1

Validation, Optimization and Simulation of Solar Thermoelectric

Generator Model

By

Ali Hamil

Rakesh Krishnappa Harish

Hadi Madkhali

The Final Project of Thermoelectric I (ME 6590)

College of Engineering and Applied Sciences

Western Michigan University

Prof. HoSung Lee

August 19, 2015

2

Abstract

In this project, a model of solar thermoelectric generator (STEG) is analyzed based on the

concept of converting thermal energy into electricity. A recent paper [1] on solar thermoelectric

generator reported a highest efficiency of 4.6%, in which the system consisted of a vacuum glass

inside enclosure, flat panel (absorber), thermoelectric generator and water circulation for cold

side. A validation was applied which was in good agreement with this paper. In our new design,

a heat sink using air was added to the system instead of water circulation. Higher efficiency of

5.8% was obtained by applying Dr. Lee’s theory of optimal design using dimensionless

parameters. Finally, a numerical simulation using ANSYS software was created to compare with

analytical solutions.

3

Acknowledgment

We would like to express our appreciation to Prof. Lee who has given us this opportunity

working in this project. This project would not be useful for us without his gaudiness. Good

amount of experience has been gained during this semester. We are very fortunate taking ME

6590 (Thermoelectric I) class with a modest Professor like Dr. Lee. In addition, we are very

thankful to Dr. Alla Alttar for his efforts helping us.

4

TABLE OF CONTENTS

Topics Page

No.

Chapter 1

Introduction to Solar Thermoelectric Generator

I. General

II. Thermoelectric generators devices

III. Solar Thermoelectric Generator

IV. Recent works

1

1

2

2

Chapter 2

Analytical Part

I. Validation of A Model

II. New Design

III. Optimizing the New Design

4

8

10

Chapter 3

Numerical part

13

Chapter 4

Comparisons, Discussions & Conclusion

16

References 18

Appendices 19

5

Chapter 1

Introduction

1.1 General

Due to the raising in energy prices, growing in the demand of energy, and increasing in

environmental pollution, researchers have been working toward developing the phenomena of

generating electrical power depending on thermal process which is called thermoelectric effect.

Fossil burning of fuel in energy systems has led to environmental problems such as climate

change, acid rain and gases emissions. Thermoelectric generator is a solid state device that

converts thermal energy into electricity depending on Seebeck effect between its two layers. A

hundred years ago, thermoelectric devices were not sufficient in technology due to their low

efficiencies and the massive designs. However, now days all thermoelectric applications is

considered as a solution for human activities of burning fuel.

1.2 Thermoelectric Devices

At present, thermoelectric generators have been widely used because of their advantages

of reliability such as in space or for terrestrial uses. Thermoelectric generators devices based on

heat sources are classified into two parts, waste recovery energy and renewable energy systems.

Waste recovery systems use the waste heat of combustion systems to recover power and most

common applications are in power plant and in automobiles. These systems are considered as

large scale size. However, there is a small scale size such in space probe and satellites called

radioisotope thermoelectric generators (RTG). Renewable or clean energy systems are the

second applications that use the nature sources such as the solar, geothermal, and ocean to

generator electrical power.

6

1.3 Solar Thermoelectric Generator

Solar thermoelectric generator represents a new technique of using solar energy as a way

of generating electricity. There are two methods of using solar energy which are photovoltaic

and solar thermal processes. Photovoltaic technology uses flat panels on the building, houses

and farms. This technology has wider use than solar thermal process due to its amount of power

that can be produced. On other hand, thermal process technique has grown quickly in last ten

years because of its ability to store solar energy and generator power even though no light sun

especially in nights or due to clouds. Many benefits of using STEGs have been clearly noticed

which are life time stabilities, no vibration, no moving parts, low scale systems.

1.4 Recent Papers

In order to carry out this project, some technical research papers have been referred to

inculcate the basic idea of design and efficiencies achieved in solar thermoelectric generators in

the past years. In 1954, Maria Telkes reported the first significant experimental STEG efficiency

of 3.35%, in which a concentrating optical lens of 50 times was used in order to increase the

incident solar flux and achieved a temperature difference of 247 0C across a thermoelectric

elements made of zinc antimony (ZnSb) and bismuth antimony (BiSb). However this efficiency

was insufficient for commercial and domestic purposes. Also, the system was not cost effective

due to the use of optical concentrators, which required tracking device.

