Entropy generation for forced convection in a porous channel with isoflux or isothermal walls

TLDR: In this article, a numerical study was performed to investigate the entropy generation due to forced convection in a parallel plate channel filled by a saturated porous medium, where two different thermal boundary conditions were considered being isoflux and isothermal walls.

Abstract: A numerical study is reported to investigate the entropy generation due to forced convection in a parallel plate channel filled by a saturated porous medium. Two different thermal boundary conditions are considered being isoflux and isothermal walls. Effects of the Peclet number, the porous medium shape factor, the dimensionless temperature difference for isothermal walls, the dimensionless heat flux for isoflux walls, and the Brinkman number on the Bejan number as well as the local and average dimensionless entropy generation rate are examined.

Figures

Table 1 The summary of the present and benchmark results for Nu (S=1).

Table 2 The summary of the present and benchmark results for Nu (S=1).

Figure 1-a,b Definition sketch

Figure 5 Plots of Ns and Be versus y at some streamwise locations (Br*=1, S=1)

Figure 6 Plots of Ns and Be versus y at some streamwise locations (Br*=10, S=1)

Figure 4 Plots of Ns and Be versus y at some streamwise locations (Br*=10)

Full text

Kamel Hooman et al. (2008) Int. J. Exergy, 5 (1) 78-96
1
Entropy generation for forced convection in a porous channel with isoflux or
isothermal walls
K. Hooman
1
, F. Hooman
2
, S.R. Mohebpour
3
1
School of Engineering, The University of Queensland, Brisbane, Australia
2
Chemical Engineering Faculty, Sharif University of Technology, Tehran, Iran
3
Mechnical Engineering Department, Persian Gulf University, Bushehr, Iran
and
3
School of Engineering, Islamic Azad University of Bushehr, Bushehr, Iran
Abstract
A numerical study is reported to investigate the entropy generation due to forced
convection in a parallel plate channel filled by a saturated porous medium. Two different
thermal boundary conditions are considered being isoflux and isothermal walls. Effects of
the Péclet number, the porous medium shape factor, the dimensionless temperature
difference for isothermal walls, the dimensionless heat flux for isoflux walls, and the
Brinkman number on the Bejan number as well as the local and average dimensionless
entropy generation rate are examined.
Key words: forced convection, channel, entropy generation, irreversibility, Bejan
number

Kamel Hooman et al. (2008) Int. J. Exergy, 5 (1) 78-96
2
Nomenclature
A area
a channel aspect ratio H/L
Be Bejan number
Br Darcy-Brinkman number
2 2
( )
i w
U H
k T T K
µ
−
for T and
2
U H
q K
µ
′′
for H
r
B
′
clear fluid Brinkman number Br/S
2
C
F
Forchheimer coefficient
c
P
specific heat at constant pressure
FFI
fluid friction irreversibility
H
half channel width
HTI
heat transfer irreversibility
k
porous medium thermal conductivity
K
permeability
L
channel length
Ns*
Area-weighted average of Ns
Ns
Entropy generation number
Nu
Nusselt number
P*
pressure
p
dimensionless pressure
Pe
the Péclet number
k
UHc
p
ρ
2
q"
wall heat flux

Kamel Hooman et al. (2008) Int. J. Exergy, 5 (1) 78-96
3
q*
dimensionless heat flux
Re*
2 /
UH
ρ µ
Re modified Reynolds number, Re*/
ε
2
S the shape factor
H/ K
gen
S
ɺ
Entropy generation rate per unit volume
T* dimensionless temperature difference
T temperature
T
in
Fluid inlet temperature
T
w
wall temperature
u* x-velocity
u u*/U
U inlet velocity
v* y-velocity
v v*/U
*x longitudinal coordinate
x x*/H
*y transverse coordinate
y y*/H
Greek symbols
ε
porosity
θ
dimensionless temperature

Kamel Hooman et al. (2008) Int. J. Exergy, 5 (1) 78-96
4
b
θ
dimensionless bulk temperature
µ
fluid viscosity
ρ
fluid density
ψ
dimensionless stream function
φ
dimensionless viscous dissipation function
*
φ
viscous dissipation function,
2
* /
U K
φ φ
=
ω
dimensionless vorticity
Ω
temperature ratio equal to (T
in
-T
w
)/ T
w
(
* /( )
in
q q H kT
′′
=
for
T (H)
case

