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Study of Thermoelectric Generation Unit for Radiant Waste Heat
Available online at www.sciencedirect.com
ScienceDirect Materials Today: Proceedings 2 (2015) 804 – 813
12th European Conference on Thermoelectrics
Study of Thermoelectric Generation Unit for Radiant Waste Heat Takeshi Kajihara1,*, Kazuya Makino1, Yong Hoon Lee1, Hiromasa Kaibe2 and Hirokuni Hachiuma1 1
Thermo Generation Business Development Div., KELK Ltd., 3-25-1 Shinomiya, Hiratsuka, Kanagawa 254-8543, Japan 2
Core Technology Dept., KELK Ltd., 3-25-1 Shinomiya, Hiratsuka, Kanagawa 254-8543, Japan [email protected]
Abstract
Thermoelectric generation technology is a promising technology which converts the industrial process waste heat energy to useful electrical energy. Using thermoelectric generation unit which consists of several thermoelectric generation modules, verification experiments have been held at some industrial process. In this paper, the output power and thermal performance of the thermoelectric generation unit are described in radiant waste heat recovery. The output power of thermoelectric generation unit depends on thermoelectric element size and number. We discuss the optimum performance for various sizes and number of thermoelectric elements in practical thermoelectric generation unit. Also, the comparison of generation performance of thermoelectric generation unit using Bi-Te material and high temperature thermoelectric material is discussed. © 2014 Elsevier Ltd. All rights reserved. © 2015 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee members of the 12th European Conference on Selection and peer-review under responsibility of Conference Committee members of the 12th European Conference on Thermoelectrics. Thermoelectrics.
Keywords: Thermoelectric generation, Seebeck effect, waste heat recovery, Bismuth Telluride solid solutions
1. Introduction
Thermoelectric generation is a technology which converts heat directly into electrical energy using Seebeck effect. This technology is attracting technology for CO2 reduction, energy-saving and waste heat recovery. The benefit of thermoelectric generation is no moving parts, compact and no CO2 emissions on working. The applications of thermoelectric generation are mentioned as the industrial waste heat recovery, vehicle waste heat recovery and energy harvest. KELK has been continuing the verification test of a thermoelectric generating system using carburizing furnace at
2214-7853 © 2015 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee members of the 12th European Conference on Thermoelectrics. doi:10.1016/j.matpr.2015.05.104
Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
the Awazu Plant of Komatsu [1]. This verification test is the first grid connection of thermoelectric generation in Japan [2,3]. In this test, the thermoelectric generation unit which consists of 16 thermoelectric modules was installed. Also, JFE Steel Corporation installed a 10-kW class thermoelectric power generation system for the continuous casting line and stared verification test using radiant heat from the continuous casting slabs [4,5]. As explained above, the thermoelectric generation technology has been progressing to the verification test at the real plant line from material research. There are many studies about the design of thermoelectric generation modules and system. For example, the models for the optimization of the thermoelectric generation system have been investigated and utilized for the design parameter [6−10]. The possibility of the thermoelectric generation system from industrial waste heat energy has been also investigated in detail [11−13]. In practical thermoelectric generation system, we think that there are many situations used in the form of a unit rather than a module. In this paper, the performance of thermoelectric generation unit using Bi-Te material is considered in the case of various thermoelectric elements sizes in practical thermoelectric generation unit. Similarly, we calculate the performance of the unit using a high temperature thermoelectric material. As an actual example, we consider the output power of thermoelectric generation unit in the case of radiant waste heat recovery. 2. Model of Thermoelectric Generation Unit We refer to the size of the thermoelectric generation unit in Refs. 1 and 4. Figure 1 shows the schematic illustration of the thermoelectric generation unit. The size of unit is 0.3m×0.4m. Thermoelectric modules connected in series are sandwiched between the heat collection plate and water cooled plate. In this paper, we simplify the structure of the unit as Fig. 2. In Figure 2, thermoelectric elements are arranged in the same gap. Figure 3 illustrates the gap of the element.
