# Thermal Analysis of a Thermal Energy Storage Unit to Enhance a Workshop Heating System Driven by Industrial Residual Water

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions are reduced by 1204 ton/year, in the investigated waste heat system.

_{2}O, Al

_{2}O

_{3}, and TiO

_{2}. This type of TES has been used to control the temperature in living or working spaces. In some cases, the amount of storage material can be quite large, so that there is the obvious concern about its huge equipment limiting its further development. A different mechanism for the storage of thermal energy involves phase transitions with no change in chemical composition. In this case, latent heat is absorbed or supplied at a constant temperature, which is ease of control, rather than over a range of temperature, as it is with sensible heat. The PCMs can be divided into two types: high-temperature PCMs and low-temperature PCMs, according to the phase change temperature. High-temperature PCMs, including high-temperature molten salts [22], salt-mixtures [23], metals and alloys [24], are mainly used for aerospace application; while low-temperature PCMs, such as calcium chloride hexahydrate [25], sodium acetate trihydrate [26], organic alcohol [27], and paraffin [28], are mainly used for waste heat recovery, solar energy utilization, domestic heating, and air conditioning system. Additionally, chemical reactions generally result in the generation or absorption of heat, similar to the thermal effects related to phase transitions in materials in which there are no changes in chemical composition. The thermal effects related to chemical reactions are often described in terms of quasi-latent heat [29]. Though quasi-latent heat storage has the characteristics of large storage density and pollution free, it is not easy to commercially promote due to its high cost. Besides, there is another new type, adsorption heat storage, which stores and converts heat through the thermal effect of an adsorption process [30,31]. It has a large storage density of appropriate 800~1000 kJ/kg, loses less heat, is non-toxic and does not pollute. However, there are few applications because of its dissatisfied heat transfer characteristic and complex storage process.

_{n}H

_{2n+2}. It has many advantages such as wide melting/solidification temperature ranges [35], relatively large latent heat [35], small volume change during the phase change process [35,36], chemically stable property [35,36], non-toxic [35], and moderate price [35,37]. Compared with inorganic PCMs, paraffin has no problems of phase separation on melting and has good self-nucleating properties on freezing, so that nucleating agents are not required [36,38]. It also has no subcooling effects [35] and corrosion problems of the conventional materials of construction [35,38]. Depended on the phase change temperature ranges, paraffin is widely used in industrial waste heat recovery, phase change building wall, heat storage floor, solar energy storage, etc., undergoing a phase change from solid to liquid, or vice versa [36,39].

## 2. Problem Description and System Design

## 3. Mathematical Model

#### 3.1. Heat Storage Process

_{i}, r

_{o}, and r

_{0}are the internal radius of the tube, the external radius of the tube, and the internal radius of the shell, respectively; and r

_{p}(x,τ) is the melting radius of the paraffin wax.

- It is assumed that the paraffin wax is smooth and with constant physical properties.
- IRW and pool water are incompressible fluid and Newtonian fluid.
- The entrance effects of fluid flow and heat transfer are ignored.
- The initial temperature of the paraffin wax is uniform.
- The external wall of the shell is thermally insulated.
- The axial heat conductions of IRW, pool water, and paraffin wax are neglected.
- Natural convection when the phase change occurs in paraffin wax is not considered.
- The specific volumetric dilatation of paraffin wax is regarded as 0.

_{w}is the temperature of IRW; h is the convection coefficient of IRW; t

_{s}is the temperature of tube wall; ρ is the density of paraffin wax; and H is the latent heat of paraffin wax.

_{m}is the phase change temperature of paraffin wax; and R

_{p}and R

_{w}are thermal resistances of paraffin wax, and heat transfer between IRW and the tube, respectively, and are expressed as

_{in}is the IRW temperature at the inlet of TES unit.

- (1)
- When $x>X\left(\tau -\Delta \tau \right)$, it is a heat storage in phase change process, then x in Equations (11) and (12) is replaced by $\left(x-X\left(\tau -\Delta \tau \right)\right)$ before the next recurrence.
- (2)
- When $x\le X\left(\tau -\Delta \tau \right)$, it is a heat transfer in single liquid phase, then ${r}_{\mathrm{p}}\left(x,\tau \right)={r}_{0}$, ${t}_{\mathrm{w}}\left(x,\tau \right)={t}_{\mathrm{in}}\left(\tau \right)$.

