Ahsan A. (ed.) Evaporation, Condensation and Heat transfer
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Metal Foam Effective Transport Properties
299
5.3 Boiling heat transfer
The boiling curve (Figure 19) shows the heat flux as a function of the wall superheat (ΔT:
temperature difference between the wall and the fluid) in log-log scale. This curve was
measured for two cases (i) the foam welded to the wall and (ii) the foam just inserted in the
channel. The onset of boiling starts at very low superheat (
ΔT ~0.1 and 1°C, respectively)
compared to the “empty” channel whose
ΔT is about 10 °C. The heat flux strongly increases
when the superheat increases. The fluid velocity has no influence on the heat flux, even at
low superheat and very low fluid velocity (10–40 kg m-
2
.s
-1
). The critical heat flux, for which
the walls dry out (formation of an insulating vapor film on the walls leading to a
overheating), was not reachable with our set-up, and so, largely exceeds 30 kW.m
-2
even at
lowest tested velocity.
Performances of copper foam were compared to other fibrous materials. The boiling curve
obtained in the same conditions for bronze sintered fibers, which are known for their high
thermal performances (Tadrist et al., 2004) is similar to the foam inserted at low superheat.
However, when the superheat exceeds 10 °C, the heat flux is far smaller than the one
obtained in the foam.
The high performance of the foam is linked to its open structure that permits an easy
evacuation of the vapor formed near the wall. This improves the heat transfer and avoids
the phenomenon of dry out. Moreover, the pressure drop generated in the foam is 10 times
smaller than those in the sintered fibers for the same heat transfer and velocity conditions.
We present, on Figure 20, channel global heat exchange coefficient in boiling condition.
Local thermal disequilibrium associated with (partial) dryout of the wall is observable for
very low mass flux values for heat flux density greater than 10 Wcm
-2
. For all other tested
configurations the heat exchange coefficient decreases slightly with heat flux density. For a
given velocity the heat transfer coefficient is proportional to the heat flux in the studied
boiling regime. This indicates a stable behavior (no risk of burn-out) of any biphasic heat
exchanger working in these conditions of heat and mass flux.
Fig. 19. Boiling Curve: copper foam compared to sintered bronze fibers. *: inserted; x:
welded; stars: bronze fibers (Miscevic et al., 2002)
Evaporation, Condensation and Heat Transfer
300
1000
10000
100000
1 10 100
75
58
39
20
8
G (Kg m-2 s-1)
P (W/cm2)
h (W/m2 °C)
Déséquilibre
thermique
Fig. 20. Global Boiling heat transfer coefficient in a rectangular foamed channel versus heat
flux density for different n-pentane mass flux density. Copper Foam 40PPI.
6. Conclusion
We have discussed effective foam transport properties needed for heat exchanger design.
Size and determination method of representative elementary volume were given. Both pore
scale and macro-scale numerical simulations were used in conjunction with specific
experimental set up to achieve this comprehensive study. We have shown that 5 pores are
needed to get an accurate representation of metal foam for geometrical parameters as well
as pore diameter, specific surface or porosity, and for physical properties (Pressure, Darcy
scale velocity ...). Experimental set-up and direct numerical simulation Have been presented
to determine single- and two-phase flow laws as well as single-phase and boiling heat
exchange coefficients.
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15
Heat Transfer Performances and
Exergetic Optimization for Solar Heat Receiver
Jian-Feng Lu
1
and Jing Ding
School of Engineering,
Sun Yat-sen University,
China
1. Introduction
Solar energy is one kind of important resource for clean and renewable energy, and is
widely investigated in many fields. In order to increase the operating temperature and
thermodynamic efficiency, concentrated solar radiation is widely used to heat the working
fluid in solar thermal power system (Trieb & Nitsch, 1998) and other industrial engineerings
(Klein et al., 2007; Ali et al., 2008). Concentrated solar radiation (Kalogirou, 2004) can be
collected by the parabolic trough collector, parabolic dish reflector, heliostat field, etc. The
concentrated energy flux has been studied in kinds of solar energy system. Moustafa et al.
