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Magnetocaloric heat circulator based on self-heat recuperation technology
Chemical Engineering Science 101 (2013) 5–12
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Magnetocaloric heat circulator based on self-heat recuperation technology Yui Kotani a, Muhammad Aziz b, Yasuki Kansha a, Chihiro Fushimi c, Atsushi Tsutsumi a,n a Collaborative Research Center for Energy Engineering, Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan b Solution Research Laboratory, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan c Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei-shi, Tokyo 184-8588, Japan
H I G H L I G H T S
Magnetocaloric heat circulator for thermal process based on self-heat recuperation is proposed. Magnetization of magnetic material instead of compression is used for process heat circulation. Magnetic heat circulation cycle has been described in terms of temperature–entropy diagram. The simulation results show potential for drastic energy saving in thermal processes.
art ic l e i nf o
a b s t r a c t
Article history: Received 26 July 2012 Received in revised form 20 May 2013 Accepted 30 May 2013 Available online 6 June 2013
A concept of a novel magnetocaloric heat circulator based on self-heat recuperation technology for application in thermal processing is proposed. In the heat circulator, process heat is recirculated by using the magnetocaloric effect of ferromagnetic materials subjected to cyclic magnetization and demagnetization. The ferromagnetic material is magnetized or demagnetized adiabatically at the highest or lowest process temperature to create the temperature difference required for heat exchange so that all heat is recirculated inside the thermal process without heat addition. The magnetocaloric heat circulation cycle has been analyzed in terms of the temperature–entropy diagram to evaluate its energy consumption. Simulation has been conducted to clarify the theoretical potentials of applying magnetocaloric effect to self-heat recuperation. The simulation results show that the total energy consumption of the magnetocaloric heat circulator is reduced below 1/5 compared to conventional processes with heat recovery, thus showing its potential for energy saving in thermal processes. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Self-heat recuperation Magnetocaloric effect Energy Entropy Chemical processes Thermodynamic process
1. Introduction Over the last few decades, carbon dioxide (CO2) reduction and fossil fuel consumption have been of global concern. In chemical processes that involve heating, the provision of heat by fossil fuel combustion or joule heating is associated with large exergy losses, leading to large amounts of CO2 emissions. Thus far, heat recovery technologies represented by Pinch Technology based on the principle of heat cascading utilization have been applied to reduce energy consumption (Linnhoff and Hindmarsh, 1983; Linnhoff and Eastwood, 1997). However, because of the temperature difference required for heat exchange, not all of the heat can be recovered and addition of make-up heat is needed. Heat pump is a wellknown technology to reduce the energy consumption and exergy
n
Corresponding author. Tel.: +81 3 5452 6727; fax: +81 3 5452 6728. E-mail address: [email protected] (A. Tsutsumi).
0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.05.064
loss of thermal processes compared to furnace heater. But the large temperature difference between the heat source and the heat sink reduces the coefficient of performance (COP) and increase the energy consumption and exergy loss. Recently, self-heat recuperation technology based on the exergy recuperative heat utilization principle has been developed, which can recirculate all process heat providing temperature difference needed for self-heat exchange by compression (Kansha et al., 2009). The amount of energy required for the self-heat recuperative thermal process is much smaller than that for conventional thermal process with heat recovery because no make-up heat is added. A system based on the principle of self-heat recuperation is called a heat circulator. In heat circulator for gaseous materials, it is essential that self-heat recuperation gives the temperature difference for self-heat exchange of process material by adiabatic compression. In general, the temperature for self-heat exchange is smaller than that between external heat source and heat sink. Thus, larger energy saving could be expected for heat circulators in many processes. In the case of gas
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systems, the compression energy can be recovered partially by the expander after heat exchange. In the last few years, several applications of self-heat recuperation technology have been studied in various processes, such as distillation (Kansha et al., 2010), biomass drying (Fushimi et al., 2011; Aziz et al., 2011), cryogenic air separation (Kansha et al., 2011) and chemical absorption CO2 separation (Kishimoto et al., 2011). From process simulation results, it was shown that energy consumption in these self-heat recuperative processes can be reduced to 1/5–1/20 compared to conventional processes with heat recovery. In this paper, a novel magnetocaloric heat circulator for thermal processing based on the magnetocaloric effect (MCE) of ferromagnetic materials is proposed, where adiabatic magnetization instead of compression is applied to ferromagnetic materials to cause a reversible temperature change. The performance of magnetocaloric heat circulator was evaluated in terms of the temperature– entropy diagram and its theoretical energy saving potential has been clarified.
2. Magnetocaloric heat circulation 2.1. Magnetocaloric effect The magnetocaloric effect is the heating or cooling of magnetic materials subjected to varying magnetic field (Tishin and Spichkin, 2003; Oliveira and Ranke, 2010). When the magnetic field is applied adiabatically to a magnetic material, its magnetic moments become ordered so that the magnetic part of the total entropy is reduced. In order to keep constant the total entropy in the adiabatic process, the crystalline lattice entropy increases, raising the temperature. The opposite effect occurs when the magnetic field is removed adiabatically, the temperature decreases. The variation in temperature owing to the magnetocaloric effect is called the adiabatic temperature change, ΔTad, and is a function of the initial magnetic flux density, B1, final magnetic flux density, B2, and its initial temperature, T. For paramagnetic materials in the temperature regions above 15–20 K, the entropy change from the ordering of the magnetic spins of paramagnetic materials is insufficient to cause any practical temperature change. On the other hand, in the case of ferromagnetic materials, it is possible to gain a practical temperature change where the maximum magnetocaloric effect occurs, near the magnetic ordering temperature, known as the Curie temperature, θc. Giauque and MacDougall first realized the use of the magnetocaloric effect to reach extremely low temperatures ( o1 K) by the adiabatic demagnetization of paramagnetic salts (Giauque and MacDougall, 1933). Brown introduced the concept of magnetic heat pumping using a regenerative cycle of a ferromagnetic material and extended the temperature range of magnetocaloric effect applications to room temperature (Brown, 1976). After this work by Brown, Barclay introduced the concept of active magnetic regenerator (Barclay, 1982) and substantial research has been conducted into magnetic heat pumping at room temperature regions, using superconducting (Zimm et al., 1998; Hirano et al., 2002; Blumenfeld et al., 2002) and permanent magnets (Bohigas et al., 2000; Okamura et al., 2006; Zimm et al., 2006; Engelbrecht et al., 2012) to create a magnetic field. These studies show that magnetic heat pumps are energy efficient and fully compatible with conventional compression heat pumps. Much effort is being put into modeling the active magnetic regenerative heat pumps to optimize their parameters and the geometry of the regenerators to gain further efficiency (Nielsen et al., 2011; Tura et al., 2012). Although by applying heat pumps, it is often possible to reduce the energy consumption of a thermal process, the heat load and
Fig. 1. (a) Schematic and (b) its temperature–heat diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is ferromagnetic.