#### 3.2. Heat Release Process

- (1)
- When $x>{X}^{\prime}\left(\tau -\Delta \tau \right)$, x in Equations (13) and (14) is replaced by $\left(x-{X}^{\prime}\left(\tau -\Delta \tau \right)\right)$ before the next recurrence.
- (2)
- When $x\le {X}^{\prime}\left(\tau -\Delta \tau \right)$, ${r}_{\mathrm{p}}^{\prime}\left(x,\tau \right)={r}_{0}$, ${t}_{\mathrm{w}}^{\prime}\left(x,\tau \right)={t}_{\mathrm{in}}^{\prime}\left(\tau \right)$.

#### 3.3. Parameters Determination

^{®}thermal analyzer is used. Figure 4 depicts the DSC measuring result of heat flux. It can be found that there were two absorption peaks during the whole temperature change process. The first one means the solid-to-solid phase change, at which the crystal form changes while the heat absorbed is relatively small. The latter is the solid-to-liquid phase change with a distinct heat absorption. By using the software Proteus Analysis, the latent heat of the paraffin wax was obtained as 171.4 kJ/kg.

## 4. Model Validation

## 5. Results and Discussions

_{r}are the real yield and rated yield of the medicine production unit, respectively.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

## Variables

b | specific energy consumption of medicine production unit [MJ/kg] |

c | specific heat capacity of water [kJ/(kg·K)] |

h | convection coefficient of IRW [W/(m^{2}·K)] |

${h}^{\prime}$ | convection coefficient of pool water [W/(m^{2}·K)] |

H | latent heat of paraffin wax [kJ/kg] |

L | length of a tube in TES unit [m] |

m | flow rate of IRW into TES unit [kg/s] |

${m}^{\prime}$ | flow rate of pool water into TES unit [kg/s] |

P | real yield of medicine production unit [kg/h] |

P_{r} | rated yield of medicine production unit [kg/h] |

r_{i} | internal radius of tube [m] |

r_{o} | external radius of tube [m] |

r_{p} | melting radius of solid paraffin wax [m] |

${r}_{\mathrm{p}}^{\prime}$ | solidification radius of liquid paraffin wax [m] |

r_{0} | internal radius of shell [m] |

R_{p} | thermal resistance of paraffin wax [m^{2}·K/W] |

R_{w} | thermal resistance of IRW-tube heat transfer [m^{2}·K/W] |

t_{in} | IRW temperature at TES unit inlet [°C] |

${t}_{\mathrm{in}}^{\prime}$ | pool water temperature at TES unit inlet [°C] |

t_{m} | phase change temperature [°C] |

t_{s} | temperature of tube wall [°C] |

t_{w} | temperature of IRW [°C] |

${t}_{\mathrm{w}}^{\prime}$ | temperature of pool water [°C] |

x | axial direction |

X | location at the maximum melting radius |

${X}^{\prime}$ | location at the maximum solidification radius |

## Greek Symbols

θ | nondimensional yield of medicine production unit [–] |

λ | thermal conductivity of solid paraffin wax [W/(m·K)] |

${\lambda}^{\prime}$ | thermal conductivity of liquid paraffin wax [W/(m·K)] |

ρ | paraffin wax density [kg/m^{3}] |

τ | time [s, h] |

φ | energy saving rate [%] |

## Abbreviations

DSC | differential scanning calorimeter |

IRW | industrial residual water |

PCM | phase change material |

TES | thermal energy storage |

## References

- Erdem, H.H.; Dagdas, A.; Sevilgen, S.H.; Cetin, B.; Akkaya, A.V.; Sahin, B.; Teke, I.; Gungor, C.; Atas, S. Thermodynamic analysis of an existing coal-fired power plant for district heating/cooling application. Appl. Therm. Eng.
**2010**, 30, 181–187. [Google Scholar] [CrossRef] - Arteconi, A.; Patteeuw, D.; Bruninx, K.; Delarue, E.; D’haeseleer, W.; Helsen, L. Active demand response with electric heating systems: Impact of market penetration. Appl. Energy
**2016**, 177, 636–648. [Google Scholar] [CrossRef] - Joubert, E.C.; Hess, S.; van Niekerk, J.L. Large-scale solar water heating in South Africa: Status, barriers and recommendations. Renew. Energy
**2016**, 97, 809–822. [Google Scholar] [CrossRef] - Ma, H.; Li, C.; Lu, W.; Zhang, Z.; Yu, S.; Du, N. Experimental study of a multi-energy complementary heating system based on a solar-groundwater heat pump unit. Appl. Therm. Eng.
**2016**, 109, 718–726. [Google Scholar] [CrossRef] - Li, Y.; Xia, J.; Fang, H.; Su, Y.; Jiang, Y. Case study on industrial surplus heat of steel plants for district heating in Northern China. Energy
**2016**, 102, 397–405. [Google Scholar] [CrossRef] - Togawa, T.; Fujita, T.; Dong, L.; Fujii, M.; Ooba, M. Feasibility assessment of the use of power plant-sourced waste heat for plant factory heating considering spatial configuration. J. Clean. Prod.
