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Transport in Porous Media

, Volume 75, Issue 2, pp 249–267 | Cite as

Effects of Temperature-Dependent Viscosity on Forced Convection Inside a Porous Medium

  • K. HoomanEmail author
  • H. Gurgenci
Article

Abstract

Considering the exponential viscosity–temperature relation, effect of temperature-dependent viscosity on forced convection of a liquid through a porous medium, bounded by isoflux parallel plates, is investigated numerically based on the general model of momentum transfer. Local effects of viscosity variation on the distribution of velocity and temperature are analyzed. Moreover, global aspects of the problem are investigated where corrections are proposed for total pressure drop and the fully developed Nusselt number, in the form of out/in viscosity ratio. Results are obtained over a wide range of permeabilities from clear (of solid material) fluid to very low permeability, where for constant properties one expects a nearly slug flow.

Keywords

Forced convection Property variation Porous media Thermohydraulic 

Nomenclature

a

Aspect ratio, a = L/H

b

Viscosity variation number

CF

Inertia coefficient

Cf

Boundary frictional drag coefficient

Da

Darcy number, Da = K/H 2

eNu

Relative effect of viscosity variation on Nu, |Nu − Nu cp|/Nu cp

ep

Relative effect of viscosity variation on pressure drop, |ΔP − ΔP cp|/ΔP cp

H

Half-channel width, m

k

Porous medium thermal conductivity, W/m K

K

Permeability, m2

L

Channel length, m

Nu

Nusselt number

p*

Pressure, Pa

p+

Dimensionless pressure, p + =  − εp */(μU)in

Pr

Modified Prandtl number, Pr = εν/α

q′′

Wall heat flux, W/m2

Re

Reynolds number, Re = 4ρ HU in/(εμ in)

s

Porous media shape parameter (ε/Da)1/2

\({S_{\varphi}}\)

Source term for \({\varphi}\) equation

Sω

Source term for vorticity transport equation

T*

Temperature, K

Tinv

Invariant temperature profile, T inv = (T − T w)/(T m − T w),

u*, v*

(x *, y *) velocity, m/s

(u, v)

(u *,v*)/U in

|U*|

Mean velocity \({\sqrt{u^{\ast 2}+v^{\ast 2}}}\) , m/s

|U|

Dimensionless mean velocity\({\sqrt{u^{2}+v^{2}}}\)

(x*, y*)

Longitudinal/transverse coordinate, m

(x, y)

(x *, y *)/H

Greek symbols

α

Thermal diffusivity of the porous medium, m2/s

ε

Porosity

\({\Gamma_{\varphi}}\)

Diffusion parameter, m2/s

Λ

Inertial parameter, Λ  = C F ε 3/2

θ

Dimensionless temperature, k(T * − T in)/(q′′H)

η

Fluid viscosity ratio, μ/μ in

μ

Fluid viscosity, N s/m2

ρ

Fluid density, kg/m3

υ

Kinematic viscosity, m2/s

\({\varphi}\)

Generic variable

ψ

Dimensionless streamfunction

ω

Dimensionless vorticity

Subscript

cp

Constant property

in

Inlet condition

m

Bulk mean

o

Outlet condition

r

Ratio of variable/constant property for a variable

w

Wall

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of EngineeringThe University of QueenslandBrisbaneAustralia

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