This document summarizes research analyzing heat losses in a compact Fresnel linear reflector solar power system with trapezoidal absorbers. The system aims to directly heat water to generate steam, improving efficiency over thermal oil systems. Heat loss is analyzed through adjusting cavity angles, depths, and insulation thickness. A thermal resistance circuit model is used to calculate heat losses from the absorber and cavity through convection and radiation. The goal is to determine the most efficient configuration for this concentrated solar power technology.

1. Page 1
Analysis of the Thermal Losses in the Innovative
Technology, the Compact Fresnel Linear Reflector with the
trapezoidal absorbers.
Capstone Research Course (E 194)
Name: Fang-Ming Lin
Department of Engineering Science
Major: Energy Engineering
Course supervisor: Van Carey
Department of Mechanical Engineering
Abstract
Concentrated Solar Power System (CSP) is the most proven technology for the solar energy
technology. The compact Fresnel Linear Reflector takes the concept of trough design and
enhance the efficiency and reduce the cost with a set of rows, flattening the parabolic
reflectors into flat mirrors. With this change, the mirrors are able to avoid the thermal oil used
in traditional receiver technology, the concentrated sun light is then used directly to heat
water, produce the superheated steam and improve the thermal efficiency. Since the efficiency
for the solar power system is extremely important, it would be analyzed through the heat loss
happens at the light absorber, with the adjusting cavity angles cavity depth and the insulation
thickness, heat loss would be analyzed for obtaining the most efficient configuration for the
technology of CSP.

2. Page 2
1. INTRODUCTION
1.1 The Compact Fresnel Linear Reflector
Concentrated solar power (CSP) is one of the most important candidate for providing the
majority of the energy source because of its cost-effective electricity technologies and its
potential for further technology improvements. The Compact Fresnel Linear Reflector is the
innovative design which is suitable for the large-scale solar thermal energy collection but also
efficiently uses the available power plant area, further reducing the cost with the low-cost
materials([3] Edkins et al). In traditional Fresnel Linear Reflector, there is only one absorber,
reflectors concentrate the sun light all to the only one linear system. For this design, it contains
many optical losses, especially the shading loss, with its geometric configuration that produces
the limits. With the Compact Fresnel Linear Reflector, its design system contains at least two
absorbers, which absorbs reflected sun light from a series of mirror that are put into different
configuration, the mirrors placed on the outside of the two absorbers maintain the same
configuration as the traditional Fresnel Linear Reflector, but for the mirrors sit between two
absorbers, each mirror faces to the opposite direction as to the adjacent one so that it reduces
the shading loss and enhance the optical efficiency ([10] Pye, John D et al).
1.2 Direct Steam Generation
For most of the innovative design of the Compact Fresnel Linear Reflector, it uses the
technology of direct steam generation to do the heat conversion. The basic idea of the Direct
Steam Generation is heating the water directly and generating steam from it without going
through from various energy mechanisms and transitions. Unlike the most common chosen
heat transfer fluids (HTF), the synthetic thermal oil or the molten salt; the direct steam
generation uses water as the heat transfer fluid and directly generates the steam with a more
simplified model by eliminating the complex heat exchanger component. With the usage of the
synthetic thermal oil or the molten salt, the maximum temperature the system can reach is
around 400 Celsius. With the application of direct steam generation, it is able to exceed the
limited temperature and reaches up to 550 Celsius ([1] Alguacil, M. et al). With this, the direct
steam generation enhances the efficiency by increasing the steam temperature, and avoids the
environmental risk that the traditional HTF can have.
2. DATA COLLECTION
2.1 Heat Transfer and Heat Loss on the Receiver
For the solar power collectors, each collector contains a concentrator and a receiver.
Two main types of concentrators are the nonimaging concentrator or the focusing
concentrator, and the two main types of receivers are the refracting lens type or the reflecting
mirror type. Therefore the performance for each solar collector is determined by two
parameter, the concentration and the acceptance angle ([14] Vieira, 2005).

