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Transport in Porous Media

, Volume 86, Issue 1, pp 177–198 | Cite as

Steady and Unsteady Heat Transfer in a Channel Partially Filled with Porous Media Under Thermal Non-Equilibrium Condition

  • Pourya Forooghi
  • Mahdi Abkar
  • Majid Saffar-Avval
Article

Abstract

Steady and pulsatile flow and heat transfer in a channel lined with two porous layers subject to constant wall heat flux under local thermal non-equilibrium (LTNE) condition is numerically investigated. To do this, a physical boundary condition in the interface of porous media and clear region of the channel is derived. The objective of this work is, first, to assess the effects of local solid-to-fluid heat transfer (a criterion indicating on departure from local thermal equilibrium (LTE) condition), solid-to-fluid thermal conductivity ratio and porous layer thickness on convective heat transfer in steady condition inside a channel partially filled with porous media; second, to examine the impact of pulsatile flow on heat transfer in the same channel. The effects of LTNE condition and thermal conductivity ratio in pulsatile flow are also briefly discussed. It is observed that Nusselt number inside the channel increases when the problem is tending to LTE condition. Therefore, careless consideration of LTE may lead to overestimation of heat transfer. Solid-to-fluid thermal conductivity ratio is also shown to enhance heat transfer in constant porous media thickness. It is also revealed that an increase in the amplitude of pulsation may result in enhancement of Nusselt number, while Nusselt number has a minimum in a certain frequency for each value of amplitude.

Keywords

Local thermal non-equilibrium condition Porous media Pulsatile flow Heat transfer enhancement 

List of Symbols

A

Amplitude

asf

Specific solid–fluid interface area

Bi

Modified Biot number

CF

Forchheimer coefficient

cp

Specific heat capacity of fluid

Da

Darcy number

dp

Diameter of particles forming porous medium

e

Thickness of porous layer

f

Frequency

h

Solid-to-fluid heat transfer coefficient

H

Channel’s half width

k

Thermal conductivity

K

Permeability

Nu

Nusselt number

p

Pressure

Pr

Prandtl number

Q

Rate of heat transfer

Reff

Ratio of thermal diffusivity

R

Radius of pipe

Re

Reynolds number

T

Dimensional temperature

u

Axial velocity

U

Velocity

x, y

Dimensional coordinates

X, Y

Dimensionless coordinates

Greek symbols

β

Womersley number

ε

Porosity

Φ

Phase lag

γ

Experimental constant

μ

Viscosity

θ

Dimensionless temperature

ρ

Density

σ

Thermal capacity ratio

Subscripts

ave

Time-averaged value

e

Effective value

f

Fluid

in

Inlet

p

Pressure

r

Ratio

s

Solid

S

Steady

sf

Solid-to-fluid ratio

w

Wall

u

Velocity

US

Unsteady

0, m

Mean value

Superscript

*

Dimensional variable

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Pourya Forooghi
    • 1
  • Mahdi Abkar
    • 1
  • Majid Saffar-Avval
    • 1
  1. 1.Department of Mechanical EngineeringAmirkabir University of TechnologyTehranIran

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