capacity of the process stream are often different from those of the pumped heat. In heat circulators the feed process stream is heated by the recuperated effluent process stream, thus the exergy destruction due to heat transfer is minimized. 2.2. Magnetocaloric heat circulator In the magnetocaloric heat circulator, the adiabatic magnetization is applied to ferromagnetic materials to cause a reversible temperature change. The process heat is recirculated by the magnetocaloric effect of magnetic material subjected to cyclic magnetization and demagnetization. Fig. 1 shows a schematic of the magnetocaloric heat circulator when the process material is ferromagnetic. It consists of a feed effluent counter-flow heat exchanger and a high field region. The temperature of the process material is raised from the environmental temperature, T0, to its set temperature, Tset, in the counter-flow heat exchanger (HEX) (1-2) receiving the heat from effluent process material (4-5). The temperature difference needed for heat exchange is provided by adiabatic magnetization (3-4). Part of the magnetizing work is recovered when demagnetizing (5-6), and rest of the heat is discarded at the cooling water (CW) (6-7). Thus, all of the heat is circulated without heat addition. Note that there is a temperature gradient within the heat exchanger for it is a counter-flow heat exchanger. Fig. 2 shows a schematic of the magnetocaloric heat circulator when the process material is non-magnetic. The magnetocaloric heat circulator consists of two heat exchangers, a closed cycle with ferromagnetic working material, and a high field region. The ferromagnetic material circulates in and out of the magnetic field. The temperature of the working material rises when it is magnetized (2-3), and decreases when it is demagnetized (4-1). The process material is inserted at environmental temperature, T0, and is heated in HEX1 (a-b) to its set temperature, Tset. The process material is then cooled in HEX2 (c-d) and the remaining heat is discarded at the cooling water (d-e). The remaining heat is discarded from the fluid, thus point 1 is shifted to point 1' in the temperature–heat diagram but both points are of the same state.
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Fig. 4. Image of Styert-like magnetocaloric heat circulator.
Fig. 2. (a) Schematic and (b) its temperature–heat diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is non-magnetic.
to compensate part of the magnetizing force and recover part of the magnetizing work. Modifying the magnetic heat pump designed by Steyert (Steyert, 1978) and actualized by Coelho (Coelho et al., 2009) for self-heat recuperation, the device will look as shown in Fig. 4. Temperature gradient exists within the magnetocaloric wheel. The process fluid comes in to the wheel at environmental temperature, T0, from 1, is heated to its set temperature, Tset, and exits at 2. Via the next process, it is cooled back to environmental temperature, T0, in between 3 and 4. The wheel of magnetocaloric material rotates so that the heat is exchanged in counter-flow. Discussion about different magnetic heat pumping designs has been performed by Scarpa (Scarpa et al., 2012) including the above mentioned design by Steyert. Most magnetic heat pump designs can be applied for self-heat recuperation with small modifications.
3. Performance evaluation of magnetocaloric heat circulator 3.1. Simulation method
Fig. 3. Configuration of magnetocaloric heat circulator to recover magnetizing work.
The working material is used to raise the temperature of the material and transfer heat so that the process heat can be recirculated without heat addition. In a magnetocaloric heat circulator, there is no need to pump heat between large temperature differences, thus the temperature elevation that needs to be gained by adiabatic magnetization is only the temperature difference for self-heat exchange (ΔTad in Figs. 1 and 2b). The magnetocaloric heat circulator must be constructed such that the magnetizing work can be recovered when demagnetizing. For this purpose, the magnetocaloric heat circulator can be configured in a circular shape as shown in Fig. 3. When part A of the circle is demagnetized, part B is automatically magnetized. The work required from outside the process, Wnet, can be expressed as: Z Z W net ¼ F 2 dl− F 1 dl ð1Þ where F2 and F1 are magnetizing forces in parts A and B, respectively and dl is the length of the movement. This allows us
The net energy consumption, Wnet, and the heat circulated, Qcir, are derived in terms of the temperature–entropy diagram. When the process material is ferromagnetic, the cycle of the magnetocaloric heat circulator consists of isomagnetic heating, adiabatic magnetization, isomagnetic cooling and adiabatic demagnetization. This magnetocaloric heat circulator cycle can be described as a reverse Brayton-like cycle (Fig. 5). The two solid lines represent the isomagnetic lines when the magnetic flux density is B1 (¼ 0) and B2 ( 4 0). If the set temperature, Tset, is above the environmental temperature, T0, the process material is heated at the heat exchanger from the environmental temperature, T0, to its set temperature, Tset (1-2), adiabatically magnetized (3-4), cooled (4-5), adiabatically demagnetized (5-6) and the remainder of the heat is discarded (6-7). In the reverse Brayton heat pump cycle, the amount of entropy change owing to heating is equal to the amount of entropy change owing to cooling because heat is transferred outside the system. In the case of the magnetocaloric heat circulator, all heat is circulated inside the system so the entropy change owing to heating is larger than the entropy change owing to cooling. The heat provided to the stream when heating Q12 (1–2 – c – a) is equal to the heat discharged when cooling Q45 (b – c – 4 – 5). Q 12 ¼ −Q 45 Z 2 Z TdS ¼ − 1
5
TdS 4
ð2Þ
The heat in Eq. (2) represents the heat circulated (|Q12| ¼|Q45| ¼ Qcir). The pinch point will be at the smaller of temperature difference between state points 4 and 3, ΔT43, or temperature difference between state points 5 and 7, ΔT57. Because the
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Fig. 5. Temperature–entropy diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is ferromagnetic: reverse Brayton-like cycle (note numbers of each stream correspond to Fig. 1).
enthalpy of state points 1 and 7 are the same, from the conservation law of energy, the heat discarded Qdiscard (a – b – 6 – 7) is equal to the total work required, Wnet. Q discard ¼ W net
ð3Þ
Note that the magnetization and the demagnetization are assumed to be a complete adiabatic process. Irreversible loss has been considered in terms of hysteresis loss and electromagnetic induction heating (EIH) in the discussion. Fig. 6 shows the temperature–entropy diagram of magnetocaloric heat circulator when the process material is non-magnetic. The amount of ferromagnetic material is chosen so that its heat capacity will match the heat capacity of the fluid which is the subject of heating. If the set temperature, Tset, is above environmental temperature, T0, the non-magnetic material at environmental temperature, T0, is heated (a-b) to its set temperature, Tset, while the magnetized magnetic material is cooled (3-4) in HEX1. The process material is then cooled (c-d) while the demagnetized magnetic material is heated (1-2) in HEX2. The remaining heat is finally discarded at cooling water (d-e). The following equations may be realized through the energy balance: Q ab ¼ Q 12 ¼ Q cd þ Q discaard ¼ Q 34 þ Q discard
ð4Þ
Q discard ¼ W net
ð5Þ
where Qab (a – b – IV – I) and Q12 (1 – 2 – IV – I) are the heat exchanged in HEX1, Qcd (c – d – III – IV) and Q34 (3 – 4 – II – IV) are the heat exchanged in HEX2 and Qdiscard (d – e – I – III) is the heat discarded at the cooling water. Total energy consumption, Wnet, is equal to the heat discarded at the cooling water, Qdiscard. The pinch point will be the smallest out of the temperature differences ΔT3c, ΔTb2, ΔT4a and ΔTd1. Similar discussion can be made in the case where the set temperature, Tset, is below environmental temperature, T0, for magnetic and non-magnetic process material (Fig. 7). In all cases, from the conservation law of energy, total energy consumption or the net work input, Wnet, is equal to the heat discarded at the cooling water, Qdiscard. Magnetic flux density, B2, is chosen so that the pinch point temperature is larger than the minimum temperature difference for heat exchange, ΔTmin. The total entropy, ST, of the magnetic material can be expressed by the sum of the magnetic (SM), lattice (SL) and electron (SE) entropies as: ST ðB; TÞ ¼ SM ðB; TÞ þ SL ðTÞ þ SE ðTÞ
ð6Þ
Fig. 6. Temperature–entropy diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is ferromagnetic (note numbers of each stream correspond to Fig. 2).
where B and T denote the magnetic flux density and temperature, respectively. The magnetic entropy is a function of magnetic flux density and temperature, while the lattice and electron entropies are functions of temperature only. The magnetic, lattice and electron entropies can be expressed as shown in Table 1 (Tishin and Spichkin, 2003; Huang and Teng, 2004). The magnetic entropy change, ΔSM, when the magnetic flux density was changed from B1 to B2 is expressed by: ΔSM ¼ SM ðB1 ; TÞ−SM ðB2 ; TÞ
ð7Þ
The energy consumption is compared with a benchmark process with heat recovery (Fig. 8). The same benchmark process can be used for processes with process materials of ferromagnetic and non-magnetic material. Total energy consumption of the benchmark process is equal to the heat provided at the furnace heater, QFH.
