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Heat and Mass Transfer

, Volume 41, Issue 6, pp 568–575 | Cite as

Conjugate heat transfer inside a porous channel

  • Shohel MahmudEmail author
  • Roydon Andrew Fraser
Original

Abstract

Analytical and numerical analyses have been performed for fully developed forced convection in a fluid-saturated porous medium channel bounded by two parallel plates. The channel walls are assumed to be finite in thickness. Conduction heat transfer inside the channel wall is also accounted and the full problem is treated as a conjugate heat transfer problem. The flow in the porous material is described by the Darcy–Brinkman momentum equation. The outer surfaces of the solid walls are treated as isothermal. A temperature dependent volumetric heat generation is considered inside the solid wall only. Analytical expressions for velocity, temperature, and Nusselt number are obtained after simplifying and solving the governing differential equations with reasonable approximations. Subsequent results obtained by numerical calculations show an excellent agreement with the analytical results.

Keywords

Porous Medium Nusselt Number Solid Wall Darcy Number Axial Conduction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Cm

constants of integration, m=1, 2, 3, and 4

Cp

specific heat of the fluid at constant pressure (kJ kg−1 °C−1)

Da

Darcy number = K/w2

Ec

Eckert number

G

dimensionless heat generation parameter

h

convective heat transfer coefficient (W m−2 °C−1)

K

permeability of the porous media (m2)

kf

thermal conductivity of the fluid (W m−1 °C−1)

ks

thermal conductivity of the solid (W m−1 °C−1)

L

length of the channel (m)

Nu

Nusselt number = hw/kf

p

dimensionless pressure

p*

pressure (Pa)

Re

Reynolds number

T

temperature of the fluid (°C)

u

dimensionless axial velocity

u*

axial velocity inside the channel (m s−1)

v

dimensionless transverse velocity

v*

transverse velocity (m s−1)

w

half width of a channel (m)

Greek symbols

α

clearance ratio

β

blockage ratio

αf

thermal diffusivity of the fluid (m2 s−1)

αs

thermal diffusivity of the solid (m2 s−1)

Γ

a parameter (see Eq. 22)

Φ0

a parameter (see Eq. 16)

ε

solid–fluid conductivity ratio = ks/kf

μ

dynamic viscosity of the fluid (Pa s)

ν

kinematic viscosity of the fluid (m2 s−1)

Ψ

a parameter (see Eq. 21)

Θ

dimensionless temperature

ρf

density of the fluid (kg m−3)

ρs

density of the solid (kg m−3)

Subscripts and superscripts

0

reference value

m

mean value

s

property or parameter related to solid

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Department of Mechanical Engineering (E3–2136C)University of WaterlooWaterlooCanada

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