In 2011, Daniel Kraemer [1] demonstrated a promising flat-panel solar thermal energy to

electric power conversion method, based on Seeback effect and high thermal concentration

without any optical concentrators. STEG model consists of flat panel absorber inside vacuum

glass, TEG module and circulation of pumping water for cold side as shown in Fig (1). The

developed STEG reached a peak efficiency of 4.6%. This was a major breakthrough and was

7

achieved using a new design. This approach consisted of a highly solar-absorbing surface that

converts the solar radiation into heat and thermally concentrates onto the thermoelectric elements

by means of lateral conduction.

In 2015 Sue & Chen [2] investigated a new model of STEG consists of solar collector,

Nano structures of thermoelectric generator (TEG), and heat sink as shown in Fig (2). Solar

collector has two parts, optical lens and selective absorber which they are in evacuated enclosure

to prevent convective and conductive losses. Main reason of using solar collector is to create

large amount of thermal concentration. TEG with inhomogeneous doping has a pair of p& n -

type material using Silicon based quantum. This paper reported a high efficiency of 14.8% of

STEG.

Figure (1)

Figure (2)

Figure (2)

8

Chapter 2

Analytical Part

2.1 Model Validation

First step in this project was validating Kraemer’s model of STEG. This Model that was

validated in this project was tested experimentally by Kraemer et al.[1], see Fig (1). The basic

parts of the model are:

1. Glass vacuum enclosure in order to eliminate the convection losses.

2. Thermoelectric element; the thermocouple material for both (p-type) and (n-type) is

Bismuth Telluride (Bi2Te3). Therefore, specifying the material properties (, Seebeck

coefficient (α), electrical resistivity (ρ), and thermal conductivity (k)) of Bi2Te3 was

from chart ….(SEE APPENDIX) for nanostructure and at average temperature of

(100 ) , α = 426 V/K, ρ = 2.2 Ωm, k = 1.87 W/mK

3. Wavelength selective solar absorber: The absorber has high absorptivity (αa = 0.95)

towards short-wave incident solar radiation but low emissivity at long-wave reradiated

radiation from the surface to the surroundings.

The dimensions of the thermo-element (p-type and n-type) are 1.35 X 1.35 X 1.65 mm3.

After specifying the materials properties and dimensions of thermocouple, defining each element

in Kramer’s model is the second task.

𝐶𝑡ℎ =𝐴𝑎

𝐴𝑒

Where Cth is the thermal concentration, Aa is the area of the absorber that is equal to 874.8 mm2,

and Ae the cross-sectional area of the thermoelectric elements. The corresponding thermal

concentration (Cth) of the STEG used for 1000 W/m2 at AM1.5G conditions is 299. The

9

temperature of the cold side is 20). The transmissivity (τg) of the cover glass is 0.94 and

ZTaver =1

2.2 The Basic Equations of Solar Thermoelectric Generator:

I. The Ideal Equations of Thermoelectric Generator (TEG):

The figure above shows a simple schematic of heat balances across a pair of thermoelectric

elements. The Ideal Equations describe the heat transfer rates across the junctions of the

thermoelectric couple. Qh represents the hot side heat transfer rate that occurs at the hot junction

with the higher temperature Th. Qc is the cold side heat transfer rate that occurs at the cold

junction with the lower temperature Tc . Therefore, the hot and the cold side heat transfer rate can

be represented by the following equations:

𝑄ℎ = 𝛼𝑇ℎ𝐼 −1

2𝐼2 𝜌𝐿𝑒

𝐴𝑒 +

𝐴𝑒𝑘

𝐿𝑒(𝑇ℎ − 𝑇𝑐) (1)

𝑄𝑐 = 𝛼𝑇𝑐𝐼 +1

2𝐼2 𝜌𝐿𝑒

𝐴𝑒 +

𝐴𝑒𝑘

𝐿𝑒(𝑇ℎ − 𝑇𝑐) (2)

Figure (3): Schematic of heat balances across a thermoelectric couple

10

Where 𝐼 is the electrical current, 𝐴𝑒 & 𝐿𝑒 are the cross-sectional area and length of

thermoelectric elements (p-type & n- type) respectively, 𝛼, 𝜌 and 𝑘 are the Seebeck coefficient,

electrical resistivity and thermal resistance respectively.

As mentioned before, theses equations are ideal; they are due to assumptions:

A. Thomson effects are negligible

B. Steady state conditions.

C. Material properties are constant and evaluated at the mean operating temperature; means

uniform properties at any temperature.