3.2. Simulation conditions A simulation of energy consumption was performed under four conditions. Gadolinium (Gd) was selected as reference magnetic material because it shows a large magnetocaloric effect at room temperature (θc ¼ 293 K) and its physical properties have been well studied (Benford and Brown, 1981; Dan'kov et al., 1998). Water was selected as reference non-magnetic material. The initial magnetic flux density was assumed as 0 T. In the case when Gd is the subject of heating, commencing from environmental temperature (T0 ¼298 K), the Gd temperature was raised to 308 K (condition 1) and 318 K (condition 2). Similarly in the case when water is the subject of heating, water at environmental temperature (T0 ¼298 K) is heated to 308 K (condition 3) and 318 K (condition 4) as shown in Table 2. The starting magnetic flux density, B1, was set to 0 T and the minimum temperature difference required for heat exchange, ΔTmin, was set to 2 K. The efficiency of the heat exchanger was assumed as 100% (i.e., no heat loss). The total energy consumption is compared with the total energy consumption of the benchmark process for evaluation. Fig. 9 shows the numerical magnetic entropy change, ΔSM, and total entropy, ST, when Gd was subjected to various magnetic flux densities at different temperatures calculated by the methods provided in Table 1. The adiabatic temperature change, ΔTad, can be determined by comparing the total entropy curves at different magnetic fields.
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Table 1 Entropy calculation method; R is the gas constant, J is the total angular momentum, kB is the Boltzmann constant, g is the spectroscopic splitting factor, μB is the Bohr magneton, θD is the Debye temperature, θc is the Curie temperature and γ is the electron heat capacity (Tishin and Spichkin, 2003; Huang and Teng, 2004). Magnetic entropy h i 1 SM ¼ R ln sinh 2Jþ1 2J X −ln sinh 2J X −XBJ ðXÞ 2Jþ1 1 1 BJ ðXÞ ¼ 2Jþ1 2J coth 2J X − 2J coth 2J X X¼
gJμB B kB T
þ
Lattice entropy SL ¼ −3Rlnð1−e−x Þ þ 12 x13
Electron entropy Rx
SE ¼ γT
ξ3 0 eξ −1 dξ
x ¼ θD =T
3θc JBJ ðXÞ TðJþ1Þ
Fig. 7. Schematic (a) and temperature–entropy diagram (b) of the magnetocaloric heat circulator when the set temperature, Tset, is below environmental temperature, T0. (1) Process material is magnetic and (2) non-magnetic.
Table 2 Simulation conditions T0 is the environmental temperature, and Tset is the set temperature. Conditions
Process material
1 2 3 4
Gd Gd Water Water
T0 [K]
298
Tset [K]
Temperature change [K]
308 318 308 318
+10 +20 +10 +20
Table 3 Magnetic flux density, B; heat circulated, Qcir; net work required, Wnet; heat provided at fired heater, QFH per unit mass of process material at various conditions. Condition ΔTmin [K]
B2 [T] 1 2 3 4
Fig. 8. Schematic of the benchmark process with heat recovery.
4. Results and discussion The simulation results are summarized in Table 3. Potential of significant energy reduction was gained by the magnetocaloric
Magnetocaloric heat circulator
2.0
Qcir [J kg−1]
1.35 1680 1.93 3366 2.10 41,286 2.98 82,073
Benchmark process
Wnet [J kg−1]
Qcir [J kg−1]
QFH [J kg−1]
16.3 35.9 513 1517
1344 3046 33,440 75,240
336.5 320.0 8360 8350
W net =Q FH [%]
4.8 11.2 6.13 18.2
heat circulator. Compared with the energy consumption in the benchmark process, QFH, the energy consumption in the magnetocaloric heat circulator, Wnet, was reduced to 4.8–18.2%. Less energy saving was obtained for conditions with non-magnetic process material compared to conditions with ferromagnetic process material because larger magnetic field is needed to ensure the minimum temperature differences at the two heat exchangers. Also, the energy consumption for the magnetocaloric heat circulator becomes larger as the set temperature move away from the Curie temperature, θc, because the adiabatic temperature change, ΔTad, at the set temperature, Tset, becomes smaller and thus larger magnetic field is needed to ensure the minimum temperature
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Fig. 9. Entropy calculation of Gd subjected to various magnetic flux densities; (a) numerical magnetic entropy change, −ΔSM, (b) total entropy, ST.
difference for heat exchange. Nevertheless, large energy saving was obtained compared to conventional thermal process with heat recovery. In an adiabatic process, the area surrounded by the two isomagnetic lines (Fig. 3; 3 – 4 – 5 – 6) is equal to the area representing the heat that is discarded at the cooling water (6 – 7 – a – b). This indicates that the smaller the temperature difference required for heat exchange, ΔTmin (i.e. slower heat exchange), the smaller the work required, Wnet, for magnetocaloric heat circulation. Smaller temperature difference for heat exchange is also preferable because it is difficult to create strong magnetic field using permanent magnets and extra energy will be needed if superconducting magnets or electromagnets are used. Exergy losses owing to the irreversibility of the magnetizing or demagnetizing process are induced by hysteresis loss and electromagnetic induction heating. The former depends on the physical properties of the material that is subjected to varying magnetic flux density. It is assumed very small if not any for Gd (Dan'kov et al., 1998). The latter is the joule heat generated by the eddy current induced by the change in magnetic flux applied to the material and the material resistance. In the magnetocaloric heat circulator, the rate in which the magnetic flux change is probably merely few teslas per second and the specific resistivity of Gd is only few micro-ohms per meter, thus the effect of electromagnetic induction heating may be assumed very small. Another factor that
may affect the value of the total energy consumption is the demagnetizing effect caused by varying magnetic permeability in the ferromagnetic material (Peksoy and Rowe, 2005). The demagnetization effect is dependent on geometry and non-uniform properties of the magnetic material, thus needs to be taken into account when designing the actual device. Two patterns for processes with set temperature, Tset, above the environmental temperature, T0, are presumed depending on the temperature at which the magnetization and demagnetization takes place and similarly, two patterns for processes with set temperature, Tset, below the environmental temperature, T0, are presumed (Fig. 10). Patterns 1 and 2 are processes with set temperature, Tset, above environmental temperature, T0. In pattern 1, the temperature difference is larger between state points 4 and 2 than that between state points 5 and 1 (ΔT42 4ΔT51). In this case, the minimal temperature difference is ΔT51. On the contrary, in pattern 2, the temperature difference is larger between state points 5 and 1 than that between state points 4 and 2 (ΔT51 4 ΔT42). Hence, the minimal temperature difference is ΔT42. A similar discussion can be made processes with set temperature, Tset, below environmental temperature, T0, where the minimal temperature difference is the temperature difference between state points 3 and 5, ΔT35, for pattern 3 and the temperature difference between state points 2 and 6, ΔT26, for pattern 4. The magnetic flux density is determined such that the
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Fig. 10. Temperature–heat diagrams of different magnetocaloric heat circulator patterns. Pattern 1 and 2 are processes with set temperature, Tset, above the environmental temperature, T0, and pattern 3 and 4 are processes with set temperature, Tset, below the environmental temperature, T0.