Water Cooled Plate
.3m
0
0.4
m
Heat Collection C Plate Thermoelectric Generation Module
Fig. 1 Illustration of thermoelectric generation unit
Heat Collection Plate 㻱㼘㼑㼏㼠㼞㼛㼐㼑
Thermoelectric Element
Water Cooled Plate
Fig. 2 Illustration of simplified model unit structure
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T hermoelectric element
G ap of element
Fig. 3 Illustration of gap of element in unit 3. Calculation Model The properties of thermoelectric generation unit are calculated using the Eq. 1 and 2.
1 (1) 2 (2) 1 Qc DeT cj I re I 2 . e 'T j 2 Here, Equations 1 and 2 are the basic equation of thermoelectric generation. [14] Heat Qh is supplied by the thermal source at the hot surface, Qc is the heat flowing out at cold surface. De is the Seebeck coefficient , re is the internal electric resistance, .e is the thermal conductance and I represents the electric current. Thj is the temperature of the hot junction of thermoelectric element, Tcj is the temperature of the cold junction of thermoelectric element and 'Tj is the temperature difference Thj – Tcj. The maximum generation output Pmax is expressed by Eq. 3. Qh
DeT hjI re I 2 . e 'T j
2 (3) 1 (D e 'T j ) Pmax re 4 In this model, the TEG unit consists of heat collection plate, module and water cooled plate. The module has electrical insulation plate, electrode and thermoelectric element. The thermal resistance model is shown in Fig. 4. Temperature of heat collection plate
Thermal resistance of heat collection plate Thermal resistance of thermal grease Thermal resistance of electrical insulation plate Thermal resistance of thermal grease
Thj Tcj
Thermal resistance of electrode Thermal resistance of thermoelectric element Thermal resistance of electrode Thermal resistance of thermal grease Thermal resistance of electrical insulation plate Thermal resistance of thermal grease
Temperature of cooling water
Thermal resistance of water cooled plate
Fig. 4 Illustration of the thermal resistance model
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4. Calculation result of BiTe unit In this calculation, the thermoelectric element size range is based on it on the commercial thermoelectric module [15,16]. In order to investigate the element size dependence of the property of a unit, we set the size range as follows., the cross section of the thermoelectric element is 1mm×1mm−5×5mm2ǃheight is 0.3−10mm. Also, we set that the gap of element is 0.55, 1.6, 2.5mm. Figure 5 shows the relation between the element width in each gap, and the number of element pairs. We calculated the unit performance with typical thermoelectric properties of BiTe. It is that ZT is about 0.8~0.9 at 100−150ć. The material and properties of unit components are shown in table1. We calculate the power output, efficiency, optimum operation current Imax, Qh, 'Tj in the condition of temperature of the heat collection plate surface is 265ć and temperature of cooling water is 25ć. 16000 gap:0.55mm gap:1.6mm gap:2.5mm
number of pairs
14000 12000 10000 8000 6000 4000 2000 0
0
1
2 3 4 5 6 element width(mm) Fig. 5. Element width dependence of number of pairs
Material : Al Heat collection plate
Thermal Conductivity : 180(W/mK) Thickness : 10mm
Thermal grease
Thermal Conductivity : 0.84(W/mK) Thickness : 15䃛m 15䃛 䃛m Material : AlO2
Electrical insulation plate
Thermal Conductivity : 24(W/mK) Thickness : 0.5mm Material : Cu
Electrode
Thermal Conductivity : 400(W/mK) Thickness : 0.5mm
Water cooled plate
Thermal resistance : 0.004(K/W)
Table 1 The material and properties of unit components The calculation result of power output and inflow heat are shown in Fig. 6 and Fig. 7. The unit which has narrower gap can generate larger power output. Similarly, the inflow heat becomes larger. It is found that there is the element size range, which gives the maximum power output. About the element size dependence of power output, the unit that the element height is lower has larger power output, however, from specific height, the power output decrease. This tendency can be understood as, for lower element height, the thermal resistance of unit decrease, therefore, the unit can transfer large heat flow. However, for specific larger inflow heat, the temperature difference of element, 'Tj
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is too small and the output becomes small.
