# Phase Change Materials-Assisted Heat Flux Reduction: Experiment and Numerical Analysis

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{3}-NaNO

_{3}, LiCL-NaCL and Li

_{2}CO

_{3}-Na

_{2}CO

_{3}) are consistent with the ones obtained from standard methods. Meanwhile, many efforts are made to produce high performance PCM integration in building walls. Romero-Sanchez et al. [8] evaluated the thermal performance of PCMs by incorporating in natural stone. Experiments and numerical simulation are carried out to improve the thermal properties of natural stone, where concrete pilot houses are constructed. These pilot houses are covered with trans-ventilated facade designs via Spanish Bateigazul natural stone. An improvement in human comfort with the reduction in energy consumption is evidenced upon implementing PCMs.

_{2}+ 4.3% NaCl + 0.4% KCl + 47.3% H

_{2}O) as the PCM. The measured room temperatures are observed to vary ~27 ± 3 °C during the experiment. Despite many dedicated efforts, a comprehensive understanding of the PCM-mediated reduction in heat flux inside the building is far from being achieved.

## 2. Numerical Scheme

- (i)
- One dimensional heat conduction in the composite wall is considered, and the end impacts are not taken into account.
- (ii)
- The thermal conductivity of the aluminum frame and the roof top slab are constant irrespective of temperature variation.
- (iii)
- The PCM is uniform and isotropic.
- (iv)
- The convection impact in the molten PCM is not considered.
- (v)
- The interfacial resistances are negligible.
- (vi)
- The value of C
_{p}for the PCM panel is considered as follows:$$T<{T}_{\text{m}}-\Delta T,{C}_{\text{p}}={C}_{\text{ps}}$$$$T>{T}_{\text{m}}+\Delta T,{C}_{\text{p}}={C}_{\text{pl}}$$$${T}_{\text{m}}-\Delta T<T<{T}_{\text{m}}+\Delta T,{C}_{\text{p}}={h}_{\text{sl}}/2\Delta T$$_{sl}is the enthalpy change of solid-liquid, ΔT is half of the temperature range over which the phase change occurs and T_{m}is the phase transition temperature. - (vii)
- The latent heat being highly sensitive to the phase transition process of the PCM is modeled over a range of temperatures, where${C}_{\text{p}}$ is considered to be uniform during the phase conversion. Although, in reality, ${C}_{\text{p}}$varies with temperature.

## 3. Development of the Numerical Model

#### 3.1. One-Phase Solution

#### 3.2. Two-Phase Solution

_{max}indicates the fully-melted state.

_{m}.

_{max}, implying the complete melting of nodes. In such an instance, the temperature is again allowed to alter according to Equation (12). For the nodes that are below ${T}_{m}$, the temperatures are governed by the one-phase equations until they exceed ${T}_{m}$. At this time, the node is in two phases, and the method of calculation is toggled to Equations (15)–(18).

## 4. Experimental Scheme

- (1)
- The PCM heat transfer is one-dimensional.
- (2)
- The heat flow from uncontrolled outside influences is negligible compared to the applied heat.
- (3)
- The rate of the temperature rise and fall of the PCM is comparable to reality.

Properties | Value | Unit |
---|---|---|

T_{m} | 40–44 | °C |

C_{ps} | 2.21 | kJ/kg·°C |

C_{pL} | 2.3 | kJ/kg·°C |

K_{s} | 0.51 | W/m·K |

K_{L} | 0.22 | W/m·K |

$\mathsf{\rho}$_{S} | 830 | kg/m^{3} |

$\mathsf{\rho}$_{L} | 878 | kg/m^{3} |

α_{L} | 9.59 × 10^{−8} | m^{2}/s |

α_{S} | 7.92 × 10^{−8} | m^{2}/s |

H | 146 | kJ/kg |

#### 4.1. Full-Scale Test Rooms

- (1)
- The REF is a test room without PCM. The walls (without insulation) are built using a commune brick system, cemented plaster and gypsum board. Conversely, the roof contains two layers, where the bottom slab (thickness 12 cm) is made from concrete and the top slab (thickness 10 cm) is made using a brick mixture plus mortar (Figure 4).
- (2)
- Room 1: The structure is the same as the REF together with the incorporation of a PCM layer in the southern, eastern and western walls, as well as in the roof. The PCM (paraffin) layer is 2.5 cm thick and contained in aluminum panels (Figure 4).