Fig. 12. Temperature–entropy diagram of magnetic heat pump system.
Fig. 11. Schematic (a) and temperature–entropy diagram (b) of magnetocaloric heat circulator when ferromagnetic process material is solid and working fluid is used to transfer heat.
smallest temperature difference is larger than the minimum temperature difference required for heat exchange, ΔTmin. In all cases, the net work input, Wnet, is equal to the energy discarded at the cooling water, Qdiscard. All conditions calculated are categorized as pattern 2 because the adiabatic temperature difference, ΔTad, decreases with distance from the Curie temperature, θc, which is at 293 K for Gd. In actuality, ferromagnetic material with optimal
Curie temperature in between the magnetizing and demagnetizing temperature will need to be chosen in order to satisfy the minimum temperature difference required for heat exchange with limited magnetic flux density. In the case where the process material is ferromagnetic, the process material is likely to be solid. In this case, it will become difficult for the process materials to exchange heat in counterflow. Thus, working fluid will be needed to transfer the heat between the process materials as shown in Fig. 11a. Fig. 11b shows the temperature–entropy diagram of the magnetocaloric heat circulator when the ferromagnetic process material is solid. The minimum temperature difference, ΔTmin, is needed for heat exchange between the process material and the working fluid,
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which results in doubling the area surrounded by the isomagnetic lines and thus doubling the total energy consumption, Wnet. Fig. 12 shows the temperature–entropy diagram of a magnetic heat pump system when the heat is pumped from a heat source at TC to heat sink at TH. The magnetic heat pump system consist of ferromagnetic material (1 – 2 – 3 – 4) and a working fluid (a – b – c – d). The temperature of the working fluid is raised (a-b) by receiving the heat from the ferromagnetic material (3-4). Then, the pumped heat, QH, is transferred to the heat sink (b-c). The remaining heat is transferred to the ferromagnetic material for regeneration (c-d, 1-2). After, heat, QC, is transferred from the heat source to the ferromagnetic material and comes back to its original state (d-a). In a magnetic heat pump, the heating capacity, QH, or the cooling capacity, QC, will be used to heat or cool the process material. In a magnetocaloric heat circulator (Figs. 4–7), the process material heat is circulated. Thus, the magnetocaloric heat circulator has great potential for energy saving in thermal processes where the temperature of a process material is raised to a certain temperature and finally comes back to its original state.
5. Conclusions Self-heat recuperation technology using adiabatic magnetization and demagnetization instead of compression and expansion for thermal processes was proposed. The magnetocaloric effect raises the ferromagnetic material temperature, and the magnetizing work can be recovered partially when demagnetizing by configuring the ferromagnetic material in a circular shape. All heat is recirculated inside the system without heat addition. It is shown that means to recuperate the process stream heat for heat circulation is not limited to compression and can be realized by enforcing a change of state by providing work. Although the temperature change one can gain from adiabatic magnetization or demagnetization is small in the range of permanent magnets (up to 2 T), in self-heat recuperation, the required temperature change is only that needed for heat exchange between the feed and the effluent process material. The magnetocaloric heat circulator when process material is ferromagnetic and non-magnetic has been analyzed in terms of the temperature–entropy diagram, and its theoretical energy consumption limitation has been calculated. The results were compared with the benchmark process with heat recovery and were made clear that the energy consumption could be reduced to 4.8–18.2% by applying the magnetocaloric heat circulator, indicating the significant energy saving that can be obtained in thermal processes. Therefore although heat circulation is temperature is limited by the Curie temperature of the ferromagnetic material, the magnetocaloric heat circulator can be counted as one of the future options for energy saving in certain thermal processes.
Acknowledgment The authors would like to thank Professor Masashi Tokunaga of the Institute of Solid State Physics, The University of Tokyo, for his time and valuable comments in the preparation of this research.
References Aziz, M., Fushimi, C., Kansha, Y., Mochidzuki, K., Kaneko, S., Tsutsumi, A., Matsumoto, K., Hashimoto, T., Kawamoto, N., Oura, K, Yokohama, K, Yamaguchi, Y., Kinoshita, M., 2011. Innovative energy-efficient biomass drying based on selfheat recuperation. Chem. Eng. Technol. 34, 1095–1103. Barclay, J.A., 1982. Use of a ferrofluid as a heat-exchange fluid in a magnetic refrigerator. J. Appl. Phys. 53, 2887–2894. Benford, S.M., Brown, G.V., 1981. T–S diagram for gadolinium near the Curie temperature. J. Appl. Phys. 52, 2110–2112. Blumenfeld, P.E., Prenger, F.C., Sternberg, A., Zimm, C.B., 2002. High temperature superconducting magnetic refrigeration. Adv. Cryog. Eng. 47, 1019–1026. Bohigas, X., Molins, E., Roig, A., Tejada, J., Zhang, X.X., 2000. Room-temperature magnetic refrigerator using permanent magnets. IEEE. Trans. Magn. 36, 538–544. Brown, B.V., 1976. Magnetic heat pumping near room temperature. J. Appl. Phys. 47, 3673–3680. Coelho, A.A., Gama, S., Magnus, A., Carvalho, G., 2009. Prototype of a Gd-based rotating magnetic refrigerator for work around room temperature. Proceedings of the Third International Conference on Magnetic Refrigeration at Room Temperature, Des Moines, Iowa, USA, 11–15, May. International Institute of Refrigeration, Paris, 381–386. Dan'kov, S.Y., Tishin, A.M., Pecharsky, V.K., Gschneidner Jr., K.A., 1998. Magnetic phase transitions and the magnetothermal properties of gadolinium. Phys. Rev. B 57, 3478–3490. Engelbrecht, K., Eriksen, D., Bahl, C.R.H., Bjørk, R., Geyti, J., Lozano, J.A., Nielsen, K.K., Saxild, F., Smith, A., Pryds, N., 2012. Experimental results for a novel rotary active magnetic regenerator. Int. J. Refrig. 35, 1498–1505. Fushimi, C., Kansha, Y., Aziz, M., Mochidzuki, K., Kaneko, S., Tsutsumi, A., Matsumoto, K., Kawamoto, N., Oura, K., Yokohama, K., Yamaguchi, Y., Kinoshita, M., 2011. Novel drying process based on self-heat recuperation technology. Drying Technol. 29, 105–110. Giauque, W.F., MacDougall, D.P., 1933. Attainment of temperatures below 11 absolute by demagnetization of Gd2(SO4)3 8H2O. Phys. Rev. 43, 768. Hirano, N., Nagaya, S., Takahashi, M., Kuriyama, T., Ito, K., Nomura, S., 2002. Development of magnetic refrigerator for room temperature application. Adv. Cryog. Eng. 47, 1027–1034. Huang, W.N., Teng, C.C., 2004. A simple magnetic refrigerator evaluation model. J. Magn. Magn. Mater. 282, 311–316. Kansha, Y., Tsuru, N., Sato, K., Fushimi, C., Tsutsumi, A., 2009. Self-heat recuperation technology for energy saving in chemical processes. Ind. Eng. Chem. Res. 48, 7682–7686. Kansha, Y., Tsuru, N., Fushimi, C., Tsutsumi, A., 2010. An innovative modularity of heat circulation for fractional distillation. Chem. Eng. Sci. 65, 330–334. Kansha, Y., Kishimoto, A., Nakagawa, T., Tsutsumi, A., 2011. A Novel cryogenic air separation process based on self-heat recuperation. Sep. Purif. Technol. 