Transport in Porous Media

, Volume 69, Issue 2, pp 281–288

The effect of local thermal non-equilibrium on conduction in porous channels with a uniform heat source

  • Ali Nouri-Borujerdi
  • Amin R. Noghrehabadi
  • D. Andrew S. Rees
Original Paper

DOI: 10.1007/s11242-006-9064-5

Cite this article as:
Nouri-Borujerdi, A., Noghrehabadi, A.R. & Rees, D.A.S. Transp Porous Med (2007) 69: 281. doi:10.1007/s11242-006-9064-5

Abstract

We examine the effect of local thermal non-equilibrium on the steady state heat conduction in a porous layer in the presence of internal heat generation. A uniform source of heat is present in either the fluid or the solid phase. A two-temperature model is assumed and analytical solutions are presented for the resulting steady-state temperature profiles in a uniform porous slab. Attention is then focussed on deriving simple conditions which guarantee local thermal equilibrium.

Keywords

Local thermal non-equilibriumConductionPorous mediaInternal heat generation

Nomenclature

c

Specific heat

C1, C2, C3

Constants

h

Inter-phase heat transfer coefficient

H

Non-dimensional inter-phase heat transfer coefficient

k

Thermal conductivity

L

Length scale

\({q^{\prime\prime\prime}}\)

Rate of heat generation per unit volume

Q

Overall rate of heat generation

t

Time

Tf, Ts

Fluid and solid temperatures, respectively

T0

Ambient temperature

\({\underline \upsilon}\)

Velocity vector

x

Coordinate across the channel

y

Coordinate along the channel

Greek

 

γ

Porosity-scaled conductivity ratio

δ

Constant defined by Eq. 22

\(\epsilon\)

Porosity

ζ

Constant denoting internal heating contributions

η

Similarity variable

θ

Non-dimensional fluid temperature

λ

Constant

ρ

Density

τ

Scaled time

\(\phi\)

Non-dimensional solid temperature

ω

Non-dimensional diffusivity

Subscripts and superscripts

 

f

Fluid

s

Solid

\(\hat{}\)

Dimensional

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Ali Nouri-Borujerdi
    • 1
  • Amin R. Noghrehabadi
    • 1
    • 2
  • D. Andrew S. Rees
    • 2
  1. 1.School of Mechanical EngineeringSharif University of TechnologyTehranIran
  2. 2.Department of Mechanical EngineeringUniversity of BathBathUK