Summary
The effect of uniform suction/blowing on steady two-dimensional laminar forced MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium is numerically analyzed. The nonlinear boundary-layer equation were transformed and the resulting ordinary differential equations were solved by Keller box method. Numerical results for the dimensionless velocity profiles, the temperature profiles, the local friction coefficient and the local Nusselt number are presented for various values of Prandtl number Pr, the Hartmann number M, exponent of wall temperature λ, the permeability parameter Ω, and suction/blowing parameterf w . Generally, it has been found that the local friction coefficient and the local Nusselt number increase owing to suction of fluid and increasing Ω. This trend reversed for blowing of fluid and decreasing Ω. The type of flow is from pure fluid flow for Ω is very small changed into pure Darcy flow for Ω is very large.
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Abbreviations
- A :
-
Constant defined in Eq. (4.1)
- B o :
-
Externally imposed magnetic field in the y-direction
- C :
-
Constant defined in Eq. (4.2)
- C f :
-
Local friction coefficient, 2ν(∂u/∂y) y=0 /U 2∞
- f :
-
Dimensionless stream function defined in Eq. (7.2)
- f w :
-
Suction/blowing parameter,\( - \upsilon _w /\sqrt {C\alpha } \)
- h :
-
Local heat transfer coefficient
- K :
-
Permeability of the porous medium
- k :
-
Thermal conductivity
- M:
-
Hartmann number,\(\sqrt {(\sigma B_0 ^2 )/(C\varrho )} \)
- Nux :
-
Local Nusselt number,hx/k
- Pex :
-
Local Pelect number U∞ x/a
- Pr:
-
Prandtl number, ν/α
- q w :
-
Wall heat flux
- Rex :
-
Local Reynolds number, U∞ x/ν
- T :
-
Temperature
- T w :
-
Wall temperature
- T ∞ :
-
Temperature of ambient fluid
- u :
-
Velocity component in the x-direction
- U ∞ :
-
Potential flow velocity,Cx
- υ:
-
Velocity component in the y-direction
- υ w :
-
Surface mass flux
- x :
-
Coordinate along the plate
- y :
-
Coordinate normal to the plate
- α:
-
Thermal diffusivity
- η:
-
Similarity variable defined in Eq. (7.1)
- θ:
-
Dimensionless temperature defined in Eq. (7.2)
- λ:
-
Exponent of wall temperature defined in Eq. (4.1)
- ν:
-
Kinematic viscosity
- ϱ:
-
Density
- σ:
-
Electrical conductivity
- φ:
-
Stream function
- Ω:
-
Permeability parameter, ν/(KC)
- w:
-
Surface condition
- ∞:
-
Condition far away from the surface
References
Hiemenz, K.: Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder. Dingl. Polytech. J.326, 321–410 (1911).
Eckert, E. R. G.: Die Berechnung des Wärmeüberganges in der laminaren Grenzschicht umströmter Körper. VDI Forschungsheft, p. 416. Berlin: VDI 1942.
Sparrow, E. M., Eckert, E. R., Minkowycz, W. J.: Transpiration cooling in a magnetohydrodynamic stagnation-point flow. Appl. Sci. Res. Sec. A11, 125–147 (1962).
Ariel, P. D.: Hiemenz flow in hydromagnetics. Acta Mech.103, 31–43 (1994).
Raptis, A. A., Takhar, H. S.: Flow through a porous medium. Mech. Res. Commun14, 327–329 (1987).
Takhar, H. S., Soundalgekar, V. M., Gupta, A. S.: Mixed convection of an incompressible viscous fluid in a porous medium past a hot vertical plate. Int. J. Non-Linear Mech.25, 723–728 (1990).
Takhar, H. S., Ram, P. C.: Magnetohydrodynamic free convection flow of water at 4°C through a porous medium. Int. Comm. Heat Mass Transfer21, 371–376 (1994).
Lai, F. C., Kulacki, F. A.: The influence of lateral mass flux on mixed convection over inclined surfaces in saturated porous media. ASME J. Heat Transfer112, 515–518 (1990).
Cebeci, T., Bradshaw, P.: Physical and computational aspects of convective heat transfer. p. 385. New York: Springer 1984.
Evans, H. L.: Mass transfer through laminar boundary layers. 7. Further similar solutions to the b-equation for the case B=0. Int. J. Heat Mass Transfer5, 35–57 (1962).
Lin, H. T., Lin, L. K.: Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number. Int. J. Heat Mass Transfer30, 1111–1118 (1987).
Gorla, R. S. R.: Nonsimilar axisymmetric stagnation flow on a moving cylinder. Int. J. Eng. Sci.18, 397–400 (1978).
Rosenhead, L.: Laminar boundary layer, p. 232. London: Oxford 1963).
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Yih, K.A. The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media. Acta Mechanica 130, 147–158 (1998). https://doi.org/10.1007/BF01184307
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DOI: https://doi.org/10.1007/BF01184307