77, 389–396. Kishimoto, A., Kansha, Y., Fushimi, C., Tsutsumi, A., 2011. Exergy recuperative CO2 gas separation in post-combustion capture. Ind. Eng. Chem. Res. 50, 10128–10135. Linnhoff, B., Hindmarsh, E., 1983. The pinch design method for heat exchanger networks. Chem. Eng. Sci. 5, 745–763. Linnhoff, B., Eastwood, A.R., 1997. Overall site optimization by pinch technology. Chem. Eng. Res. Des. 75, 138–144. Nielsen, K.K., Tusek, J., Engelbrecht, K., Schopfer, S., Kitanovski, A., Bahl, C.R.H., Smith, A., Pryds, N., Poredos, A., 2011. Review on numerical modeling of active magnetic regenerators for room temperature applications. Int. J. Refrig. 34, 603–616. Okamura, T., Yamada, K., Hirano, N., Nagaya, S., 2006. Performance of a roomtemperature rotary magnetic refrigerator. Int. J. Refrig. 29, 1327–1331. Oliveira, N.A., Ranke, P.J., 2010. Theoretical aspects of the magnetocaloric effect. Phys. Rep. 489, 89–159. Peksoy, O., Rowe, A., 2005. Demagnetizing effects in active magnetic regenerators. J. Magn. Magn. Mater. 288, 424–432. Scarpa, F., Tagliafico, G., Tagliafico, L., 2012. Classification proposal for room temperature magnetic refrigerators. Int. J. Refrig. 35, 453–458. Steyert, W.A., 1978. Stirling-cycle rotating magnetic refrigerators and heat engines for use near room temperature. J. Appl. Phys. 59, 1216–1226. Tishin, A.M., Spichkin, Y.I., 2003. The Magnetocaloric Effect and Its Applications, Institute of Physics Publishing, Bristol. Tura, A., Nielsen, K.K., Rowe, A., 2012. Experimental and modeling results of a parallel plate-based active magnetic regenerator. Int. J. Refrig. 35, 1518–1527. Zimm, C., Jastrab, A., Sternberg, A., Pecharsky, V., Gschneidner, K., Osborne, M., Anderson, I., 1998. Description and performance of a near-room temperature magnetic refrigerator. Adv. Cryog. Eng. 43, 1759–1766. Zimm, C., Boeder, A., Chell, J., Sternberg, A., Fujita, A., Fujieda, S., Fukamichi, K., 2006. Design and performance of a permanent-magnet rotary refrigerator. Int. J. Refrig. 29, 1302–1306.
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Chemical Engineering Science journal homepage: www.elsevier.com/locate/ces
Magnetocaloric heat circulator based on self-heat recuperation technology Yui Kotani a, Muhammad Aziz b, Yasuki Kansha a, Chihiro Fushimi c, Atsushi Tsutsumi a,n a Collaborative Research Center for Energy Engineering, Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan b Solution Research Laboratory, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan c Department of Chemical Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei-shi, Tokyo 184-8588, Japan
H I G H L I G H T S
Magnetocaloric heat circulator for thermal process based on self-heat recuperation is proposed. Magnetization of magnetic material instead of compression is used for process heat circulation. Magnetic heat circulation cycle has been described in terms of temperature–entropy diagram. The simulation results show potential for drastic energy saving in thermal processes.
art ic l e i nf o
a b s t r a c t
Article history: Received 26 July 2012 Received in revised form 20 May 2013 Accepted 30 May 2013 Available online 6 June 2013
A concept of a novel magnetocaloric heat circulator based on self-heat recuperation technology for application in thermal processing is proposed. In the heat circulator, process heat is recirculated by using the magnetocaloric effect of ferromagnetic materials subjected to cyclic magnetization and demagnetization. The ferromagnetic material is magnetized or demagnetized adiabatically at the highest or lowest process temperature to create the temperature difference required for heat exchange so that all heat is recirculated inside the thermal process without heat addition. The magnetocaloric heat circulation cycle has been analyzed in terms of the temperature–entropy diagram to evaluate its energy consumption. Simulation has been conducted to clarify the theoretical potentials of applying magnetocaloric effect to self-heat recuperation. The simulation results show that the total energy consumption of the magnetocaloric heat circulator is reduced below 1/5 compared to conventional processes with heat recovery, thus showing its potential for energy saving in thermal processes. & 2013 Elsevier Ltd. All rights reserved.
Keywords: Self-heat recuperation Magnetocaloric effect Energy Entropy Chemical processes Thermodynamic process
1. Introduction Over the last few decades, carbon dioxide (CO2) reduction and fossil fuel consumption have been of global concern. In chemical processes that involve heating, the provision of heat by fossil fuel combustion or joule heating is associated with large exergy losses, leading to large amounts of CO2 emissions. Thus far, heat recovery technologies represented by Pinch Technology based on the principle of heat cascading utilization have been applied to reduce energy consumption (Linnhoff and Hindmarsh, 1983; Linnhoff and Eastwood, 1997). However, because of the temperature difference required for heat exchange, not all of the heat can be recovered and addition of make-up heat is needed. Heat pump is a wellknown technology to reduce the energy consumption and exergy
n
Corresponding author. Tel.: +81 3 5452 6727; fax: +81 3 5452 6728. E-mail address: [email protected] (A. Tsutsumi).
0009-2509/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ces.2013.05.064
loss of thermal processes compared to furnace heater. But the large temperature difference between the heat source and the heat sink reduces the coefficient of performance (COP) and increase the energy consumption and exergy loss. Recently, self-heat recuperation technology based on the exergy recuperative heat utilization principle has been developed, which can recirculate all process heat providing temperature difference needed for self-heat exchange by compression (Kansha et al., 2009). The amount of energy required for the self-heat recuperative thermal process is much smaller than that for conventional thermal process with heat recovery because no make-up heat is added. A system based on the principle of self-heat recuperation is called a heat circulator. In heat circulator for gaseous materials, it is essential that self-heat recuperation gives the temperature difference for self-heat exchange of process material by adiabatic compression. In general, the temperature for self-heat exchange is smaller than that between external heat source and heat sink. Thus, larger energy saving could be expected for heat circulators in many processes. In the case of gas
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systems, the compression energy can be recovered partially by the expander after heat exchange. In the last few years, several applications of self-heat recuperation technology have been studied in various processes, such as distillation (Kansha et al., 2010), biomass drying (Fushimi et al., 2011; Aziz et al., 2011), cryogenic air separation (Kansha et al., 2011) and chemical absorption CO2 separation (Kishimoto et al., 2011). From process simulation results, it was shown that energy consumption in these self-heat recuperative processes can be reduced to 1/5–1/20 compared to conventional processes with heat recovery. In this paper, a novel magnetocaloric heat circulator for thermal processing based on the magnetocaloric effect (MCE) of ferromagnetic materials is proposed, where adiabatic magnetization instead of compression is applied to ferromagnetic materials to cause a reversible temperature change. The performance of magnetocaloric heat circulator was evaluated in terms of the temperature– entropy diagram and its theoretical energy saving potential has been clarified.