**2014**, 81, 60–69. [Google Scholar] [CrossRef] - Eriksson, L.; Morandin, M.; Harvey, S. Targeting capital cost of excess heat collection systems in complex industrial sites for district heating applications. Energy
**2015**, 91, 465–478. [Google Scholar] [CrossRef] - Sun, W.; Zhang, F. Design and thermodynamic analysis of a flash power system driven by process heat of continuous casting grade steel billet. Energy
**2016**, 116, 94–101. [Google Scholar] [CrossRef] - Hosseini, S.R.; Amidpour, M.; Behbahaninia, A. Thermoeconomic analysis with reliability consideration of a combined power and multi stage flash desalination plant. Desalination
**2011**, 278, 424–433. [Google Scholar] [CrossRef] - Chang, C.; Wang, Y.; Feng, X. Indirect heat integration across plants using hot water circles. Chin. J. Chem. Eng.
**2015**, 23, 992–997. [Google Scholar] [CrossRef] - De Oliveira, R.G.; Generoso, D.J. Influence of the operational conditions on the performance of a chemisorption chiller driven by hot water between 65 °C and 80 °C. Appl. Energy
**2016**, 162, 257–265. [Google Scholar] [CrossRef] - Sun, W.; Yue, X.; Wang, Y. Exergy efficiency analysis of ORC (Organic Rankine Cycle) and ORC-based combined cycles driven by low-temperature waste heat. Energy Convers. Manag.
**2017**, 135, 63–73. [Google Scholar] [CrossRef] - Kim, D.K.; Lee, J.S.; Kim, J.; Kim, M.S.; Kim, M.S. Parametric study and performance evaluation of an organic Rankine cycle (ORC) system using low-grade heat at temperatures below 80 °C. Appl. Energy
**2017**, 189, 55–65. [Google Scholar] [CrossRef] - Ergun, A.; Ozkaymak, M.; Koc, G.A.; Ozkan, S.; Kaya, D. Exergoeconomic analysis of a geothermal organic Rankine cycle power plant using the SPECO method. Environ. Prog. Sustain. Energy
**2017**, in press. [Google Scholar] [CrossRef] - Sun, W.; Hong, Y.; Wang, Y. Operation optimization of steam accumulators as a thermal energy storage and buffer unit. Energies
**2017**, 10, 17. [Google Scholar] [CrossRef] - Cheng, W.; Xie, B.; Zhang, R.; Xu, Z.; Xia, Y. Effect of thermal conductivities of shape stabilized PCM on under-floor heating system. Appl. Energy
**2015**, 144, 10–18. [Google Scholar] [CrossRef] - Xia, Y.; Zhang, X.S. Experimental research on a double-layer radiant floor system with phase change material under heating mode. Appl. Therm. Eng.
**2016**, 96, 600–606. [Google Scholar] [CrossRef] - Zhou, G.; He, J. Thermal performance of a radiant floor heating system with different heat storage materials and heating pipes. Appl. Energy
**2015**, 138, 648–660. [Google Scholar] [CrossRef] - Furbo, S. Using water for heat storage in thermal energy storage (TES) systems. In Advances in Thermal Energy Storage Systems: Methods and Applications; Cabeza, L.F., Ed.; Woodhead Publishing: Cambridge, UK, 2015; pp. 31–47. [Google Scholar]
- Okello, D.; Foong, C.W.; Nydal, O.J.; Banda, E.J.K. An experimental investigation on the combined use of phase change material and rock particles for high temperature (~350 °C) heat storage. Energy Convers. Manag.
**2014**, 79, 1–8. [Google Scholar] [CrossRef] - Guo, P.; Wang, Y.; Li, J.; Wang, Y. Thermodynamic analysis of a solar chimney power plant system with soil heat storage. Appl. Therm. Eng.
**2016**, 100, 1076–1084. [Google Scholar] [CrossRef] - Ushak, S.; Fernández, A.G.; Grageda, M. Using molten salts and other liquid sensible storage media in thermal energy storage (TES) systems. In Advances in Thermal Energy Storage Systems: Methods and Applications; Cabeza, L.F., Ed.; Woodhead Publishing: Cambridge, UK, 2015; pp. 49–63. [Google Scholar]
- Zhao, C.Y.; Ji, Y.; Xu, Z. Investigation of the Ca(NO
_{3})_{2}–NaNO_{3}mixture for latent heat storage. Sol. Energy Mater. Sol. Cells**2015**, 140, 281–288. [Google Scholar] [CrossRef] - Sun, J.Q.; Zhang, R.Y.; Liu, Z.P.; Lu, G.H. Thermal reliability test of Al–34%Mg–6%Zn alloy as latent heat storage material and corrosion of metal with respect to thermal cycling. Energy Convers. Manage.
**2007**, 48, 619–624. [Google Scholar] [CrossRef] - Li, X.; Zhou, Y.; Nian, H.; Ren, X.; Dong, O.; Hai, C.; Shen, Y.; Zeng, J. Phase change behavior of latent heat storage media based on calcium chloride hexahydrate composites containing strontium chloride hexahydrate and oxidation expandable graphite. Appl. Therm. Eng.
**2016**, 102, 38–44. [Google Scholar] [CrossRef] - Ouchi, Y.; Someya, S.; Munakata, T.; Ito, H. Visualization of the phase change behavior of sodium acetate trihydrate for latent heat storage. Appl. Therm. Eng.