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Fig. 6 Calculation results of power output
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Fig. 7 Calculation results of inflow heat In order to investigate these situations, we calculate the element height dependency of thermal resistance and inflow heat Qh. Figure 8 shows the calculation result. It is found that the element height is lower and thermal resistance of the unit becomes smaller, inflow heat become larger. Also, the relation between the thermal resistance of the unit and the power output is shown in Fig. 9. We find that specific thermal resistance has the maximum power output. This represents, as mentioned above tendency, from specific element height, the unit output decrease.
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T hermal resistance of unit (ºC /W)
Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
8
element height(mm)
Fig. 8 The element height dependence of thermal resistance and Qh (element size is 5×5mm2)
600
P (W)
500 400 300 200 100 0 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
T hermal resistance of unit (ºC /W) Fig. 9 Relation between the thermal resistance of the unit and the power output (element size is 5×5mm2)
5. Calculation result of high temperature thermoelectric material unit There are many promising thermoelectric materials in the temperature range 400Υ and above [17−20]. We assume that the typical ZT value of high temperature materials is about 0.7~0.9 at 450−500ć. The calculation procedure is same as Bi-Te. But the heat collection plate is SUS430 and the electric insulation plate is AlN. The heat collection plate surface is 450Υ. The calculation results of power output and Qh are shown in Fig. 10 and Fig. 11. Comparing BiTe unit, the high temperature material unit produces large temperature difference. Therefore, it can make large inflow heat and power output.
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Fig. 10 The calculation results of power output
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Fig. 11 The calculation results of inflow heat 6. Study of Radiant Waste Heat We consider the recovery from the radiation waste heat. Figure 12 shows the schematic illustration of a model. The size of the heat source is 2.2m×3.5m and the distance between the heat source and the thermoelectric generation unit is 0.5m. This model is based on the verification test in steel works [4]. We assume that the heat source is a continuous casting slab. The heat transfer calculation in Refs. 4 included the air convection. However the contribution is small. Therefore, only the radiation heat transfer has been considered.
Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
Fig. 12 Schematic illustration of model
The radiation heat transfer Qra is expressed by Eq. 4. Here H is the emissivity, V is the Stefan-Boltzmann constant, F is the view factor, S is the total area of thermoelectric generation units. Ts is the temperature of the heat source, Th is the temperature of the heat collection plate.
(4) Qra H F V S (Ts4 Th4 ) The calculated radiation transfer heat per one unit for various T s is shown in Fig. 13. Here, Ts of BiTe used unit is 265Υ and Ts of high temperature material used unit is 450Υ.
Qh (kW)
10 high temperature material 9 BiTe 8 7 6 5 4 3 2 1 0 600 700 800 900 1000 T s (°C )
Fig. 13 Calculated radiation transfer heat per one unit for various Ts We examine the power output for practical element size range. The practical element size range is based on the range used in the commercial thermo-module. The size range is, Width: 1.5−2.5mmǃHeight:1.0−3.5mm. Out of this size range, it is difficult to use in practice. For example, larger Imax, the thermal stress, and so on. In this element size range, the maximum power output of BiTe and high temperature material used unit is shown in Fig. 14 for various Ts. It is found that BiTe unit has a power output nearly equal to the high temperature material unit at a heat source temperature 900ºC and above. BiTe unit is generally used at low temperature. In this calculation, it is also utilizable at high temperature.