D. No convection and radiation losses between the junctions

E. No contact resistances at the interfaces of the thermoelectric.

II. STEG System Equations:

It can be obtained hot heat transfer junction from

𝑄ℎ = 𝑄𝑠𝑜𝑙𝑎𝑟 − 𝑄𝐼𝑟𝑟,𝑎𝑚𝑏 − 𝑄𝐼𝑟𝑟,𝑝𝑙𝑎𝑡𝑒

Since,

𝑄𝑠𝑜𝑙𝑎𝑟 = 𝐴𝑎𝜏𝑔𝛼𝑎𝑞𝑖 (3)

𝑄𝐼𝑟𝑟,𝑎𝑚𝑏 = 𝐴𝑎𝜀𝑎𝜎𝑠𝑏(𝑇ℎ4 − 𝑇∞

4) (4)

𝑄𝐼𝑟𝑟,𝑝𝑙𝑎𝑡𝑒 = 𝐴𝑎𝜀𝑒𝜎𝑠𝑏(𝑇ℎ4 − 𝑇𝑐

4) (5)

So, hot heat transfer junction can be written as:

𝑄ℎ = 𝐴𝑎[𝜏𝑔𝛼𝑎𝑞𝑖 − 𝜀𝑎𝜎𝑠𝑏(𝑇ℎ4 − 𝑇∞

4) + 𝜀𝑒𝜎𝑠𝑏(𝑇ℎ4 − 𝑇𝑐

4)] (6)

Where 𝑄𝑠𝑜𝑙𝑎𝑟 is the solar power absorbed by the absorber though passing the glass cover,

𝑄𝐼𝑟𝑟,𝑎𝑚𝑏 is the solar irradiation between absorber top surface and the surroundings, 𝑄𝐼𝑟𝑟,𝑝𝑙𝑎𝑡𝑒 is

11

the solar irradiation between the absorber bottom and the base of heat sink at the cold side,

𝑇∞ , 𝑇ℎ & 𝑇𝑐 are the temperatures of the ambient, hot junction and cold junction respectively, 𝐴𝑎

is the absorber surface area, 𝜏𝑔 is the transmissivity of the cover glass, 𝛼𝑎 is the absorptivity of

the absorber, 𝑞𝑖 is the solar flux of 1,000 W/m2 at AM1.5G conditions, 𝜀𝑎 is the emissivity of the

absorber to the ambient air, 𝜀𝑒 is the effective emissivity between the bottom of the absorber and

the base of the cold side heat sin and 𝜎𝑠𝑏 is the Stefan-Boltzmann constant.

For the cold side, it can be written cold heat transfer rate as;

𝑄𝑐 =

(𝑇𝑐 − 𝑇∞)

𝑅𝑡ℎ,𝑐

(7)

Where, 𝑅𝑡ℎ,𝑐 is the thermal resistance.

2.3 Validation Results:

Validation results were obtained by applying equations (1, 2, 6 &7) based on Mathcad program.

Figures ( 4) & (5) show good agreement with Kreamer’s results.

Figure (4) Efficiency versus Current

12

2.4 New Design

In this Model, heat sink in the clod side is used instead of the water circulation as shown

in Fig (6). Using forced convection for the cooling side in order to maintain the cold temperature

at a specific value needs more energy for pumping the water. The Heat sink is a great alternative

process here because it is natural convection; no pumping for the fluid. Not only, the benefits of

using the heat sink in this model consumes energy, but also the efficiency of the solar

thermoelectric generator has been raised after applying the optimizing theory that it is provided

by Dr. Lee. Same input data that were given from Kraemer’s paper is used in this design.

However, for the cold heat sink side, the convective heat transfer coefficient hc for natural air

typically ranges from about 5 to 25 W m−2K−1.

Figure (5) Efficiency versus Current

13

The new proposed design uses the same thermoelectric material and dimensions. In order

to make the system as cost effective, a cold side heat sink with natural air convection is used.

The convective heat transfer coefficient ℎ𝑐 for natural air typically ranges from about 5

to 25 W m−2K−1. Assuming that the heat sink has 8 fins on a base area of 2 × 6 = 12 cm2.

The profile length is 2 cm and height of 6 cm for each fin. Both sides of a fin are exposed to the

cooling fluid i.e. air. The thickness of each fin is 0.25 cm thick and has a spacing of 0.25 cm as

well. The total surface area available for cooling is computed as 𝐴𝑐 = 8 × [2(2 + 0.25)6 +

2 × 0.25] = 220 cm2 = 0.022 m2. Also, the design of the fins has an efficiency 𝜂𝑐 of 80%, the

value for 𝐻𝑐 = 𝜂𝑐ℎ𝑐𝐴𝑐 = 0.8 × 0.022 × 5 = 0.088 W K−1. The heat sink thermal resistance

𝑅𝑡ℎ,𝑐 = 11.364 𝐾 𝑊−1 is obtained where 𝑅𝑡ℎ,𝑐 = (𝐻𝑐)−1

Figure (6)

14

2.5 New Design Results before Optimization

Figure (7) shows the efficiency and power output versus current for the new model

without optimization.