2. Magnetocaloric heat circulation 2.1. Magnetocaloric effect The magnetocaloric effect is the heating or cooling of magnetic materials subjected to varying magnetic field (Tishin and Spichkin, 2003; Oliveira and Ranke, 2010). When the magnetic field is applied adiabatically to a magnetic material, its magnetic moments become ordered so that the magnetic part of the total entropy is reduced. In order to keep constant the total entropy in the adiabatic process, the crystalline lattice entropy increases, raising the temperature. The opposite effect occurs when the magnetic field is removed adiabatically, the temperature decreases. The variation in temperature owing to the magnetocaloric effect is called the adiabatic temperature change, ΔTad, and is a function of the initial magnetic flux density, B1, final magnetic flux density, B2, and its initial temperature, T. For paramagnetic materials in the temperature regions above 15–20 K, the entropy change from the ordering of the magnetic spins of paramagnetic materials is insufficient to cause any practical temperature change. On the other hand, in the case of ferromagnetic materials, it is possible to gain a practical temperature change where the maximum magnetocaloric effect occurs, near the magnetic ordering temperature, known as the Curie temperature, θc. Giauque and MacDougall first realized the use of the magnetocaloric effect to reach extremely low temperatures ( o1 K) by the adiabatic demagnetization of paramagnetic salts (Giauque and MacDougall, 1933). Brown introduced the concept of magnetic heat pumping using a regenerative cycle of a ferromagnetic material and extended the temperature range of magnetocaloric effect applications to room temperature (Brown, 1976). After this work by Brown, Barclay introduced the concept of active magnetic regenerator (Barclay, 1982) and substantial research has been conducted into magnetic heat pumping at room temperature regions, using superconducting (Zimm et al., 1998; Hirano et al., 2002; Blumenfeld et al., 2002) and permanent magnets (Bohigas et al., 2000; Okamura et al., 2006; Zimm et al., 2006; Engelbrecht et al., 2012) to create a magnetic field. These studies show that magnetic heat pumps are energy efficient and fully compatible with conventional compression heat pumps. Much effort is being put into modeling the active magnetic regenerative heat pumps to optimize their parameters and the geometry of the regenerators to gain further efficiency (Nielsen et al., 2011; Tura et al., 2012). Although by applying heat pumps, it is often possible to reduce the energy consumption of a thermal process, the heat load and
Fig. 1. (a) Schematic and (b) its temperature–heat diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is ferromagnetic.
capacity of the process stream are often different from those of the pumped heat. In heat circulators the feed process stream is heated by the recuperated effluent process stream, thus the exergy destruction due to heat transfer is minimized. 2.2. Magnetocaloric heat circulator In the magnetocaloric heat circulator, the adiabatic magnetization is applied to ferromagnetic materials to cause a reversible temperature change. The process heat is recirculated by the magnetocaloric effect of magnetic material subjected to cyclic magnetization and demagnetization. Fig. 1 shows a schematic of the magnetocaloric heat circulator when the process material is ferromagnetic. It consists of a feed effluent counter-flow heat exchanger and a high field region. The temperature of the process material is raised from the environmental temperature, T0, to its set temperature, Tset, in the counter-flow heat exchanger (HEX) (1-2) receiving the heat from effluent process material (4-5). The temperature difference needed for heat exchange is provided by adiabatic magnetization (3-4). Part of the magnetizing work is recovered when demagnetizing (5-6), and rest of the heat is discarded at the cooling water (CW) (6-7). Thus, all of the heat is circulated without heat addition. Note that there is a temperature gradient within the heat exchanger for it is a counter-flow heat exchanger. Fig. 2 shows a schematic of the magnetocaloric heat circulator when the process material is non-magnetic. The magnetocaloric heat circulator consists of two heat exchangers, a closed cycle with ferromagnetic working material, and a high field region. The ferromagnetic material circulates in and out of the magnetic field. The temperature of the working material rises when it is magnetized (2-3), and decreases when it is demagnetized (4-1). The process material is inserted at environmental temperature, T0, and is heated in HEX1 (a-b) to its set temperature, Tset. The process material is then cooled in HEX2 (c-d) and the remaining heat is discarded at the cooling water (d-e). The remaining heat is discarded from the fluid, thus point 1 is shifted to point 1' in the temperature–heat diagram but both points are of the same state.
Y. Kotani et al. / Chemical Engineering Science 101 (2013) 5–12
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Fig. 4. Image of Styert-like magnetocaloric heat circulator.
Fig. 2. (a) Schematic and (b) its temperature–heat diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is non-magnetic.
to compensate part of the magnetizing force and recover part of the magnetizing work. Modifying the magnetic heat pump designed by Steyert (Steyert, 1978) and actualized by Coelho (Coelho et al., 2009) for self-heat recuperation, the device will look as shown in Fig. 4. Temperature gradient exists within the magnetocaloric wheel. The process fluid comes in to the wheel at environmental temperature, T0, from 1, is heated to its set temperature, Tset, and exits at 2. Via the next process, it is cooled back to environmental temperature, T0, in between 3 and 4. The wheel of magnetocaloric material rotates so that the heat is exchanged in counter-flow. Discussion about different magnetic heat pumping designs has been performed by Scarpa (Scarpa et al., 2012) including the above mentioned design by Steyert. Most magnetic heat pump designs can be applied for self-heat recuperation with small modifications.
3. Performance evaluation of magnetocaloric heat circulator 3.1. Simulation method
Fig. 3. Configuration of magnetocaloric heat circulator to recover magnetizing work.
The working material is used to raise the temperature of the material and transfer heat so that the process heat can be recirculated without heat addition. In a magnetocaloric heat circulator, there is no need to pump heat between large temperature differences, thus the temperature elevation that needs to be gained by adiabatic magnetization is only the temperature difference for self-heat exchange (ΔTad in Figs. 1 and 2b). The magnetocaloric heat circulator must be constructed such that the magnetizing work can be recovered when demagnetizing. For this purpose, the magnetocaloric heat circulator can be configured in a circular shape as shown in Fig. 3. When part A of the circle is demagnetized, part B is automatically magnetized. The work required from outside the process, Wnet, can be expressed as: Z Z W net ¼ F 2 dl− F 1 dl ð1Þ where F2 and F1 are magnetizing forces in parts A and B, respectively and dl is the length of the movement. This allows us
The net energy consumption, Wnet, and the heat circulated, Qcir, are derived in terms of the temperature–entropy diagram. When the process material is ferromagnetic, the cycle of the magnetocaloric heat circulator consists of isomagnetic heating, adiabatic magnetization, isomagnetic cooling and adiabatic demagnetization. This magnetocaloric heat circulator cycle can be described as a reverse Brayton-like cycle (Fig. 5). The two solid lines represent the isomagnetic lines when the magnetic flux density is B1 (¼ 0) and B2 ( 4 0). If the set temperature, Tset, is above the environmental temperature, T0, the process material is heated at the heat exchanger from the environmental temperature, T0, to its set temperature, Tset (1-2), adiabatically magnetized (3-4), cooled (4-5), adiabatically demagnetized (5-6) and the remainder of the heat is discarded (6-7). In the reverse Brayton heat pump cycle, the amount of entropy change owing to heating is equal to the amount of entropy change owing to cooling because heat is transferred outside the system. In the case of the magnetocaloric heat circulator, all heat is circulated inside the system so the entropy change owing to heating is larger than the entropy change owing to cooling. The heat provided to the stream when heating Q12 (1–2 – c – a) is equal to the heat discharged when cooling Q45 (b – c – 4 – 5). Q 12 ¼ −Q 45 Z 2 Z TdS ¼ − 1
5
TdS 4
ð2Þ
The heat in Eq. (2) represents the heat circulated (|Q12| ¼|Q45| ¼ Qcir). The pinch point will be at the smaller of temperature difference between state points 4 and 3, ΔT43, or temperature difference between state points 5 and 7, ΔT57. Because the
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Fig. 5. Temperature–entropy diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is ferromagnetic: reverse Brayton-like cycle (note numbers of each stream correspond to Fig. 1).