3. Page 3
In order to analyze the heat transfer and heat loss, the design of the receiver is really
important, different factors will result in different effects on each design. The choice of the type
of receiver the concentrated power system was made of would determine the analysis for the
heat loss. There are two types of receiver designs, which later receiver designs deviate from
them but still sustain those fundamental concepts from the formers. These two types are the
Heat Loss from Linear, Omnidirectional Receiver and the Heat Loss from Cavity Receiver.
Furthermore, sizing the receiver will also alter different heat loss for the receiver, finding the
optimal receiver size is crucial to the design of the receiver. ([13] Stine, William B. et al). The
fundamental calculation is conducted by including the heat loss through convection and the
heat loss through the radiation:
𝑄𝑙𝑜𝑠𝑠,𝑔
̇ = ℎ 𝑔 𝐴 𝑔(𝑇𝑔 − 𝑇𝑎) + 𝜎 𝐵 𝜖 𝑔 𝐹𝑔 𝑎 𝐴 𝑔(𝑇𝑔
4
− 𝑇𝑠
4
) 𝐿𝑖𝑛𝑒𝑎𝑟, 𝑂𝑚𝑛𝑖𝑑𝑖𝑟𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑟𝑠
𝑄𝑙𝑜𝑠𝑠,𝑐𝑎𝑣
̇ = ℎ 𝑐𝑎𝑣 𝐴 𝑐𝑎𝑣(𝑇𝑐𝑎𝑣 − 𝑇𝑎) + 𝜎 𝐵 𝜖 𝑐𝑎𝑣 𝐹𝑐𝑎𝑣 𝐴 𝑐𝑎𝑣(𝑇𝑐𝑎𝑣
4
− 𝑇𝑠
4) 𝐶𝑎𝑣𝑖𝑡𝑦 𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑟𝑠
In this paper, since the focus is on the Compact Linear Fresnel Reflector, the heat loss
analysis would deviate from the fundamental ones, and follows the experimental model
performed by Reynolds and Jance at University of New South Wales ([6] Jance et al, 2000) and
later the calculation introduced by Pye from the same school ([9] Pye et al, 2003).
Instead of using a flat plate absorber, this model of Compact Linear Fresnel Reflector
uses the multi-tube solar collector structure that within the trapezoid absorber, there are
several numbers of the cylindrical absorber side-by-side arranged with each other. Since the
concentrator is the ratio of the aperture area to the receiver area, by decreasing the area of the
receiver, the concentrator is improved. ([8] Lievre, 2011)
The material chosen for the trapezoid absorber is aluminum. “A significant benefit of
aluminum and the aluminum extrusion process is the almost unlimited opportunity to adapt
the shape of the product to optimize performance, maximize stiffness and strength, and reduce
the number of parts to assemble and fabricate; all of which contribute to lowering cost” ([4]
Hydro Solar Solutions). If we were to find the temperature difference between the aluminum
wall and the surrounding temperature, we applied the Wiedemann-Franz law, k =
Lo 𝑇
𝜌
, where Lothe Lorenz number(2.45 × 10−8
𝑊 ∙ Ω ∙ 𝐾−2
). ([15] Woodcraft, 2005)
The model developed for this trapezoid absorber contains more parameters in order to
calculate the heat loss corresponding to its dimensions to the functions of the cavity depth or
he absorber temperature ([9] Pye et al, 2003). There are two parts of heat loss analysis, the
heat loss for the absorber and the heat loss for the cavity. Deriving from the fundamental heat
loss equation, the heat loss for absorber through radiation is kept the same and for the heat
loss through convection, the Nusselt number (Nu) and the Grashof number (Gr) are used for the
analysis.
𝑄𝑡𝑜𝑡𝑎𝑙 = 𝑄 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛 + 𝑄 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛

4. Page 4
Where radiative heat lows is:
𝑄 𝑟𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 = 𝐹𝑟𝑎𝑑 𝜎𝜖 𝑎(𝑇𝑎
4
− 𝑇𝑔
4
), 𝑤ℎ𝑒𝑟𝑒 𝐹𝑟𝑎𝑑 = 0.90
And here shows the relationship between Nu, Gr numbers, and the convective heat loss:
𝑁𝑢 =
𝑄 𝑐𝑜𝑣
𝑊
(
𝑘 𝑐
𝐷
) (𝑇𝑔 − 𝑇𝑎)
𝑁𝑢 = 1.1917𝐺𝑟0.10363
(
𝐷
𝑊
)
0.6432
𝐺𝑟 =
9.8𝛽𝑐(𝑇𝑎 − 𝑇𝑔)𝐷3
𝑣𝑐
2
, 𝑤ℎ𝑒𝑟𝑒 𝛽𝑐 𝑎𝑛𝑑 𝑣𝑐 𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝑇𝑐 =
1
2
(𝑇𝑎 + 𝑇𝑔)
The heat loss for the cavity for the cavity from the cavity is much simpler but unlike the
heat loss for the absorber that only convection heat loss is geometrically dependent, the
radiation heat loss for the cavity also depends on the width of the window. The equations are
given for the heat loss of convection at two sides of the walls and at the window, and the
radiation heat loss at the window:
𝑄 𝑤,𝑐𝑜𝑛𝑣 = 𝑁ℎ 𝑤(𝑇𝑐 − 𝑇𝑒) (𝐶𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛 ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠 𝑎𝑡 𝑡ℎ𝑒 𝑤𝑎𝑙𝑙)
𝑄 𝑔,𝑐𝑜𝑛𝑣 = 𝐵ℎ 𝑤(𝑇𝑔 − 𝑇𝑒) (𝐶𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛 ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠 𝑎𝑡 𝑡ℎ𝑒 𝑤𝑖𝑛𝑑𝑜𝑤)
𝑄 𝑔,𝑟𝑎𝑑 = 𝐵𝜖 𝑔 𝜎(𝑇𝑔
4
− 𝑇𝑒
4
) (𝑅𝑎𝑑𝑖𝑎𝑡𝑖𝑜𝑛 ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠 𝑎𝑡 𝑡ℎ𝑒 𝑤𝑖𝑛𝑑𝑜𝑤)
Here we notice that the radiation heat loss for the cavity does not include the Radiation
shape factor,𝐹𝑟𝑎𝑑, this is because the B, the width of the window has already taken the
geometrical consideration into account.
2.2 Analytic calculation
In this paper, instead of general heat loss computation, the approach to analyze the
heat loss is applying the most fundamental analogy, the Thermal Resistance Circuits. Here, a
brief introduction will be given. ([5] Incropera, Frank P)
From Ohm’s law
E! − 𝐸2
𝐼
=
𝐿
𝜎𝐴
We know that heat transfer by conduction is

5. Page 5
Qcond =
kA(T2 − 𝑇1)
𝐿
𝑤ℎ𝑒𝑟𝑒 𝑇2 𝑖𝑠 𝑡ℎ𝑒 ℎ𝑖𝑔ℎ 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒, 𝑎𝑛𝑑 𝑇1 𝑖𝑠 𝑡ℎ𝑒 𝑙𝑜𝑤 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒
Qconv = hA(Tw − 𝑇∞)
𝑤ℎ𝑒𝑟𝑒 𝑇 𝑤 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑜𝑏𝑗𝑒𝑐𝑡
𝑎𝑛𝑑 𝑇∞ 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑢𝑡𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑠𝑢𝑟𝑟𝑜𝑢𝑛𝑑𝑖𝑛𝑔 𝑎𝑖𝑟 𝑜𝑟 𝑡ℎ𝑒 𝑔𝑎𝑠
When we replace the voltage drop with the temperature difference, and after the thermal
resistance circuit is arranged, the thermal resistance becomes
Rcond =
(T2 − 𝑇1)
𝑞
=
𝐿
𝑘𝐴
Rconv =
(T 𝑤 − 𝑇∞)
𝑞
=
1
ℎ𝐴
In this paper, it would be separated into two sections of resistance analysis. The first
section would be included with the hottest region, where the absorber tubes locate. The
second region would be included with the enclosed convection coefficient. We would make an
assumption that the temperature at the absorber region is 100 degree Celsius higher than the
average temperature enclosed in the absorber cavity.
Figure 1. Cross section of the absorber view
(with 0.5m length of the absorber shown), created by [12] SolidWorks