(1995) measured the solar flux density distribution on a plane receiver due to a flat heliostat.
Estrada et al. (2007) proposed a calorimeter to measure the concentrated solar power
produced by a point focus solar concentrator.
Solar thermal power system based on trough, dish or heliostat field is a very promising and
challenging technology for its high operating temperature and thermodynamic efficiency. In
solar thermal power plant (Odeh et al., 2003), the heat transfer medium in solar heat receiver
is heated by concentrated solar radiation to some high temperature, and then it can be used
to operate kinds of heat engine and generate electricity. As a result, the heat receiver (Ortega
et al., 2008) is the key problem for the photo-thermal transformation, and the heat transfer
performance of solar heat receiver is the hotspot for solar energy research. The basic types of
heat receiver in concentrated solar thermal system mainly include heat pipe receiver
(Fujiwara et al., 1990), parabolic trough solar receiver (Gong et al., 2010), cavity receiver (Wu
et al., 2010), and multistage solar receiver (Taragan, 1999), etc.
The dynamical and thermal characteristics of solar heat receiver have been investigated in
much literature (Cui et al., 2008; Grena, 2010). In general, the heat losses from solar receiver
mainly include three contributions: radiation heat loss, convective heat loss, and conduction
heat loss. The radiation heat loss (Melchior et al., 2008; Li et al., 2010) is mainly dependent
upon the receiver structure, wall temperature, and emissivity/absorptivity of the receiver
walls, while the convective heat loss (Clausing, 1981) is mainly determined by the receiver
structure, wall temperature, and wind velocity. The heat conduction loss (Zavoico, 2001)
exists in cavity receiver through the insulation wall, and it can be ignored in many solar heat
receivers.
1
Corresponding author
Evaporation, Condensation and Heat Transfer
304
In order to reduce the radiation heat loss, solar selective coatings are widely used in solar
heat receiver. Tabor (1958) first reported the solar selective coating to increase the
absorption efficiency of solar heat receiver. The ideal solar selective coating was considered
to have good optical performance with high absorptivity and low emissivity. Kennedy
(2002) introduced kinds of solar selective coatings under mid- to high-temperature
conditions. Cindrella (2007) studied the real utility ranges of the solar selective coatings.
Nilsson & Roos (2009) further evaluated the optical and thermal properties of coatings for
energy efficient windows. In general, solar selective coatings mainly have six types: intrinsic
coatings, semiconductor-metal tandems, multilayer coatings, multi-dielectric composite
coatings, textured surfaces, and selectively solar-transmitting coatings. Intrinsic coatings are
not effective enough but very stable, like metallic W (Agnihotri & Gupta, 1981), CaF
2
(Pellegrini, 1980), SnO
2
(Seraphin & Meinel, 1976) etc. Semiconductor-metal tandems as Si-
based design can be used in a wide temperature range (Seraphin, 1976). Multilayer coatings
(Andersson et al., 1980) can be very efficient for proper structure design. Metal-dielectric
composite coatings (Arancibia et al., 2000; Gao et al., 2000) have a high absorptivity in the
solar region, while that is transparent in the other region. Till now, solar selective coatings
have been critical important topic for solar energy research.
The convective heat loss (Siebers & Kraabel, 1984) is normally very difficult to determine but
very important for the total energy loss of solar heat receiver. Clausing (1983) predicted the
convective loss from solar central receivers from analytical model and experimental result.
LeQuere et al. (1981a, 1981b) experimentally reported Nusselt number correlations for
isothermal open cubical cavity for different inclination. Koenig & Marvin (1981) investigated
convective heat loss in open cavity solar receivers, and proposed a calculating model in a
large operating temperature range. Chan & Tien (1985, 1986) studied the laminar natural
convection in shallow open cavities. Leibfried & Ortjohann (1995) investigated convective
heat loss from upward and downward facing cavity receivers, and analyzed the effects of
wall temperature, tilt angle, aperture-radius, geometry, ribs, and ventilation. Khubeiznet et
al. (2002) measured natural convection heat transfer from an isothermal hemispherical
cavity. Taumoefolau et al. (2004) described the convective loss from electrically heated
cavity receiver under different inclinations and temperatures. Paitoonsurikarn et al. (2006)
simulated the convective loss from solar cylindrical receiver and dish concentrating receiver.
