizontal plate with blowing and suction. Trans ASME J Heat Transfer 110: 415–431

    Google Scholar 

  14. Keller HB (1988) Numerical methods in boundary layer theory. Ann Rev Fluid Mech 10: 793–796

    Google Scholar 

  15. Ali MM; Chen TS; Armaly BF (1984) Natural convection radiation interaction. In: Boundary layer flow over horizontal surfaces. AIAA J 22: 1797–1803

    Google Scholar 

  16. Cebeci T; Bradshaw P (1984) Physical and computational aspects of convective heat transfer, Springer, New York

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering and Technology, The University of Jordan, Amman-Jordan

    H. M. Duwairi

  2. Mechanical Engineering Department, Albalqa Applied University, Al husn University College, Irbid-Jordan

    Rebhi A. Damseh

Authors
  1. H. M. Duwairi
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  2. Rebhi A. Damseh
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Correspondence to H. M. Duwairi.

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Duwairi, H.M., Damseh, R.A. Magnetohydrodynamic natural convection heat transfer from radiate vertical porous surfaces. Heat Mass Transfer 40, 787–792 (2004). https://doi.org/10.1007/s00231-003-0476-2

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  • DOI: https://doi.org/10.1007/s00231-003-0476-2

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