enthalpy of state points 1 and 7 are the same, from the conservation law of energy, the heat discarded Qdiscard (a – b – 6 – 7) is equal to the total work required, Wnet. Q discard ¼ W net
ð3Þ
Note that the magnetization and the demagnetization are assumed to be a complete adiabatic process. Irreversible loss has been considered in terms of hysteresis loss and electromagnetic induction heating (EIH) in the discussion. Fig. 6 shows the temperature–entropy diagram of magnetocaloric heat circulator when the process material is non-magnetic. The amount of ferromagnetic material is chosen so that its heat capacity will match the heat capacity of the fluid which is the subject of heating. If the set temperature, Tset, is above environmental temperature, T0, the non-magnetic material at environmental temperature, T0, is heated (a-b) to its set temperature, Tset, while the magnetized magnetic material is cooled (3-4) in HEX1. The process material is then cooled (c-d) while the demagnetized magnetic material is heated (1-2) in HEX2. The remaining heat is finally discarded at cooling water (d-e). The following equations may be realized through the energy balance: Q ab ¼ Q 12 ¼ Q cd þ Q discaard ¼ Q 34 þ Q discard
ð4Þ
Q discard ¼ W net
ð5Þ
where Qab (a – b – IV – I) and Q12 (1 – 2 – IV – I) are the heat exchanged in HEX1, Qcd (c – d – III – IV) and Q34 (3 – 4 – II – IV) are the heat exchanged in HEX2 and Qdiscard (d – e – I – III) is the heat discarded at the cooling water. Total energy consumption, Wnet, is equal to the heat discarded at the cooling water, Qdiscard. The pinch point will be the smallest out of the temperature differences ΔT3c, ΔTb2, ΔT4a and ΔTd1. Similar discussion can be made in the case where the set temperature, Tset, is below environmental temperature, T0, for magnetic and non-magnetic process material (Fig. 7). In all cases, from the conservation law of energy, total energy consumption or the net work input, Wnet, is equal to the heat discarded at the cooling water, Qdiscard. Magnetic flux density, B2, is chosen so that the pinch point temperature is larger than the minimum temperature difference for heat exchange, ΔTmin. The total entropy, ST, of the magnetic material can be expressed by the sum of the magnetic (SM), lattice (SL) and electron (SE) entropies as: ST ðB; TÞ ¼ SM ðB; TÞ þ SL ðTÞ þ SE ðTÞ
ð6Þ
Fig. 6. Temperature–entropy diagram of the magnetocaloric heat circulator when the set temperature, Tset, is above environmental temperature, T0, and the process material is ferromagnetic (note numbers of each stream correspond to Fig. 2).
where B and T denote the magnetic flux density and temperature, respectively. The magnetic entropy is a function of magnetic flux density and temperature, while the lattice and electron entropies are functions of temperature only. The magnetic, lattice and electron entropies can be expressed as shown in Table 1 (Tishin and Spichkin, 2003; Huang and Teng, 2004). The magnetic entropy change, ΔSM, when the magnetic flux density was changed from B1 to B2 is expressed by: ΔSM ¼ SM ðB1 ; TÞ−SM ðB2 ; TÞ
ð7Þ
The energy consumption is compared with a benchmark process with heat recovery (Fig. 8). The same benchmark process can be used for processes with process materials of ferromagnetic and non-magnetic material. Total energy consumption of the benchmark process is equal to the heat provided at the furnace heater, QFH.
3.2. Simulation conditions A simulation of energy consumption was performed under four conditions. Gadolinium (Gd) was selected as reference magnetic material because it shows a large magnetocaloric effect at room temperature (θc ¼ 293 K) and its physical properties have been well studied (Benford and Brown, 1981; Dan'kov et al., 1998). Water was selected as reference non-magnetic material. The initial magnetic flux density was assumed as 0 T. In the case when Gd is the subject of heating, commencing from environmental temperature (T0 ¼298 K), the Gd temperature was raised to 308 K (condition 1) and 318 K (condition 2). Similarly in the case when water is the subject of heating, water at environmental temperature (T0 ¼298 K) is heated to 308 K (condition 3) and 318 K (condition 4) as shown in Table 2. The starting magnetic flux density, B1, was set to 0 T and the minimum temperature difference required for heat exchange, ΔTmin, was set to 2 K. The efficiency of the heat exchanger was assumed as 100% (i.e., no heat loss). The total energy consumption is compared with the total energy consumption of the benchmark process for evaluation. Fig. 9 shows the numerical magnetic entropy change, ΔSM, and total entropy, ST, when Gd was subjected to various magnetic flux densities at different temperatures calculated by the methods provided in Table 1. The adiabatic temperature change, ΔTad, can be determined by comparing the total entropy curves at different magnetic fields.
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Table 1 Entropy calculation method; R is the gas constant, J is the total angular momentum, kB is the Boltzmann constant, g is the spectroscopic splitting factor, μB is the Bohr magneton, θD is the Debye temperature, θc is the Curie temperature and γ is the electron heat capacity (Tishin and Spichkin, 2003; Huang and Teng, 2004). Magnetic entropy h i 1 SM ¼ R ln sinh 2Jþ1 2J X −ln sinh 2J X −XBJ ðXÞ 2Jþ1 1 1 BJ ðXÞ ¼ 2Jþ1 2J coth 2J X − 2J coth 2J X X¼
gJμB B kB T
þ
Lattice entropy SL ¼ −3Rlnð1−e−x Þ þ 12 x13
Electron entropy Rx
SE ¼ γT
ξ3 0 eξ −1 dξ
x ¼ θD =T
3θc JBJ ðXÞ TðJþ1Þ
Fig. 7. Schematic (a) and temperature–entropy diagram (b) of the magnetocaloric heat circulator when the set temperature, Tset, is below environmental temperature, T0. (1) Process material is magnetic and (2) non-magnetic.
Table 2 Simulation conditions T0 is the environmental temperature, and Tset is the set temperature. Conditions
Process material
1 2 3 4
Gd Gd Water Water
T0 [K]
298
Tset [K]
Temperature change [K]
308 318 308 318
+10 +20 +10 +20
Table 3 Magnetic flux density, B; heat circulated, Qcir; net work required, Wnet; heat provided at fired heater, QFH per unit mass of process material at various conditions. Condition ΔTmin [K]
B2 [T] 1 2 3 4
Fig. 8. Schematic of the benchmark process with heat recovery.
