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Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium

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Abstract

In this study, laminar boundary layer flow over a flat plate embedded in a fluid-saturated porous medium in the presence of viscous dissipation, inertia effect and suction/injection is analyzed using the Keller box finite difference method. The flat plate is assumed to be held at constant temperature. The non-Darcian effects of convection, boundary and inertia are considered. Results for the local heat transfer parameter and the local skin friction parameter as well as the velocity and temperature profiles are presented for various values of the governing parameters. The non-Darcian effects are shown to decrease the velocity and to increase the temperature. It is also shown that the local heat transfer parameter and the local skin friction parameter increase due to suction of fluid while injection reverses this trend. It is disclosed that the effect of the viscous dissipation for negative values of Ec (T w  < T ∞) is to enhance the heat transfer coefficient while the opposite is true for positive values of Ec (T w  > T ∞). The results are compared with those available in the existing literature and an excellent agreement is obtained.

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Abbreviations

c p :

Specific heat of the convective fluid

Ec :

Eckert number

f :

Dimensionless stream function

f w :

Suction/injection parameter

F :

Inertial coefficient

K :

Permeability of the porous medium

Pr :

Prandtl number

Re :

Reynolds number

T :

Temperature

u, υ:

Velocities in x and y directions, respectively

x, y :

Coordinates in horizontal and vertical directions, respectively

η :

Pseudo similarity variable, \(yRe_x^{1/2}/x\)

ε :

Porosity

ξ :

Non-similarity variable, vx/Ku ∞

γ :

Dimensionless inertia effect, F K 1/2 u ∞/v

ρ :

Fluid density

μ :

Dynamic viscosity

v :

Kinematic viscosity

θ :

Dimensionless temperature profile in Eq. 5

w :

Wall

∞:

Free stream

References

  • Al-Hadhrami A.K., Elliott L. and Ingham D.B. (2002). Combined free and forced convection in vertical channels of porous media. Transp. Porous Media 49(3): 265–289

    Article  Google Scholar 

  • Al-Hadhrami A.K., Elliott L. and Ingham D.B. (2003). A new model for viscous dissipation in porous media across a range of permeability values. Transp. Porous Media 53(1): 117–122

    Article  Google Scholar 

  • Aydin O. and Kaya A. (2005). Laminar boundary layer flow over a horizontal permeable flat plate. Appl. Math. Comput. 161(1): 229–240

    Article  Google Scholar 

  • Aydin O. and Kaya A. (2006). Mixed convection of a viscous dissipative fluid about a vertical flat plate embedded in a porous medium: constant wall temperature case. J. Porous Media 9(6): 559–580

    Article  Google Scholar 

  • Beckerman C. and Viskanta R. (1987). Forced convection boundary layer flow and heat transfer along a flat plate embedded in a porous medium. Int. J. Heat Mass Transfer 30(7): 1547–1551

    Article  Google Scholar 

  • Cebeci T. and Bradshaw P. (1984). Physical and Computational Aspects of Convective Heat Transfer. Springer, New York

    Google Scholar 

  • Chandrasekhara B.C. (1986). Solutions for axial and transverse boundary layers in the case of steady laminar flow past a horizontal plate embedded in a saturated porous medium. Warme Und Stoffubertragung-Thermo Fluid Dyn. 20(2): 105–110

    Article  Google Scholar 

  • Chang C.L. (2006). Numerical simulation of micropolar fluid flow along a flat plate with wall conduction and buoyancy effects. J. Phys. D Appl. Phys. 39(6): 1132–1140

    Article  Google Scholar 

  • Chamkha A.J., Mujtaba M., Quadri A. and Issa C. (2003). Thermal radiation effects on MHD forced convection flow adjacent to a non-isothermal wedge in the presence of heat source or sink. Heat Mass Transfer 39(4): 305–312

    Google Scholar 

  • El-Amin M.F. (2003). Combined effect of magnetic field and viscous dissipation on a power-law fluid over plate with variable surface heat flux embedded in a porous medium. J. Magn. Magn. Mater. 261(1–2): 228–237

    Article  Google Scholar 

  • Gupta A.S., Misra J.C. and Reza M. (2003). Effects of suction or blowing on the velocity and temperature distribution in the flow past a porous flat plate of a power-law fluid. Fluid Dyn. Res. 32(6): 283–294

    Article  Google Scholar 

  • Hady F.M. and Ibrahim F.S. (1997). Forced convection heat transfer on a flat plate embedded in porous media for power-law fluids. Transp. Porous Media 28(2): 125–134

    Article  Google Scholar 

  • Ingham D.B. and Pop I. (1998). Transport Phenomena in Porous Media I. Pergamon, New York

    Google Scholar 

  • Ingham D.B. and Pop I. (2002). Transport Phenomena in Porous Media II. Pergamon, New York