Kamel Hooman et al. (2008) Int. J. Exergy, 5 (1) 78-96
5
1. Introduction
Analysis of forced convection in parallel plate channels saturated with porous medium
has been a subject of fundamental importance for being relevant to a lot of industrial
applications including thermal insulation, solid matrix heat exchangers, and
microelectronic heat transfer equipment as noted by Nield and Bejan (2006) or Bejan et
al. (2004). However, a quick search of the literature shows that the Second Law (of
Thermodynamics) aspects of non-Darcy forced convection through a parallel plate
channel has not been analyzed when the hydrodynamic or thermal boundary layers are
still to develop which is the subject of this study. On the other hand, a great deal of
information is available dealing with the Second Law analysis of similar problems. Abu-
Hijleh (2002) has reported a numerical analysis of entropy generation for cross-flow heat
transfer from a cylinder covered with a porous layer. Mahmud and Fraser (2003) have
analytically reported the Second Law analysis of fundamental convective heat transfer
problems. Later, Mahmud and Fraser (2004) extended their previous work to a steady
state conjugate problem. Baytas (2004) has reported an interesting analysis of entropy
generation for both natural and forced convection in a porous medium. Hooman (2005-
a,b) has analytically investigated entropy generation for slug flow forced convection
through ducts of circular and elliptical cross-section for the case when viscous dissipation
effects are significant. Another analysis of irreversibility has been reported by Hooman
and Gurgenci (2007-a) for fully developed slug flow through a porous duct of rectangular
cross-section. Applying the Brinkman flow model, Hooman and Ejlali (2006) dealt with
entropy production for thermally developing forced convection in a porous tube with the
effects of viscous dissipation being included. Hooman (2006) has presented a theoretical

Frequently asked questions

Q1. What have the authors contributed in "Entropy generation for forced convection in a porous channel with isoflux or isothermal walls" ?

A numerical study is reported to investigate the entropy generation due to forced convection in a parallel plate channel filled by a saturated porous medium. Effects of the Péclet number, the porous medium shape factor, the dimensionless temperature difference for isothermal walls, the dimensionless heat flux for isoflux walls, and the Brinkman number on the Bejan number as well as the local and average dimensionless entropy generation rate are examined. 

Q2. What is the second law of thermodynamics?

For an engineering (real) system the generated entropy is proportional to the destroyed exergy (which is always destroyed as a result of the Second Law; see Bejan (1982)). 

Q3. What is the reason for the decrease in Ns values?

For small values of x the value of Ns becomes constant after a short distance from the wall (moving downstream the distance increases) but for large values of x, i.e. in the fully developed region, Ns values continue to decrease till the duct centerline at y=1. 

Q4. What is the reason for the vanishing of the longitudinal temperature gradient?

One notes that vanishing the longitudinal temperature gradient will reduce HTI, and consequently Be, for the thermally fully developed region compared to the developing counterpart. 

Q5. What is the computational domain of the vorticity-stream function method?

The computational domain is symmetric above the horizontal mid-plane and therefore the lower half of the flow region is considered, as shown in figure 1-b, to reduce the computational time. 

Q6. What is the effect of different arrangement of the parameters on the Second Law aspects of the problem?

It is observed that, regardless of the boundary condition, increasing the porous media shape factor and the Brinkman number, and decreasing the dimensionless heat flux or temperature difference, increases the dimensionless degree of irreversibility of the problem, as reflected in Ns. Moreover, one concludes that different arrangement of the parameters will lead to completely different behavior for both Ns and Be as described. 

Q7. What is the resulting entropy generation rate?

The resulting entropy generation rate and the Bejan number variations are investigated as a function of the effective system parameters. 

Q8. What is the way to reduce the entropy generation rate?

Knowing the components that destroy the most exergy, one improves the efficiency by setting the optimized layout of the system in such a way that the minimum entropy be generated. 

Q9. What is the reason for the difference between Be and FFI?

This means that HTI is the dominant part of Ns as reflected in Be plots which are qualitatively similar to those of Ns. Moreover, Be puts on very high values (near unity which is the maximum possible value for Be) that confirms the dominant effect of HTI contribution to Ns over that of FFI. 

Q10. What is the entropy production for forced convection in a porous tube?

Applying the Brinkman flow model, Hooman and Ejlali (2006) dealt with entropy production for thermally developing forced convection in a porous tube with the effects of viscous dissipation being included.