6. Page 6
Figure 2. Thermal resistances for the solar absorber cavity, created by [2] AutoCAD
First, with the sketch provided above, we know that for the top of the cavity, the
thermal resistance analysis consists of the insulation resistance, which would be represented by
the inverse of thermal conductance times the thickness of the insulation. This would then in
series with the convection inside the cavity, the convection coefficient here would depend on
the height of the absorber. Lastly, the resistance of the convection and radiation from the
absorber wall to the surrounding will also be included in the analysis. The thermal resistance
equations for the top side of cavity is:
𝑅𝑡𝑜𝑝 = 𝑅 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛,𝑒𝑛𝑐𝑙𝑜𝑠𝑢𝑟𝑒 + 𝑅𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 + 𝑅 𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑,𝑠𝑢𝑟𝑟
, 𝑅 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑜𝑛,𝑒𝑛𝑐𝑙𝑜𝑠𝑢𝑟𝑒 =
1
ℎ 𝑐𝑎𝑣𝑖𝑡𝑦 𝐴 𝑡𝑜𝑝
, 𝑤ℎ𝑒𝑟𝑒 ℎ 𝑐𝑎𝑣𝑖𝑡𝑦 =
𝑘 𝑎𝑖𝑟
𝐷/2
𝑅𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑 =
𝑡𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑
𝑘𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑒𝑑
𝑎𝑛𝑑 𝑅 𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑,𝑠𝑢𝑟𝑟 =
1
ℎ 𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝐴 𝑡𝑜𝑝
, 𝑤ℎ𝑒𝑟𝑒 ℎ 𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 = ℎ 𝑤 + ℎ 𝑟𝑎𝑑 , 𝑎𝑛𝑑 ℎ 𝑔 = 4 × εg × σ × Frad ∗ 𝑇 𝑚
3
, 𝑇 𝑚 =
𝑇𝑎 + 𝑇𝑔
2
, 𝑇𝑎 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 ℎ𝑜𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑟𝑒𝑔𝑖𝑜𝑛
, 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑤𝑖𝑡ℎ𝑖𝑛 𝑡ℎ𝑒 𝑐𝑎𝑣𝑖𝑡𝑦 𝑜𝑟 𝑎𝑟𝑜𝑢𝑛𝑑 𝑡ℎ𝑒 𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑟
, 𝑇𝑔 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡ℎ𝑒 𝑐𝑜𝑙𝑑 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑟𝑒𝑔𝑖𝑜𝑛, 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑡ℎ𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑜𝑢𝑡𝑠𝑖𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑣𝑖𝑡𝑦
For the sides’ walls the heat loss comes from the combined heat loss of radiation and
convection, the conduction heat loss at the wall, and also the radiation and convection heat
loss to the surrounding. The thermal resistance equations in this case would be,
Rwall = Rconvection,enclosure + Rcond,wall + 𝑅 𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑,𝑠𝑢𝑟𝑟, where Rcond,wall =
L
𝑘𝐴 𝑤𝑎𝑙𝑙
and Rconvection,enclosure ℎ𝑎𝑠 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑎𝑠 𝑡ℎ𝑒 𝑜𝑛𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑡𝑜𝑝 𝑠𝑖𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑎𝑣𝑖𝑡𝑦