    Google Scholar 

  • Israel-Cookey C., Ogulu A. and Omubo-Pepple V.B. (2003). Influence of viscous dissipation and radiation on unsteady MHD free-convection flow past an infinite heated vertical plate in a porous medium with time-dependent suction. Int. J. Heat Mass Transfer 46(13): 2305–2311

    Article  Google Scholar 

  • Kaviany M. (1995). Principles of Heat Transfer in Porous Media. Springer, New York

    Google Scholar 

  • Kuznetsov A.V. and Nield D.A. (2006). Boundary layer treatment of forced convection over a wedge with an attached porous substrate. J. Porous Media 9(7): 683–694

    Article  Google Scholar 

  • Lauriat G. and Ghafir R. (2000). Forced convective heat transfer in porous media. In: Vafai, K. (eds) Handbook of Porous Media, pp 201–204. Marcel Dekker, New York

    Google Scholar 

  • Lin H.T. and Lin L.K. (1987). Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number. Int. J. Heat Mass Transfer 30: 1111–1118

    Article  Google Scholar 

  • Ling J.X. and Dybbs A. (1992). The effect of variable viscosity on forced convection over a flat plate submersed in a porous medium. J. Heat Trans.-T. Asme. 114(4): 1063–1065

    Article  Google Scholar 

  • Lloyd J.R. and Sparrow E.M. (1970). Combined forced and free convection flow on vertical surfaces. Int. J. Heat Mass Transfer 13(2): 434–438

    Article  Google Scholar 

  • Magyari E., Pop I. and Keller B. (2003). New similarity solutions for boundary-layer flow on a horizontal surface in a porous medium. Transp. Porous Media 51(2): 123–140

    Article  Google Scholar 

  • Mureithi E.W. and Mason D.P. (2002). On the stability of a forced-free boundary layer flow with viscous heating. Fluid Dyn. Res. 31(1): 65–78

    Article  Google Scholar 

  • Murthy P.V.S.N. and Singh P. (1997). Thermal dispersion effects on non-Darcy natural convection over horizontal plate with surface mass flux. Arch. Appl. Mech. 67(7): 487–495

    Article  Google Scholar 

  • Nield D.A. (2000). Resolution of paradox involving viscous dissipation and nonlinear drag in a porous medium. Transp. Porous Media 41(3): 349–357

    Article  Google Scholar 

  • Nield D.A. and Bejan A. (1999). Convection in Porous Media. Springer, New York

    Google Scholar 

  • Nield D.A and Kuznetsov A.V. (2003). Boundary layer analysis of forced convection with a plate and porous substrate. Acta Mech. 166: 141–148

    Article  Google Scholar 

  • Pop I. and Ingham D.B. (2001). Convective Heat Transfer. Pergamon, Amsterdam

    Google Scholar 

  • Postelnicu A., Groşan T. and Pop I. (2001). The effect of variable viscosity on forced convection flow past a horizontal flat plate in a porous medium with internal heat generation. Mech. Res. Commun. 28(3): 331–337

    Article  Google Scholar 

  • Sonth R.M., Khan S.K., Abel M.S. and Prasad K.V. (2002). Heat and mass transfer in a visco-elastic fluid flow over an accelerating surface with heat source/sink and viscous dissipation. Heat Mass Transfer 38: 213–220

    Article  Google Scholar 

  • Vafai K. (1984). Convective flow and heat transfer in variable-porosity media. J. Fluid Mech. 147: 233–259

    Article  Google Scholar 

  • Vafai K. and Tien C.L. (1980). Boundary and inertia effects on convective mass transfer in porous media. Int. J. Heat Mass Transfer 25: 1183–1190

    Article  Google Scholar 

  • Vafai K. and Tien C.L. (1981). Boundary and inertia effects on flow and heat transfer in porous media. Int. J. Heat Mass Transfer 24: 195–203

    Article  Google Scholar 

  • Vafai K., Alkire R.L. and Tien C.L. (1985). An experimental investigation heat transfer in variable porosity media. J. Heat Trans.-T. Asme. 107(3): 642–647

    Article  Google Scholar 

  • Yih K.A. (1998). Blowing/suction effect on non-Darcy forced convection flow about a flat plate with variable wall temperature in porous media. Acta Mech. 131(3–4): 255–265

    Article  Google Scholar 

  • Yih K.A. (1999). MHD forced convection flow adjacent to a non-isothermal wedge. Int. Commun. Heat Mass 26(6): 819–827

    Article  Google Scholar 

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Authors and Affiliations

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

    Orhan Aydın & Ahmet Kaya

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

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Aydın, O., Kaya, A. Non-Darcian Forced Convection Flow of Viscous Dissipating Fluid over a Flat Plate Embedded in a Porous Medium. Transp Porous Med 73, 173–186 (2008). https://doi.org/10.1007/s11242-007-9166-8

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  • DOI: https://doi.org/10.1007/s11242-007-9166-8

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