Sendhil & Reddy (2007, 2008) carried out numerical analyses of convective losses in
rectangular, hemispherical solar cavity receiver and modified cavity receivers, respectively.
In addition, the convective loss from heat receiver under wind condition is also investigated.
Ma (1993) reported the experimental investigations on the convective loss under wind.
Available literature also investigated combined heat loss from solar heat receiver including
convection and radiation. Lage et al. (1992) simulated natural convection and radiation in a 2-
D cavity with open end. McDonald (1995) reported the heat loss from an open cavity including
convection and radiation. Dehghan & Behnia (1996) numerically studied combined natural
convection conduction and radiation heat transfer in a discretely heated open cavity. Reddy &
Kumar (2008) investigated the combined laminar natural convection and surface radiation heat
transfer in a modified cavity receiver of solar parabolic dish. Prakash et al. (2009) investigated
the heat losses from a solar cavity receiver, and found the natural convection and radiation
played the premier role in the heat loss of the receiver. Muftuoglu & Bilgen (2008) simulated
heat transfer in inclined rectangular receivers for concentrated solar radiation.
The optimal structure design and operating conditions of solar heat receiver have also been
investigated by various methods. Harris & Lenz (1985) found the thermal and optical losses
from a cavity solar receiver were less than other types of receiver. Kaushika and Reddy (2000)
designed the modified cavity receiver to perform minimum heat loss from the receiver with
Heat Transfer Performances and Exergetic Optimization for Solar Heat Receiver
305
fuzzy focal dish concentrators. Steinfeld & Schubnell (1993) investigated the solar cavity
receiver, and educed the optimum aperture size and operating temperature by a semi
empirical method. Segal & Epstein (2003) analyzed the optimized working temperatures of a
solar central receiver. Kongtragool & Wongwises (2005) provided a theoretical analysis on the
optimum absorber temperature of a once-reflecting full conical concentrator for maximizing
the overall efficiency of a solar-powered low temperature differential Stirling engine.
Some researchers began to analyze the exergy transfer of solar collector and receiver. Bejan
et al. (1981) considered the solar collector systems using second law analysis and synthesis.
Singh et al. (2000) carried out the basic energy and exergetic analysis for typical solar
thermal power systems to evaluate the respective losses as well as exergetic efficiency under
given operating conditions. Farahat et al. (2009) developed an exergetic optimization
method of flat plate solar collectors to determine the optimal performance and design
parameters of these solar thermal energy conversion systems. Till now, few researchers
theoretically investigated the heat and exergy transfer performances of solar heat receiver
combined with forced convection and solar selective coating effects in detail.
The objective of this chapter is to report the heat and exergy transfer characteristics of solar
heat receiver under unilateral concentrated solar radiation based on our group’s research
works. The heat and exergy transfer model coupling of forced convection inside the receiver
and heat loss outside the receiver is first established, and the heat absorption performances
are calculated under different heat transfer media, solar selective coatings, incident energy
fluxes, inlet temperatures and velocities, and receiver structure. In addition, the uneven heat
transfer characteristics on the receiver surface are described due to the unilateral
concentrated solar radiation, and the exergetic efficiency of solar heat receiver is optimized
under kinds of operating condition.
2. Physical model and exergetic analyses of solar heat receiver
2.1 Physical model for solar heat receiver
To simplify solar heat receiver in solar thermal power system, a straight pipe with solar
selective coating is demonstrated as illustrated in Fig. 1. For theoretical investigation, the
thickness and thermal resistance of the pipe wall are ignored. In practical solar thermal
power system, the heat receiver is usually a cavity (Hogan et al., 1990) or evacuated tube (Li
& Wang, 2006) and the heat losses of the natural convection and radiation can be reduced
corresponding to that of the pipe receiver. As a result, the absorption efficiency of the pipe
receiver is lower than that of cavity receiver or evacuated tube, but it does not affect its basic
heat transfer performances under different heat transfer media, solar selective coatings,
incident energy fluxes, inlet temperatures and velocities, and receiver pipe radii.