2.6 Optimizing the New Model

Using the optimization theory that is provided by Dr. Lee for the thermoelectric generator, the

dimensionless parameters of the solar thermoelectric generator can be derived.

Defining dimensionless parameters:

Th∗ =

Th

T∞ (8)

Tc∗ =

Th

T∞ (9)

Figure (7)

15

𝑅𝑟 =𝑅𝐿

𝑅 (10)

𝑍𝑇∞ =𝛼2

𝜌𝑘𝑇∞ (11)

𝑁𝑘 = 𝑛 (𝐴𝑒

𝐿𝑒) 𝑘𝑅𝑡ℎ,𝑐 (12)

From equations (1,2, 6,7, 8, 9, 10, 11 &12), we get:

𝐴𝑎𝑅𝑡ℎ,𝑐

𝑁𝑘𝑇∞[𝜏𝑔𝛼𝑎𝑞𝑖 − 𝜀𝑎𝜎𝑠𝑏[(𝑇ℎ

∗𝑇∞)4 − 𝑇∞4] − 𝜀𝑒𝜎𝑠𝑏[(𝑇ℎ

∗𝑇∞)4 − (𝑇𝑐∗𝑇∞)4]] =

𝑍𝑇∞(𝑇ℎ∗−𝑇𝑐

∗)𝑇ℎ∗

(𝑅𝑟+1)−

𝑍𝑇∞(𝑇ℎ∗−𝑇𝑐

∗)2

2(𝑅𝑟+1)2+ (𝑇ℎ

∗ − 𝑇𝑐∗) (13)

𝑇𝑐∗−1

𝑁𝑘 =

𝑍𝑇∞(𝑇ℎ∗−𝑇𝑐

∗)𝑇𝑐∗

(𝑅𝑟+1)+

𝑍𝑇∞(𝑇ℎ∗−𝑇𝑐

∗)2

2(𝑅𝑟+1)2+ (𝑇ℎ

∗ − 𝑇𝑐∗) (14)

By using Mathcad software, we solved the above two equations, and then got:

𝑇ℎ∗ = 𝑓(𝑁𝑘 , 𝑅𝑟, 𝐴𝑎 , 𝑍𝑇∞)

𝑇𝑐∗ = 𝑓(𝑁𝑘 , 𝑅𝑟, 𝐴𝑎 , 𝑍𝑇∞)

2.7 Optimizing Results

Figures (8) & (9) represent the results of optimization of new model. Similarly, the

Kraemer’s model has been optimized as shown in Fig. (10).

16

Figure (8)

Figure (8) Figure (9)

Figure (10)

17

Chapter 3

Numerical Part

3.1 Basic Approach

Attaining a good agreement with Kraemer’s papers, designing a new model that featured

with cold heat sink instead of the water pump and optimizing new model have attracted us to

simulate the new model. In fact, this part is the challenging task in this project. The net rate of

solar energy is obtained analytically then applied directly to the absorber plate. Figures (11) &

(12) show the geometry and mesh respectively.

Figure (12) Figure (11)

18

3.2 Numerical Results

Figure (13) shows the junction temperatures (Th , Tc ).

3.3 Accurate Approach

There is a proper way to simulate this system that would give much accurate results. This

way needs to divide the system into three main parts and connect them for transferring the data.

These parts are solar fluent, Thermoelectric and heat sink fluent. Meanwhile, this way has not

been used in this project due to there are many missing inputs which makes this option much

complicated. Analysis fluent of radiation systems has two ways as in following;

I. Solar ray tracing; it is highly efficient and practical means of applying solar loads as a heat

source in the energy equation. The input data that are required for the solar ray tracing

Figure (13)

19

algorithm are sun direction vector, direct solar irradiation, diffuse solar irradiation, spectral

fraction, direct and IR absorptivity (opaque wall), direct and IR absorptivity and

transmissivity (semi-transparent wall), diffuse hemispherical absorptivity and transmissivity

(semi-transparent wall), quad tree refinement factor, scattering fraction, and ground

reflectivity.