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600 high temperature material BiTe
500 400
P (W)
300 200 100 0 600
700
800
900
T s (°C )
1000
1100
Fig. 14 Power output for various Ts
7. Summary In this work, the performance of thermoelectric generation unit using Bi-Te is considered in the case of various thermoelectric element sizes and gap. As the gap dependency of power output, the unit which has narrower gap is the tendency for power output becoming large. It is found that there is the element size range, which gives the maximum power output. About the element size dependence of power output, the unit that the element height is lower has larger power output, however, from specific height, the power output decrease. Also, we calculate the performance of the unit using a high temperature thermoelectric material. We consider the recovery from the radiation waste heat. In the practical element size range, it is found that Bi-Te unit has a power output nearly equal to the high temperature material unit at a heat source temperature 900ºC and above. In our model calculation, Bi-Te unit is also utilizable at high temperature.
References: [1]H. Kaibe, T. Kajihara, S. Fujimoto, K. Makino and H. Hachiuma, KOMATSU TECHNICAL REPORT, vol. 57, No. 164, pp. 26-30, (2011) [2]http://www.meti.go.jp/policy/safety_security/industrial_safety/oshirase/2013/07/250705-1.html [3] ]H. Kaibe, T. Kajihara, K. Nagano, H. Hachiuma, K. Makino and D. Natsuume, Journal of electronic materials vol.43, No.6, P.2099-2103(2014) [4] T. Kuroki, K. Kabeya, K. Makino, T. Kajihara , H. Kaibe, H. Hachiuma, H. Matsuno and A. Fujibayashi, Journal of electronic materials Vol.43,No.6, p2045,(2014) [5]http://www.jfe-steel.co.jp/release/2013/07/130710-1.html [6]J. Henderson,14th Intersociety Energy Conversion Engineering Conference(1979) [7] P.M. Mayer and R.J. Ram, Nanoscale and Microscale Thermophysical Engineering, 10: 143–155, (2006) [8] K. Yazawa and A. Shakouri, in Proceedings of the ASME 2010 International Mechanical Engineering Congress and Exposition, Vancouver, British Columbia, 12–18 November 2010 [9] K. Yazawa and A. Shakouri,Environ. Sci. Technol., 2011, 45 (17), pp 7548–7553 [10]R. Mccarity, Journal of electronic materials Vol.42,No.7, p1504, (2013) [11] T. Hendricks, Engineering Scoping Study of Thermoelectric Generator Systems for Industrial Waste Heat
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Recovery(2006) [12]R. Funahashi, K. Kimura, K. Kurosaki and T. Takeuchi, Fundamentals and Applications of Thermoelectrics, Chap. 5, CMC Publishing, Tokyo 2011 [13]T. Kajikawa, Thermoelectric Power Generation System Technology, Chap. 3, S &T Publishing , Tokyo 2013 [14]K. Uemura and I. Nishida, Thermoelectric semiconductor and its application p26-33, Nikkan Kogyo Shinbunsya, Tokyo 1988 [15] http://www.kelk.co.jp/thermo/index.html#thermo_list3 [16] http://www.marlow.com/power-generators/standard-generators.html [17]H. Geng, T. Ochi, S. Suzuki, M. Kikuchi, S. Ito and J. Guo, Journal of electronic materials Vol.42, No.7, p1999, (2013) [18]T. Nemoto, T. Iida, J. Sato, T. Sakamoto, N. Hirayama, T. Nakajima and Y. Takanashi, Journal of electronic materials Vol.42, No.7, p2192, (2013) [19]W. Liu, Q. Zhang, X. Tang, H. Li and J. Sharp, Journal of electronic materials Vol.40, No.5, p1062, (2011) [20]W. Xie, A. Weidenkaff, X. Tang, Q. Zhang, J. Poon and T.M. Tritt, Namomaterials 2012, 2 p379-412. D.A. Pshenai-Steverin, M.I. Fedorov and YU. Samunin, Journal of electronic materials Vol.42, No.7, p1707, (2013)
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12th European Conference on Thermoelectrics
Study of Thermoelectric Generation Unit for Radiant Waste Heat Takeshi Kajihara1,*, Kazuya Makino1, Yong Hoon Lee1, Hiromasa Kaibe2 and Hirokuni Hachiuma1 1
Thermo Generation Business Development Div., KELK Ltd., 3-25-1 Shinomiya, Hiratsuka, Kanagawa 254-8543, Japan 2
Core Technology Dept., KELK Ltd., 3-25-1 Shinomiya, Hiratsuka, Kanagawa 254-8543, Japan [email protected]
Abstract
Thermoelectric generation technology is a promising technology which converts the industrial process waste heat energy to useful electrical energy. Using thermoelectric generation unit which consists of several thermoelectric generation modules, verification experiments have been held at some industrial process. In this paper, the output power and thermal performance of the thermoelectric generation unit are described in radiant waste heat recovery. The output power of thermoelectric generation unit depends on thermoelectric element size and number. We discuss the optimum performance for various sizes and number of thermoelectric elements in practical thermoelectric generation unit. Also, the comparison of generation performance of thermoelectric generation unit using Bi-Te material and high temperature thermoelectric material is discussed. © 2014 Elsevier Ltd. All rights reserved. © 2015 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee members of the 12th European Conference on Selection and peer-review under responsibility of Conference Committee members of the 12th European Conference on Thermoelectrics. Thermoelectrics.