Fig. 1. The physical model of heat transport in solar heat receiver
Evaporation, Condensation and Heat Transfer
306
The incident energy is directly concentrated by solar collector system, and its energy flux
density can be calculated by I
0
= Cк
0
I
s
, here C means concentration ratio, к
0
, the reflectivity of
the collector system, I
s
, solar energy flux. The incident energy flux on the receiver wall can
be expressed as:
0
IIsin=θ for sin 0θ≥ (1a)
I0= for sin 0θ< (1b)
The energy flux directly absorbed by solar heat receiver is only αI for the reflective effect,
here α means the absorptivity of solar selective coating. The natural convection outside the
receiver plays an important role in the heat loss, and its heat transfer coefficient is assumed
to be h
n
. At high temperature, the infrared radiation heat loss is very significant, and it can
be calculated as εσ(T
w
4
- T
s
4
), here T
w
means the receiver temperature, ε is the emissivity of
solar selective coating. Beside the optical reflection and heat losses, the incident energy is
used to increase the inner energy of the working fluid. According to the previous analyses,
the energy conservation equation can be expressed as (Lu et al., 2010a):
()
44
nw s w s f
Ih(T T) T T qα= − +ε⋅σ − + (2)
where T
s
denotes the environment temperature, q
f
means the convective heat flux inside the
receiver, and this equation has a good agreement with that derived by Kongtragool &
Wongwises (2005).
The convective heat flux inside the receiver can be calculated as:
()
ffwf
qhT T=⋅ −
(3)
where
R
p
0
f
R
p
0
cuT2rdr
T
cu2rdr
ρπ
=
ρπ
∫
∫
,
f
k
hNu
D
=⋅
.
For fully developed turbulent flow inside the receiver, the Nusselt number can be correlated
as (Lienhard IV & Lienhard V, 2002):
0.8 0.4
Nu 0.0243Re Pr= (4)
Substituting Eq. (3) into Eq. (2) yields
()
()
44
nw s w s f w f
Ih(T T) T T hT Tα= − +ε⋅σ − + − (5)
The local wall temperature can be directly derived from Eq. (5), and the energy transport
along the flow direction is:
22R
2
f
fp p av
000
T
qRd c uTrdrd c Ru
xx
ππ
∂∂
⋅ θ=ρ ⋅ θ=ρ ⋅π
∂∂
∫∫∫
(6)
where
T
f
and u
av
means the average fluid temperature and flow velocity.
Heat Transfer Performances and Exergetic Optimization for Solar Heat Receiver
307
2.2 Heat absorption and exergetic efficiency of heat receiver
The local heat absorption efficiency can be described as:
()
fw f
f
ab
hT T
q
II
−
η= = (7)
From Eq. (7), the absorption efficiency for a certain circumference can be calculated as:
2
f
0
ab
0
qRd
I2R
π
θ
η=
⋅
∫
(8)
From Eq. (8), the absorption efficiency of the whole receiver is:
L2 L
fab
00 0
ab
0
q(x)Rddx dx
I2RL L
π
⋅θ η
η= =
⋅
∫∫ ∫
(9)
Integrating Eq. (6) yields
x2 x
'2'
f
fpav
'
00 0
T
qRddx c Rudx
x
π
∂
⋅θ =ρ ⋅π
∂
∫∫ ∫
(10)
From Eq. (10), the inner energy increment due to heat absorption along the flow direction is
()
()
x2
'2
fpavff0
00
Ex q Rddx c Ru T T
π
Δ= ⋅θ=ρ⋅π ⋅−
∫∫
(11)
where
T
f0
is the inlet fluid temperature.