II. Discrete Ordinates Irradiation (DO); it is available to supply outside beam direction and

intensity parameters directly to the DO model. In this option, the irradiation flux is applied

directly to semi-transparent walls as a boundary condition, so the radiative heat transfer is

derived from the solution of the DO transfer equation. This option does not compute the heat

fluxes and apply them as heat sources to the energy equation. The inputs that are required in

this option are total irradiation, beam direction, beam width, and diffuse fraction.

Solar load model includes a solar calculator utility that can be used to construct the sun’s

location in the sky for a given time of day, date, and position. Also, it can be used for modeling

steady and unsteady flows. Global position, starting date and time, grid orientation, solar

irradiation method, and sunshine factor are the inputs needed for the solar calculator.

20

Chapter 4

Comparisons, Discussions & Conclusion

4.1 Comparisons

Table 1: Comparison of results obtained.

Parameters Kraemer et al.’s

Design

Optimum

Kraemer et

al.’s Design

New Design

before

optimization

Optimized New

Design

𝑨𝒂 874.8 mm2 874.8 mm2 874.8 mm2 874.8 mm2

𝑻𝒉 162.46°𝐶 162.50°𝐶 166.48°𝐶 185.40°𝐶

𝑻𝒄 20°𝐶 20.23°𝐶 25.34°𝐶 25.92°𝐶

𝜼𝑺𝑻𝑬𝑮 4.6% 4.7% 4.5% 5.37%

46.2 𝑚𝑊 46.2 𝑚𝑊 34.2 𝑚𝑊 55.61 𝑚𝑊

Rr 1.62 1.6 1.53 1.62

Similar input conditions: 𝜏𝑔 = 0.94, 𝛼𝑎 = 0.95, 𝜀𝑎 = 0.125, 𝑇∞ = 20°𝐶

From the numerical results, Th = 156.92°𝐶 , Tc = 39.06°𝐶

4.2 Discussions

The dimensions of the thermoelectric elements to be 1.35 × 1.35 ×

1.65 mm3 and the material to be nanostructured bismuth telluride.

Kraemer’s et al. design did not consist any heat sinks at the cold side. Instead

used a cold water circulation, making the system cost to high. The system

accounted an overall efficiency of 4.6% and power output of 46.2mW.

21

The new design is optimized with the help of dimensional analysi to obtain a

higher efficiency. The optimized design shows 5.37% overall efficiency and

is possible when the correct thermoelectric element geometry and load

resistance are used so that the optimum values of 𝑁𝑘 and 𝑅𝑟 are met. Also,

the power output of 55.61 𝑚𝑊 is obtained with respect to optimum values

of 𝑁𝑘 and 𝑅𝑟 , which is higher than Kraemer’s power output The bottom line

is, the optimized model has more efficiency than Kraemer et al. model. These

maximum values are achieved with just the natural air cooling, making the

optimized model to be more efficient and cost effective.

4.3 Conclusion

The Kraemer’s work is a breakthrough since it has experimental results

demonstrate its analytical analysis. This work validates Kraemer’s results. The

obtained values in this project are in good agreement with Kraemer values. Also,

here it is confirmed that Kraemer’s results are optimized values. The proposed

new design gives higher efficiency and power output than Kraemer’s work.

These higher values are achieved through applying Dr. Lee theory of optimal

design.

22

References

1. Kraemer, Daniel, Bed Poudel, Hsien-Ping Feng, J. Christopher Caylor, Bo Yu, Xiao Yan,

Yi Ma, et al. 2011. High-performance flat-panel solar thermoelectric generators with high

thermal concentration. Nature materials 10, (7): 532-538

2. Su, Shanhe, and Jincan Chen. "Simulation Investigation of High-Efficiency Solar

Thermoelectric Generators With Inhomogeneously Doped Nanomaterials." EEE

TRANSACTIONS ON INDUSTRIAL ELEC 62, no. 6 (June 2015)

3. Lee, HoSung. "Optimal Design of Thermoelectric Devices with Dimensional Analysis."

Applied Energy (February 14, 2013)

4. Lee, HoSung. Thermal Design Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat

Exchangers, and Solar Cells. Hoboken, New Jersey: JOHN WILEY & SONS, INC, 2010

5. Yu, Xiao Yan, et al. 2008. High-thermoelectric performance of nanostructured bismuth

antimony telluride bulk alloys. Science 320, (5876): 634-638

6. Kraemer, Daniel, Kenneth McEnaney, Matteo Chiesa, and Gang Chen. 2012. Modeling

and optimization of solar thermoelectric generators for terrestrial applications. Solar

Energy 86, (5): 1338-1350

23

Appendices