Keywords: Thermoelectric generation, Seebeck effect, waste heat recovery, Bismuth Telluride solid solutions
1. Introduction
Thermoelectric generation is a technology which converts heat directly into electrical energy using Seebeck effect. This technology is attracting technology for CO2 reduction, energy-saving and waste heat recovery. The benefit of thermoelectric generation is no moving parts, compact and no CO2 emissions on working. The applications of thermoelectric generation are mentioned as the industrial waste heat recovery, vehicle waste heat recovery and energy harvest. KELK has been continuing the verification test of a thermoelectric generating system using carburizing furnace at
2214-7853 © 2015 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of Conference Committee members of the 12th European Conference on Thermoelectrics. doi:10.1016/j.matpr.2015.05.104
Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
the Awazu Plant of Komatsu [1]. This verification test is the first grid connection of thermoelectric generation in Japan [2,3]. In this test, the thermoelectric generation unit which consists of 16 thermoelectric modules was installed. Also, JFE Steel Corporation installed a 10-kW class thermoelectric power generation system for the continuous casting line and stared verification test using radiant heat from the continuous casting slabs [4,5]. As explained above, the thermoelectric generation technology has been progressing to the verification test at the real plant line from material research. There are many studies about the design of thermoelectric generation modules and system. For example, the models for the optimization of the thermoelectric generation system have been investigated and utilized for the design parameter [6−10]. The possibility of the thermoelectric generation system from industrial waste heat energy has been also investigated in detail [11−13]. In practical thermoelectric generation system, we think that there are many situations used in the form of a unit rather than a module. In this paper, the performance of thermoelectric generation unit using Bi-Te material is considered in the case of various thermoelectric elements sizes in practical thermoelectric generation unit. Similarly, we calculate the performance of the unit using a high temperature thermoelectric material. As an actual example, we consider the output power of thermoelectric generation unit in the case of radiant waste heat recovery. 2. Model of Thermoelectric Generation Unit We refer to the size of the thermoelectric generation unit in Refs. 1 and 4. Figure 1 shows the schematic illustration of the thermoelectric generation unit. The size of unit is 0.3m×0.4m. Thermoelectric modules connected in series are sandwiched between the heat collection plate and water cooled plate. In this paper, we simplify the structure of the unit as Fig. 2. In Figure 2, thermoelectric elements are arranged in the same gap. Figure 3 illustrates the gap of the element.
Water Cooled Plate
.3m
0
0.4
m
Heat Collection C Plate Thermoelectric Generation Module
Fig. 1 Illustration of thermoelectric generation unit
Heat Collection Plate 㻱㼘㼑㼏㼠㼞㼛㼐㼑
Thermoelectric Element
Water Cooled Plate
Fig. 2 Illustration of simplified model unit structure
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T hermoelectric element
G ap of element
Fig. 3 Illustration of gap of element in unit 3. Calculation Model The properties of thermoelectric generation unit are calculated using the Eq. 1 and 2.