Exergy is defined as the maximum amount of work which can be produced by a system or a
flow of matter or energy as it comes to equilibrium with a reference environment (Kotas,
1995). In solar thermal power system, the electricity generation in the turbine cycle is
directly determined by the exergy increment in the heat receiver. Since concentrated solar
heat flux density is high enough, the pressure loss can be normally ignored in exergetic
analyses, and the exergy flow at a certain place of solar receiver will be:
2
f
pavfss
s
T
EcRu TTTln
T
•
⎡
⎤
⎛⎞
=ρ ⋅π ⋅ − −
⎢
⎥
⎜⎟
⎜⎟
⎢
⎥
⎝⎠
⎣
⎦
(12)
The exergy flow increment along the flow direction is:
() () ()
2
f
pavff0s
f0
T
Ex Ex E0 c Ru T T Tln
T
•••
⎡
⎤
⎛⎞
Δ=−=ρ⋅π ⋅−−
⎢
⎥
⎜⎟
⎜⎟
⎢
⎥
⎝⎠
⎣
⎦
(13)
From Eqs. (11) and (13), the exergetic efficiency of the absorbed energy is:
ff
s
ex,ab
ff f
ET T
T
E
1
EETT T
•
•
∂Δ ∂ ⋅ δ
δΔ
η= = =−
δΔ ∂Δ ∂ ⋅ δ
(14)
Evaporation, Condensation and Heat Transfer
308
Obviously, the exergetic efficiency of the absorbed energy is just equal to the Carnot
efficiency. From Eqs. (8) and (14), the exergetic efficiency of the incident energy flux is:
ex ab ex,ab
η=ηη (15)
The exergetic efficiency of the whole heat receiver (Lu et al., 2010b) is:
()
L
ex ex
0
0
EL
1
dx
I2RL L
•
Δ
η= = ⋅ η
⋅
∫
(16)
2.3 Caculation parameters
The heat transfer media in solar thermal power plant mainly include water/steam (Zarza et
al., 2004), molten salts (Reilly & Kolb, 2001) and air (Bai, 2010), etc. In order to analyze the heat
transfer performance of solar heat receiver in detail, the heat transfer media are assumed to be
Hitec heat transfer salt and air in present article. If the air is used as the heat transfer medium
at high temperatures, it can replace natural gas in a gas turbine with high thermodynamic
efficiency. In addition, Hitec heat transfer salt can also be used in a wide temperature range.
Though the properties of heat transfer media and solar selective coatings are normally
temperature dependent, the temperature non-dependent parameters of heat transfer media
and coatings are helpful for theoretical analyses. The properties of Hitec heat transfer salt
(Brenntag Company) and air (Lienhard IV & Lienhard V, 2002) are assumed to be constant
at the reference temperature of 573 K and atmospheric pressure, and their associated
parameters are presented in Table 1. The radiation parameters of solar selective coatings
(Cindrella, 2007) are illustrated in Tables 2.
Properties
Hitec heat transfer salt Air
ρ
1862 kgm
-3
1.77 kgm
-3
c
p
1510 Jkg
-1
K
-1
1006 Jkg
-1
K
-1
k
0.571 Wm
-1
K
-1
0.0181 Wm
-1
K
-1
μ
0.0030 kgm
-1
s
-1
0.0000134 kgm
-1
s
-1
Table 1. Properties of Hitec heat transfer salt and air (T
ref
=573 K, P
ref
=1 atm)
Material
α ε α/ε
Co-Cd-BT 0.96 0.12 8
Pyromark 0.93 0.83 1.12
Table 2. Radiation parameters of solar selective coatings
The heat transfer coefficient of natural convection
h
n
is 5.0 Wm
-2
K
- 1
, and the environment
temperature
T
s
=293 K. Besides, the basic geometrical parameters of solar heat receiver are
assumed to be
R=0.010 m.
3. Local heat transfer performances of heat receiver
3.1 Heat transfer performances with different heat transfer media
According to previous analyses, the local wall temperature and absorption efficiency can be
directly derived from Eqs. (5) and (7). Fig. 2 illustrates the wall temperature and absorption