4. Results and discussion The simulation results are summarized in Table 3. Potential of significant energy reduction was gained by the magnetocaloric
Magnetocaloric heat circulator
2.0
Qcir [J kg−1]
1.35 1680 1.93 3366 2.10 41,286 2.98 82,073
Benchmark process
Wnet [J kg−1]
Qcir [J kg−1]
QFH [J kg−1]
16.3 35.9 513 1517
1344 3046 33,440 75,240
336.5 320.0 8360 8350
W net =Q FH [%]
4.8 11.2 6.13 18.2
heat circulator. Compared with the energy consumption in the benchmark process, QFH, the energy consumption in the magnetocaloric heat circulator, Wnet, was reduced to 4.8–18.2%. Less energy saving was obtained for conditions with non-magnetic process material compared to conditions with ferromagnetic process material because larger magnetic field is needed to ensure the minimum temperature differences at the two heat exchangers. Also, the energy consumption for the magnetocaloric heat circulator becomes larger as the set temperature move away from the Curie temperature, θc, because the adiabatic temperature change, ΔTad, at the set temperature, Tset, becomes smaller and thus larger magnetic field is needed to ensure the minimum temperature
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Fig. 9. Entropy calculation of Gd subjected to various magnetic flux densities; (a) numerical magnetic entropy change, −ΔSM, (b) total entropy, ST.
difference for heat exchange. Nevertheless, large energy saving was obtained compared to conventional thermal process with heat recovery. In an adiabatic process, the area surrounded by the two isomagnetic lines (Fig. 3; 3 – 4 – 5 – 6) is equal to the area representing the heat that is discarded at the cooling water (6 – 7 – a – b). This indicates that the smaller the temperature difference required for heat exchange, ΔTmin (i.e. slower heat exchange), the smaller the work required, Wnet, for magnetocaloric heat circulation. Smaller temperature difference for heat exchange is also preferable because it is difficult to create strong magnetic field using permanent magnets and extra energy will be needed if superconducting magnets or electromagnets are used. Exergy losses owing to the irreversibility of the magnetizing or demagnetizing process are induced by hysteresis loss and electromagnetic induction heating. The former depends on the physical properties of the material that is subjected to varying magnetic flux density. It is assumed very small if not any for Gd (Dan'kov et al., 1998). The latter is the joule heat generated by the eddy current induced by the change in magnetic flux applied to the material and the material resistance. In the magnetocaloric heat circulator, the rate in which the magnetic flux change is probably merely few teslas per second and the specific resistivity of Gd is only few micro-ohms per meter, thus the effect of electromagnetic induction heating may be assumed very small. Another factor that
may affect the value of the total energy consumption is the demagnetizing effect caused by varying magnetic permeability in the ferromagnetic material (Peksoy and Rowe, 2005). The demagnetization effect is dependent on geometry and non-uniform properties of the magnetic material, thus needs to be taken into account when designing the actual device. Two patterns for processes with set temperature, Tset, above the environmental temperature, T0, are presumed depending on the temperature at which the magnetization and demagnetization takes place and similarly, two patterns for processes with set temperature, Tset, below the environmental temperature, T0, are presumed (Fig. 10). Patterns 1 and 2 are processes with set temperature, Tset, above environmental temperature, T0. In pattern 1, the temperature difference is larger between state points 4 and 2 than that between state points 5 and 1 (ΔT42 4ΔT51). In this case, the minimal temperature difference is ΔT51. On the contrary, in pattern 2, the temperature difference is larger between state points 5 and 1 than that between state points 4 and 2 (ΔT51 4 ΔT42). Hence, the minimal temperature difference is ΔT42. A similar discussion can be made processes with set temperature, Tset, below environmental temperature, T0, where the minimal temperature difference is the temperature difference between state points 3 and 5, ΔT35, for pattern 3 and the temperature difference between state points 2 and 6, ΔT26, for pattern 4. The magnetic flux density is determined such that the
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Fig. 10. Temperature–heat diagrams of different magnetocaloric heat circulator patterns. Pattern 1 and 2 are processes with set temperature, Tset, above the environmental temperature, T0, and pattern 3 and 4 are processes with set temperature, Tset, below the environmental temperature, T0.
Fig. 12. Temperature–entropy diagram of magnetic heat pump system.
Fig. 11. Schematic (a) and temperature–entropy diagram (b) of magnetocaloric heat circulator when ferromagnetic process material is solid and working fluid is used to transfer heat.
smallest temperature difference is larger than the minimum temperature difference required for heat exchange, ΔTmin. In all cases, the net work input, Wnet, is equal to the energy discarded at the cooling water, Qdiscard. All conditions calculated are categorized as pattern 2 because the adiabatic temperature difference, ΔTad, decreases with distance from the Curie temperature, θc, which is at 293 K for Gd. In actuality, ferromagnetic material with optimal
Curie temperature in between the magnetizing and demagnetizing temperature will need to be chosen in order to satisfy the minimum temperature difference required for heat exchange with limited magnetic flux density. In the case where the process material is ferromagnetic, the process material is likely to be solid. In this case, it will become difficult for the process materials to exchange heat in counterflow. Thus, working fluid will be needed to transfer the heat between the process materials as shown in Fig. 11a. Fig. 11b shows the temperature–entropy diagram of the magnetocaloric heat circulator when the ferromagnetic process material is solid. The minimum temperature difference, ΔTmin, is needed for heat exchange between the process material and the working fluid,
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which results in doubling the area surrounded by the isomagnetic lines and thus doubling the total energy consumption, Wnet. Fig. 12 shows the temperature–entropy diagram of a magnetic heat pump system when the heat is pumped from a heat source at TC to heat sink at TH. The magnetic heat pump system consist of ferromagnetic material (1 – 2 – 3 – 4) and a working fluid (a – b – c – d). The temperature of the working fluid is raised (a-b) by receiving the heat from the ferromagnetic material (3-4). Then, the pumped heat, QH, is transferred to the heat sink (b-c). The remaining heat is transferred to the ferromagnetic material for regeneration (c-d, 1-2). After, heat, QC, is transferred from the heat source to the ferromagnetic material and comes back to its original state (d-a). In a magnetic heat pump, the heating capacity, QH, or the cooling capacity, QC, will be used to heat or cool the process material. In a magnetocaloric heat circulator (Figs. 4–7), the process material heat is circulated. Thus, the magnetocaloric heat circulator has great potential for energy saving in thermal processes where the temperature of a process material is raised to a certain temperature and finally comes back to its original state.
5. Conclusions Self-heat recuperation technology using adiabatic magnetization and demagnetization instead of compression and expansion for thermal processes was proposed. The magnetocaloric effect raises the ferromagnetic material temperature, and the magnetizing work can be recovered partially when demagnetizing by configuring the ferromagnetic material in a circular shape. All heat is recirculated inside the system without heat addition. It is shown that means to recuperate the process stream heat for heat circulation is not limited to compression and can be realized by enforcing a change of state by providing work. Although the temperature change one can gain from adiabatic magnetization or demagnetization is small in the range of permanent magnets (up to 2 T), in self-heat recuperation, the required temperature change is only that needed for heat exchange between the feed and the effluent process material. The magnetocaloric heat circulator when process material is ferromagnetic and non-magnetic has been analyzed in terms of the temperature–entropy diagram, and its theoretical energy consumption limitation has been calculated. The results were compared with the benchmark process with heat recovery and were made clear that the energy consumption could be reduced to 4.8–18.2% by applying the magnetocaloric heat circulator, indicating the significant energy saving that can be obtained in thermal processes. Therefore although heat circulation is temperature is limited by the Curie temperature of the ferromagnetic material, the magnetocaloric heat circulator can be counted as one of the future options for energy saving in certain thermal processes.
Acknowledgment The authors would like to thank Professor Masashi Tokunaga of the Institute of Solid State Physics, The University of Tokyo, for his time and valuable comments in the preparation of this research.
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