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Combined free and forced convection in a porous medium between two vertical walls with viscous dissipation

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Abstract

Viscous dissipation effects in the problem of a fully-developed combined free and forced convection flow between two symmetrically and asymmetrically heated vertical parallel walls filled with a porous medium is analyzed. The equation of motion contains the modified Rayleigh number for a porous medium and the small-order viscous dissipation parameter. Particular attention is given to the solutions near the critical Rayleigh numbers at which infinite flow rates are predicted. Information concerning the multiplicity of solutions at critical Rayleigh numbers is also deduced from perturbation solutions of the governing equation.

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Abbreviations

A :

temperature gradient up the walls

C p :

specific heat of fluid

g :

gravitational acceleration

k :

effective thermal conductivity of the porous medium

K :

permeability of the porous medium

L :

distance between walls

m, n :

constants

q :

heat transfer rate

Q :

heat transfer parameter

Ra:

Rayleigh number

T :

temperature

T1, T2 :

wall temperatures atx=0 andx=L fory=0

T r :

reference temperature

v :

velocity in the vertical direction

v r :

reference velocity

V :

dimensionless velocity

x, y :

coordinates in horizontal and vertical directions

X :

dimensionless horizontal coordinate

α :

effective thermal diffusivity of the porous medium

β :

coefficient of volumetric expansion of the fluid

ɛ:

small parameter

μ :

dynamic viscosity of fluid

ν:

kinematic viscosity of fluid

ρ 0 :

fluid density at y=0

γ :

viscous dissipation parameter

λ :

constant

θ :

dimensionless temperature

ω :

constant involving pressure gradient

w:

condition at the wall

/:

differentiation with respect toX

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Authors and Affiliations

  1. Department of Applied Mathematical Studies, The University of Leeds, LS2 9JT, Leeds, West Yorkshire, England

    D. B. Ingham

  2. Faculty of Mathematics, University of Cluj, 253, Cluj, CP, Romania

    I. Pop

  3. Department of Mechanical Engineering, University of Hawaii at Manoa, 96822, Honolulu, HI, USA

    P. Cheng

Authors
  1. D. B. Ingham
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  2. I. Pop
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  3. P. Cheng
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Ingham, D.B., Pop, I. & Cheng, P. Combined free and forced convection in a porous medium between two vertical walls with viscous dissipation. Transp Porous Med 5, 381–398 (1990). https://doi.org/10.1007/BF01141992

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  • DOI: https://doi.org/10.1007/BF01141992

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