1 (1) 2 (2) 1 Qc DeT cj I re I 2 . e 'T j 2 Here, Equations 1 and 2 are the basic equation of thermoelectric generation. [14] Heat Qh is supplied by the thermal source at the hot surface, Qc is the heat flowing out at cold surface. De is the Seebeck coefficient , re is the internal electric resistance, .e is the thermal conductance and I represents the electric current. Thj is the temperature of the hot junction of thermoelectric element, Tcj is the temperature of the cold junction of thermoelectric element and 'Tj is the temperature difference Thj – Tcj. The maximum generation output Pmax is expressed by Eq. 3. Qh
DeT hjI re I 2 . e 'T j
2 (3) 1 (D e 'T j ) Pmax re 4 In this model, the TEG unit consists of heat collection plate, module and water cooled plate. The module has electrical insulation plate, electrode and thermoelectric element. The thermal resistance model is shown in Fig. 4. Temperature of heat collection plate
Thermal resistance of heat collection plate Thermal resistance of thermal grease Thermal resistance of electrical insulation plate Thermal resistance of thermal grease
Thj Tcj
Thermal resistance of electrode Thermal resistance of thermoelectric element Thermal resistance of electrode Thermal resistance of thermal grease Thermal resistance of electrical insulation plate Thermal resistance of thermal grease
Temperature of cooling water
Thermal resistance of water cooled plate
Fig. 4 Illustration of the thermal resistance model
Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
4. Calculation result of BiTe unit In this calculation, the thermoelectric element size range is based on it on the commercial thermoelectric module [15,16]. In order to investigate the element size dependence of the property of a unit, we set the size range as follows., the cross section of the thermoelectric element is 1mm×1mm−5×5mm2ǃheight is 0.3−10mm. Also, we set that the gap of element is 0.55, 1.6, 2.5mm. Figure 5 shows the relation between the element width in each gap, and the number of element pairs. We calculated the unit performance with typical thermoelectric properties of BiTe. It is that ZT is about 0.8~0.9 at 100−150ć. The material and properties of unit components are shown in table1. We calculate the power output, efficiency, optimum operation current Imax, Qh, 'Tj in the condition of temperature of the heat collection plate surface is 265ć and temperature of cooling water is 25ć. 16000 gap:0.55mm gap:1.6mm gap:2.5mm
number of pairs
14000 12000 10000 8000 6000 4000 2000 0
0
1
2 3 4 5 6 element width(mm) Fig. 5. Element width dependence of number of pairs
Material : Al Heat collection plate
Thermal Conductivity : 180(W/mK) Thickness : 10mm
Thermal grease
Thermal Conductivity : 0.84(W/mK) Thickness : 15䃛m 15䃛 䃛m Material : AlO2
Electrical insulation plate
Thermal Conductivity : 24(W/mK) Thickness : 0.5mm Material : Cu
Electrode
Thermal Conductivity : 400(W/mK) Thickness : 0.5mm
Water cooled plate
Thermal resistance : 0.004(K/W)
Table 1 The material and properties of unit components The calculation result of power output and inflow heat are shown in Fig. 6 and Fig. 7. The unit which has narrower gap can generate larger power output. Similarly, the inflow heat becomes larger. It is found that there is the element size range, which gives the maximum power output. About the element size dependence of power output, the unit that the element height is lower has larger power output, however, from specific height, the power output decrease. This tendency can be understood as, for lower element height, the thermal resistance of unit decrease, therefore, the unit can transfer large heat flow. However, for specific larger inflow heat, the temperature difference of element, 'Tj
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is too small and the output becomes small.
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Fig. 6 Calculation results of power output
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Fig. 7 Calculation results of inflow heat In order to investigate these situations, we calculate the element height dependency of thermal resistance and inflow heat Qh. Figure 8 shows the calculation result. It is found that the element height is lower and thermal resistance of the unit becomes smaller, inflow heat become larger. Also, the relation between the thermal resistance of the unit and the power output is shown in Fig. 9. We find that specific thermal resistance has the maximum power output. This represents, as mentioned above tendency, from specific element height, the unit output decrease.