7. Page 7
, 𝑎𝑛𝑑 𝑠𝑜 𝑑𝑜𝑒𝑠 𝑡ℎ𝑒 ℎ 𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑐𝑜𝑛𝑣𝑒𝑐𝑡𝑖𝑣𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒.
Lastly, for the heat loss analysis at the glass side, the heat loss is the same as the sides’
walls, except the thermal conductivity and the thickness of the glass are different, which the
heat loss from conduction would be different. However, another assumption would be made
here is that we would neglect the thickness of the glass window. Therefore, the equations for
the thermal resistance is:
Rglass = Rconvection,enclosure + 𝑅 𝑐𝑜𝑚𝑏𝑖𝑛𝑒𝑑,𝑠𝑢𝑟𝑟
In order to find the final total heat loss, besides the series thermal resistance analysis
we did on the top side of the solar absorber, we would also do a parallel analysis on the glass
side and the wall sides. Furthermore, here we notice that the absorber is geometrically
symmetric, 𝑅 𝑠𝑖𝑑𝑒 can then be doubled to represents both sides of the absorber walls.
Therefore, the parallel resistance will become:
𝑅 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = (
1
Rglas
+
1
2 × 𝑅 𝑠𝑖𝑑𝑒
)
−1
𝑎𝑛𝑑 𝑡ℎ𝑒 ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠 ℎ𝑒𝑟𝑒 𝑤𝑜𝑢𝑙𝑑 𝑏𝑒:
𝐻𝑒𝑎𝑡 𝐿𝑜𝑠𝑠, 𝑄ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠_𝑏𝑜𝑡𝑡𝑜𝑚 =
(𝑇𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 − 𝑇𝑠𝑢𝑟𝑟)
𝑅 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙
With the heat loss obtained earlier from the absorber’s top side,
, ℎ𝑒𝑟𝑒 𝑡ℎ𝑒 ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠 𝑤𝑜𝑢𝑙𝑑 𝑏𝑒 𝑄ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠_𝑡𝑜𝑝 =
𝑇𝑎𝑏𝑠𝑜𝑟𝑏𝑒𝑟 − 𝑇𝑠𝑢𝑟𝑟
𝑅𝑡𝑜𝑝
The total heat loss would be 𝑄ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠_𝑡𝑜𝑡𝑎𝑙 = 𝑄ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠_𝑡𝑜𝑝 + 𝑄ℎ𝑒𝑎𝑡 𝑙𝑜𝑠𝑠_𝑏𝑜𝑡𝑡𝑜𝑚
Now the analysis would be emphasized on changing three variables with two varying
bases. The two varying bases are the temperature outside of the absorber cavity (𝑇𝑔) and the
temperature inside of the cavity (𝑇𝑎). The three parameters will be changed are the depth of
the absorber, the angle of the absorber inclination, and the thickness of the insulation. We
would analyze the changes for the total heat loss after each adjustment. When one parameter
is changing, the other two parameters would be set to the middle values, such as when we are
changing the depth of the absorber from 50mm, 100mm, 150mm, the values used for the
inclination angle and the 45⁰, and 20mm.

8. Page 8
2.3 Graphical results
2.3.1 Adjustments on the depth of the absorber
Figure 3. Heat Loss with D=0.05m, θ=45⁰, t=0.02m
Figure 4. Heat Loss with D=0.1m, θ=45⁰, t=0.02m
Figure 5. Heat Loss with D=0.15m, θ=45⁰, t=0.02m

9. Page 9
2.3.2 Adjustments on the inclination angle of the absorber
Figure 6. Heat Loss with D=0.1m, θ=30⁰, t=0.02m
Figure 7. Heat Loss with D=0.1m, θ=45⁰, t=0.02m
Figure 8. Heat Loss with D=0.1m, θ=60⁰, t=0.02m

10. Page 10
2.3.3 Adjustments on the thickness of the insulation
Figure 9. Heat Loss with D=0.1m, θ=45⁰, t=0.0m
Figure 10. Heat Loss with D=0.1m, θ=45⁰, t=0.02m
Figure 11. Heat Loss with D=0.1m, θ=45⁰, t=0.05m

11. Page 11
3. DISCUSSION AND CONCLUSION
3.1 Discussion
First, from figure 3, figure 4, and figure 5 above, we notice that the higher the depth,
the less the heat loss is. Secondly, from figure 6, figure 7, and figure 8, the plots show us that
the smaller angle is, the more the heat loss is. These two sets of plots agree with each other
that more space for the internal side of the absorber reduces the heat loss, since that the
absorber can enclose more warm air within the cavity. Another set of plots, figure 9, figure 10,
and figure 11 show that the thickness of insulation also have huge impact on the heat loss. The
insulating material is meant to enclose the heat inside the cavity and prevent the heat from
losing. These three graphs prove the prediction that the heat loss decreases as the thickness of
the insulation is increased.
Since all the previous plots showed each different case for a given x-axis and y-axis, the
following plots compare the heat loss for all different 7 cases at a given surrounding
temperature. It is clear to see from the figure 12 that when the surrounding temperature is
lower (here Temperature = 373 K is chosen), the heat enters into the cavity is less hence the
overall heat loss is less. The high surrounding temperature chosen for comparing is shown in
the figure 13 that when the surrounding temperature is 673 K, the overall heat loss increases.
Figure 12. Heat loss for seven combinations at temperature = 373 (K)