**2015**, 91, 547–555. [Google Scholar] [CrossRef] - Aydin, A.A.; Okutan, H. High-chain fatty acid esters of myristoyl alcohol with even carbon number: Novel organic phase change materials for thermal energy storage—1. Sol. Energy Mater. Sol. Cells
**2011**, 95, 2752–2762. [Google Scholar] [CrossRef] - Li, C.; Fu, L.; Ouyang, J.; Tang, A.; Yang, H. Kaolinite stabilized paraffin composite phase change materials for thermal energy storage. Appl. Clay Sci.
**2015**, 115, 212–220. [Google Scholar] [CrossRef] - Kerskes, H.; Mette, B.; Bertsch, F.; Asenbeck, S.; Drück, H. Chemical energy storage using reversible solid/gas-reactions (CWS)—Results of the research project. Energy Proc.
**2012**, 30, 294–304. [Google Scholar] [CrossRef] - Lefebvre, D.; Tezel, F.H. A review of energy storage technologies with a focus on adsorption thermal energy storage processes for heating applications. Renew. Sustain. Energy Rev.
**2017**, 67, 116–125. [Google Scholar] [CrossRef] - Lim, K.; Che, J.; Lee, J. Experimental study on adsorption characteristics of a water and silica-gel based thermal energy storage (TES) system. Appl. Therm. Eng.
**2017**, 110, 80–88. [Google Scholar] [CrossRef] - Sobolčiak, P.; Abdelrazeq, H.; Gözde Özerkan, N.; Ouederni, M.; Nógellová, Z.; AlMaadeed, M.A.; Karkri, M.; Krupa, I. Heat transfer performance of paraffin wax based phase change materials applicable in building industry. Appl. Therm. Eng.
**2016**, 107, 1313–1323. [Google Scholar] [CrossRef] - Moreno, P.; Solé, C.; Castell, A.; Cabeza, L.F. The use of phase change materials in domestic heat pump and air-conditioning systems for short term storage: A review. Renew. Sustain. Energy Rev.
**2014**, 39, 1–13. [Google Scholar] [CrossRef] - Aadmi, M.; Karkri, M.; El Hammouti, M. Heat transfer characteristics of thermal energy storage for PCM (phase change material) melting in horizontal tube: Numerical and experimental investigations. Energy
**2015**, 85, 339–352. [Google Scholar] [CrossRef] - Trp, A. An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shell-and-tube latent thermal energy storage unit. Sol. Energy
**2005**, 79, 648–660. [Google Scholar] [CrossRef] - He, B.; Martin, V.; Setterwall, F. Phase transition temperature ranges and storage density of paraffin wax phase change materials. Energy
**2004**, 29, 1785–1804. [Google Scholar] [CrossRef] - Eftekhar, J.; Haji-Sheikh, A.; Lou, D.Y.S. Hear transfer enhancement in a paraffin wax thermal storage system. J. Sol. Energy Eng.
**1984**, 106, 299–306. [Google Scholar] [CrossRef] - Himran, S.; Suwono, A.; Mansoori, G.A. Characterization of alkanes and paraffin waxes for application as phase change energy storage medium. Energy Sources
**1994**, 16, 117–128. [Google Scholar] [CrossRef] - Zhou, D.; Zhao, C.Y.; Tian, Y. Review on thermal energy storage with phase change materials (PCMs) in building applications. Appl. Energy
**2012**, 92, 593–605. [Google Scholar] [CrossRef][Green Version] - Zhang, Y.; Faghri, A. Analysis of thermal energy storage system with conjugate turbulent forced convection. J. Thermophys. Heat Transf.
**1995**, 9, 722–726. [Google Scholar] [CrossRef] - Liu, M.J.; Fan, L.W.; Zhu, Z.Q.; Feng, B.; Zhang, H.C.; Zeng, Y. A volume-shrinkage-based method for quantifying the inward solidification heat transfer of a phase change material filled in spherical capsules. Appl. Therm. Eng.
**2016**, 108, 1200–1205. [Google Scholar] [CrossRef] - Wang, C.; Lin, T.; Li, N.; Zheng, H. Heat transfer enhancement of phase change composite material: Copper foam/paraffin. Renew. Energy
**2016**, 96, 960–965. [Google Scholar] [CrossRef] - Song, S.H.; Liao, Q.; Shen, W.D. Laminar heat transfer and friction characteristics of microencapsulated phase change material slurry in a circular tube with twisted tape inserts. Appl. Therm. Eng.
**2013**, 50, 791–798. [Google Scholar] [CrossRef] - Ma, Z.W.; Zhang, P. Modeling the heat transfer characteristics of flow melting of phase change material slurries in the circular tubes. Int. J. Heat Mass Transf.
**2013**, 64, 874–881. [Google Scholar] [CrossRef] - Sun, D.; Wang, L. Research on heat transfer performance of passive solar collector-storage wall system with phase change materials. Energy Build.
**2016**, 119, 183–188. [Google Scholar] [CrossRef] - Shaikh, S.; Lafdi, K. Effect of multiple phase change materials (PCMs) slab configurations on thermal energy storage. Energy Convers. Manag.
**2006**, 47, 2103–2117. [Google Scholar] [CrossRef] - Regin, A.F.; Solanki, S.C.; Saini, J.S. Latent heat thermal energy storage using cylindrical capsule: Numerical and experimental investigations. Renew. Energy
**2006**, 31, 2025–2041. [Google Scholar] [CrossRef]