**Figure 4.**Geometry of the constructed test rooms, reference room (REF) (

**left**, without PCM) and PCM2 (

**right**).

## 5. Results and Discussion

**Figure 5.**Temperature variation of the test rooms with and without PCM (REF) at a 1.5 m height in the month of August.

^{2}and 162 W/m

^{2}, respectively. Conversely, the heat flux (at 21.5 h) through the internal east wall of the room with and without PCM is discerned to be 26 W/m

^{2}and 44 W/m

^{2}, respectively. Furthermore, heat storage is observed to be maximum at 12 h with values of 240 W/m

^{2}and 135 W/m

^{2}for the PCM integrated and non-integrated east walls, respectively.

**Figure 6.**Temperature variation of the test room with and without PCM (REF) at a height of 1.5 m in the month of January.

^{2}·°C and 23.3 W/m

^{2}·°C for the internal and external wall surface, respectively. The amount of stored heat in the walls containing PCMs is found to be larger than the traditional (REF) walls. This elevated storage in PCM walls is ascribed to the high heat capacity and heat-retaining susceptibility without connecting any storage space to the air conditioner. The observed higher thermal storage for the western walls is related to the longest exposure to the solar radiation.

- (1)
- The room ceiling is influenced by interior condition, where an actual temperature variation occurred.
- (2)
- The effective thermal conductivity of the PCM in the experiment is higher due to the presence of uniformly-distributed high conductivity heat exchanger material in the PCM panel.
- (3)
- The actual phase change may not occur during the phase change temperature as prescribed in the theory.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclatures

C_{1}, C_{3} | Specific heat of roof top slab and concrete slab (kJ/kg·K) |

C_{pl} | Specific heat of liquid PCM (kJ/kg·K) |

C_{ps} | Specific heat of solid PCM (kJ/kg·K) |

f | Implicit factor |

Gr_{L} | Grashof number |

h_{i} | Inside heat transfer coefficient (W/m^{2}·K) |

h_{o} | Outside heat transfer coefficient (W/m^{2}·K) |

k_{1}, k_{2}, k_{3} | Thermal conductivity of roof top slab, PCM panel and bottom concrete slab (W/m·K) |

L_{1}, L_{2}, L_{3} | Thickness of roof top slab, PCM panel and bottom concrete slab (m) |

Nu_{L} | Nusselt number |

P_{r} | Prandtl number |

q_{rad} | Radiation flux (W/m^{2}) |

Re | Reynolds number |

T | Temperature |

T_{∞} | Ambient temperature |

T_{i}^{0} | Previous time step temperature at i-th volume cell |

T_{i} | Current time step temperature at i-th volume cell |

T_{in} | Initial temperature |

T_{room} | Room temperature |

T_{s} | Surface temperature |

T_{sky} | Sky temperature |

α | Absorptivity |

ε | Emissivity |

h_{sl} | Solid-liquid enthalpy change (kJ/kg) |

$\sigma $ | Stefan-Boltzmann constant |

$\mathsf{\rho}$_{1}, $\mathsf{\rho}$_{2}, $\mathsf{\rho}$_{3} | Density of roof top slab, PCM panel and bottom concrete slab (kg/m^{3}) |

$\Delta $t | Time step (s) |

$\mathsf{\delta}$x_{1,}$\mathsf{\delta}$x_{2}$,\mathsf{\delta}$x_{3} | Nodal distances (m) |

$\Delta {x}_{1},\Delta {x}_{2},\Delta {x}_{3}$ | Control volume length of roof top slab, PCM panel and bottom concrete slab (m) |

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**MDPI and ACS Style**

Akeiber, H.J.; Hosseini, S.E.; Wahid, M.A.; Hussen, H.M.; Mohammad, A.T. Phase Change Materials-Assisted Heat Flux Reduction: Experiment and Numerical Analysis. *Energies* **2016**, *9*, 30.
https://doi.org/10.3390/en9010030

**AMA Style**

Akeiber HJ, Hosseini SE, Wahid MA, Hussen HM, Mohammad AT. Phase Change Materials-Assisted Heat Flux Reduction: Experiment and Numerical Analysis. *Energies*. 2016; 9(1):30.
https://doi.org/10.3390/en9010030

**Chicago/Turabian Style**

Akeiber, Hussein J., Seyed Ehsan Hosseini, Mazlan A. Wahid, Hasanen M. Hussen, and Abdulrahman Th. Mohammad. 2016. "Phase Change Materials-Assisted Heat Flux Reduction: Experiment and Numerical Analysis" *Energies* 9, no. 1: 30.
https://doi.org/10.3390/en9010030