12. Page 12
Figure 13. Heat loss for seven combinations at temperature = 673 (K)
It is interesting to observe from the results that the combinations, [0.1, 30, 0.02], [0.1,
45, 0.0], and [0.05, 45, 0.02] (the depth of the absorber, the inclination angle, the thickness of
insulation) have higher heat losses for both surrounding temperatures compared to the other
four combinations. They either have small inclination angle, small insulation thickness, or small
height of the absorber, and these characteristics also agree to the results concluded earlier.
3.2 Conclusion
In this paper, the heat loss for the trapezoid solar absorber used for the Concentrated
Solar Power System is analyzed and the adjustments for the geometry (the height of the
absorber cavity and the inclination angle for the absorber), and the insulation thickness are
made to find the optimal combination for the absorber design.
The conclusion comes that no matter for high or low surrounding temperatures, the
combination for the absorber design should include high cavity depth and larger inclination
angle to make a larger enclosed space. Excluding the material cost for now, the insulation
thickness should be maximized to secure the hot air enclosed within the absorber cavity.
The future work for this project includes analyzing the impact how Direct Steam
Generation would help to reduce the heat loss and maximize the system overall efficiency.
More parameters and tests could be carried out and present another more accurate report, and
to find the best geometric configuration for this concentrated power absorber system.

13. Page 13
4. Appendix
4.1 Constant and varied parameters ([10] Pye, John D et al, [7] Lai, Yanhua et al)
Constant
Parameter
Definition
𝜎 5.6696 × 10−8
𝑊/𝑚2
𝐾4 Stefan-Boltzmann constant
𝜖 𝑡 0.5 Absorber top emissi vity
𝜖 𝑎 0.1 Absorber wall emissivity
𝜖 𝑔 0.85 Glass cover emissivity
𝑘 𝑐 0.58 W/m ∙ 𝐾 Thermal conductivity
ρ 2.65 × 10−8
Ω ∙ 𝑚 Resistivity for aluminum
𝑘 𝑎𝑖𝑟 0.024 W/m ∙ 𝐾 Air conductivity
ℎ 𝑔 2.6 W/m2
∙ 𝐾
Convection coefficient outside of the cavity
window (glass side)
ℎ 𝑤 0.5 W/m2
∙ 𝐾
External heat loss coefficient outside of cavity
side walls
L 60 m Length of the absorber
W 160 mm Width of the receiver
T 20 mm The thickness of the wall
𝑘𝑖 0.04 W/m ∙ 𝐾 Insulation thermal conductivity
Varied
Parameter
Definition
D 50,100,150 (mm) Depth of the absorber
ℎ 𝑤
kair
𝐷/2
Convection coefficient inside of the cavity
t 0, 20, 50 mm The thickness of the insulation
𝜃 30,45,60 (°) Inclination of the wall
𝑇𝑎 100,200,300,400 (℃) Temperature enclosed in the absorber
𝑇𝑔 270,280,290,300,310 (K)
Temperature at the outside surface of the
absorber

