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


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.


Forced convection Property variation Porous media Thermohydraulic 



Aspect ratio, a = L/H


Viscosity variation number


Inertia coefficient


Boundary frictional drag coefficient


Darcy number, Da = K/H 2


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


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


Half-channel width, m


Porous medium thermal conductivity, W/m K


Permeability, m2


Channel length, m


Nusselt number


Pressure, Pa


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


Modified Prandtl number, Pr = εν/α


Wall heat flux, W/m2


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


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


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


Source term for vorticity transport equation


Temperature, K


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


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


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

(x*, y*)

Longitudinal/transverse coordinate, m

(x, y)

(x *, y *)/H

Greek symbols


Thermal diffusivity of the porous medium, m2/s




Diffusion parameter, m2/s


Inertial parameter, Λ  = C F ε 3/2


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


Fluid viscosity ratio, μ/μ in


Fluid viscosity, N s/m2


Fluid density, kg/m3


Kinematic viscosity, m2/s


Generic variable


Dimensionless streamfunction


Dimensionless vorticity



Constant property


Inlet condition


Bulk mean


Outlet condition


Ratio of variable/constant property for a variable




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© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.School of EngineeringThe University of QueenslandBrisbaneAustralia

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