0.08
16
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10
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Q h(kW)
T hermal resistance of unit (ºC /W)
Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
8
element height(mm)
Fig. 8 The element height dependence of thermal resistance and Qh (element size is 5×5mm2)
600
P (W)
500 400 300 200 100 0 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
T hermal resistance of unit (ºC /W) Fig. 9 Relation between the thermal resistance of the unit and the power output (element size is 5×5mm2)
5. Calculation result of high temperature thermoelectric material unit There are many promising thermoelectric materials in the temperature range 400Υ and above [17−20]. We assume that the typical ZT value of high temperature materials is about 0.7~0.9 at 450−500ć. The calculation procedure is same as Bi-Te. But the heat collection plate is SUS430 and the electric insulation plate is AlN. The heat collection plate surface is 450Υ. The calculation results of power output and Qh are shown in Fig. 10 and Fig. 11. Comparing BiTe unit, the high temperature material unit produces large temperature difference. Therefore, it can make large inflow heat and power output.
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Fig. 10 The calculation results of power output
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Fig. 11 The calculation results of inflow heat 6. Study of Radiant Waste Heat We consider the recovery from the radiation waste heat. Figure 12 shows the schematic illustration of a model. The size of the heat source is 2.2m×3.5m and the distance between the heat source and the thermoelectric generation unit is 0.5m. This model is based on the verification test in steel works [4]. We assume that the heat source is a continuous casting slab. The heat transfer calculation in Refs. 4 included the air convection. However the contribution is small. Therefore, only the radiation heat transfer has been considered.
Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
Fig. 12 Schematic illustration of model
The radiation heat transfer Qra is expressed by Eq. 4. Here H is the emissivity, V is the Stefan-Boltzmann constant, F is the view factor, S is the total area of thermoelectric generation units. Ts is the temperature of the heat source, Th is the temperature of the heat collection plate.
(4) Qra H F V S (Ts4 Th4 ) The calculated radiation transfer heat per one unit for various T s is shown in Fig. 13. Here, Ts of BiTe used unit is 265Υ and Ts of high temperature material used unit is 450Υ.
Qh (kW)
10 high temperature material 9 BiTe 8 7 6 5 4 3 2 1 0 600 700 800 900 1000 T s (°C )
Fig. 13 Calculated radiation transfer heat per one unit for various Ts We examine the power output for practical element size range. The practical element size range is based on the range used in the commercial thermo-module. The size range is, Width: 1.5−2.5mmǃHeight:1.0−3.5mm. Out of this size range, it is difficult to use in practice. For example, larger Imax, the thermal stress, and so on. In this element size range, the maximum power output of BiTe and high temperature material used unit is shown in Fig. 14 for various Ts. It is found that BiTe unit has a power output nearly equal to the high temperature material unit at a heat source temperature 900ºC and above. BiTe unit is generally used at low temperature. In this calculation, it is also utilizable at high temperature.
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Takeshi Kajihara et al. / Materials Today: Proceedings 2 (2015) 804 – 813
600 high temperature material BiTe
500 400
P (W)
300 200 100 0 600
700
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900
T s (°C )
1000
1100
Fig. 14 Power output for various Ts
7. Summary In this work, the performance of thermoelectric generation unit using Bi-Te is considered in the case of various thermoelectric element sizes and gap. As the gap dependency of power output, the unit which has narrower gap is the tendency for power output becoming large. It is found that there is the element size range, which gives the maximum power output. About the element size dependence of power output, the unit that the element height is lower has larger power output, however, from specific height, the power output decrease. Also, we calculate the performance of the unit using a high temperature thermoelectric material. We consider the recovery from the radiation waste heat. In the practical element size range, it is found that Bi-Te unit has a power output nearly equal to the high temperature material unit at a heat source temperature 900ºC and above. In our model calculation, Bi-Te unit is also utilizable at high temperature.
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