14. Page 14
4.2 Heat Loss calculated data for seven different combinations
Heat Loss with D=0.05m, θ=45⁰, t=0.02m
270 280 290 300 310
373 1655.399 1514.63 1372.945 1230.337 1086.801
473 3203.453 3062.641 2920.872 2778.145 2634.462
573 4841.027 4699.569 4557.13 4413.717 4269.337
673 6556.416 6413.532 6269.673 6124.85 5979.076
Heat Loss with D=0.1m, θ=45⁰, t=0.02m
270 280 290 300 310
373 1351.658 1235.93 1119.734 1003.067 885.9264
473 2580.439 2464.632 2348.34 2231.565 2114.309
573 3853.429 3737.244 3620.567 3503.404 3385.757
673 5164.483 5047.544 4930.12 4812.219 4693.844
Heat Loss with D=0.15m, θ=45⁰, t=0.02m
270 280 290 300 310
373 1224.433 1118.656 1012.555 906.1277 799.3736
473 2331.65 2225.807 2119.629 2013.118 1906.275
573 3469.148 3363.032 3256.577 3149.787 3042.665
673 4632.588 4525.937 4418.953 4311.641 4204.004
Heat Loss with D=0.1m, θ=30⁰, t=0.02m
270 280 290 300 310
373 1789.983 1632.542 1474.455 1315.717 1156.325
473 3462.927 3305.417 3147.235 2988.382 2828.859
573 5197.915 5039.911 4881.222 4721.854 4561.811
673 6986.456 6827.421 6667.709 6507.328 6346.286
Heat Loss with D=0.1m, θ=60⁰, t=0.02m
270 280 290 300 310
373 1105.324 1013.056 920.4156 827.4016 734.0129
473 2084.903 1992.555 1899.825 1806.713 1713.221
573 3099.189 3006.536 2913.497 2820.074 2726.27
673 4143.413 4050.168 3956.541 3862.538 3768.163
Heat Loss with D=0.1m, θ=45⁰, t=0.0m
270 280 290 300 310
373 1938.686 1796.096 1652.748 1508.653 1363.826
473 3483.757 3340.231 3196.002 3051.08 2905.479
573 5079.264 4934.585 4789.248 4643.268 4496.654
673 6715.535 6569.45 6422.756 6275.464 6127.587
Heat Loss with D=0.1m, θ=45⁰, t=0.05m
270 280 290 300 310
373 1212.22 1103.185 993.7068 883.7812 773.4053
473 2370.017 2260.98 2151.478 2041.51 1931.077
573 3571.551 3462.204 3352.379 3242.08 3131.311
673 4810.958 4700.912 4590.391 4479.402 4367.95

15. Page 15
References
[1] Alguacil, M., C. Prieto, A. Rodriguez, and J. Lohr. "Direct Steam Generation in Parabolic
through Collectors." (2013): n. pag. ScienceDirect. Web. 24 Sept. 2014.
[2] AutoCAD. Sausalito, CA: Autodesk, 2013. Computer software.
[3] Edkins, Max, Harald Winkler, and Andrew Marquard. "Large-Scale Rollout of Concentrating
Solar Power in South Africa." Climate Strategies, Sept. 2009. Web. 1 Oct. 2014.
[4] Hydro Solar Solutions. "Solar Design Manual." (n.d.): n. pag. Web. 3 Dec. 2014.
[5] Incropera, Frank P. Principles of Heat and Mass Transfer. Hoboken, NJ: Wiley, 2013. Print.
[6] Jance M.J., Morrison G.L and Behnia M. (2000) “Natural Convection and Radiation within
an Enclosed Inverted Absorber Cavity”, Proceedings of ANZSES Annual Conference – From
Fossils to Photons, Brisbane, pp563-569.
[7] Lai, Yanhua, Tao Wu, Shuping Che, Zhen Dong, and Mingxin Lyu. "Thermal Performance
Prediction of a Trapezoidal Cavity Absorber for a Linear Fresnel Reflector." Advances in
Mechanical Engineering 2013 (2013): 1-7. Web. 28 Nov. 2014.
[8] Lievre, Peter Le. Multi-tube Solar Collector Structure. Areva Solar Pty Limited, assignee.
Patent PCT/AU2005/000208. 17 Feb. 2005. Print.
[9] Microsoft Excel. Redmond, WA: Microsoft Corp., 2013. Computer software.
[10] Pye, John D., Graham L. Morrison, and Masud Behnia. "Transient Modeling of Cavity
Receiver Heat Transfer for the Compact Linear Fresnel Reflector." (2003): n. pag. Web. 2
Oct. 2014.
[11] Pye, John D., Graham L. Morrison, Masud Behnia, and David R. Mills. "Modelling of
Cavity Receiver Heat Transfer for the Compact Linear Fresnel Reflector." (2003): n. pag.
Web. 29 Oct. 2014.
[12] SolidWorks. Concord: SolidWorks, 2013. Computer software.
[13] Stine, William B., and Raymond W. Harrigan. Solar Energy Fundamentals and Design:
With Computer Applications. New York: Wiley, 1985. Print.
[14] Vieira, Da Rosa Aldo. Fundamentals of Renewable Energy Processes. Amsterdam: Elsevier
Academic, 2005. Print.
[15] Woodcraft, Adam L. "Predicting the Thermal Conductivity of Aluminum Alloys in the
Cryogenic to Room Temperature Range." (2005): n. pag. Web. 3 Dec. 2014.