**Figure 1.**The proposed workshop heating system: (

**a**) System configuration; (

**b**) Schematic diagram of the shell-and-tube structure of the TES unit; and (

**c**) sets of shell-and-tube pipe columns.

**Figure 2.**Schematic diagram of the phase change process: (

**a**) axial direction; and (

**b**) radial direction.

**Figure 6.**Comparison between simulation data and experimental results: (

**a**) heat storage process; and (

**b**) heat release process.

Item | Symbol | Value | Unit |
---|---|---|---|

phase change temperature | t_{m} | 47–56 | °C |

latent heat | H | 171.4 | kJ/kg |

density | ρ | 900 | kg/m^{3} |

thermal conductivity (solid phase) | λ | 0.3 | W/(m·K) |

thermal conductivity (liquid phase) | λ’ | 0.1 | W/(m·K) |

Item | Symbol | Value | Unit |
---|---|---|---|

flow rate | m | 0.278 | kg/s |

specific heat capacity | c | 4.18 | kJ/(kg·K) |

convection coefficient | h | 498 | W/(m^{2}·K) |

IRW temperature at the inlet of TES unit | t_{in} | 70 | °C |

pool water temperature at the inlet of TES unit | t’_{in} | 35 | °C |

Item | Symbol | Value | Unit |
---|---|---|---|

tube length | L | 3000 | mm |

internal radius of the interior tube | r_{i} | 26 | mm |

external radius of the interior tube | r_{o} | 30 | mm |

internal radius of the exterior shell | r_{0} | 45 | mm |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Sun, W.; Zhao, Z.; Wang, Y.
Thermal Analysis of a Thermal Energy Storage Unit to Enhance a Workshop Heating System Driven by Industrial Residual Water. *Energies* **2017**, *10*, 219.
https://doi.org/10.3390/en10020219

**AMA Style**

Sun W, Zhao Z, Wang Y.
Thermal Analysis of a Thermal Energy Storage Unit to Enhance a Workshop Heating System Driven by Industrial Residual Water. *Energies*. 2017; 10(2):219.
https://doi.org/10.3390/en10020219

**Chicago/Turabian Style**

Sun, Wenqiang, Zuquan Zhao, and Yanhui Wang.
2017. "Thermal Analysis of a Thermal Energy Storage Unit to Enhance a Workshop Heating System Driven by Industrial Residual Water" *Energies* 10, no. 2: 219.
https://doi.org/10.3390/en10020219