Analyzing the impact of using phase change materials on energy consumption in buildings: A case study

The use of phase change material (PCM) in buildings has been shown to be a promising method for reducing energy consumption. This study investigates the effectiveness of using PCM in reducing energy consumption in a typical residential building located in Podgorica, Montenegro, a city with mild winters and hot and dry summers. EnergyPlus software was used to simulate the thermal performance of a building with and without the incorporation of PCM. Building models were created in a way to incorporate PCM in form of a panel, and simulations were done with five different types of PCM, five different thicknesses and three different positions (outside, inside and middle of building envelope). The simulations were performed over a one-year period to account for seasonal variations in temperature and humidity. The simulation results indicate that the use of PCM in buildings design can significantly reduce energy consumption in buildings located in climates similar to Podgorica. This approach can also lead to a reduction in greenhouse gas emissions associated with energy consumption. These findings provide valuable insights for building designers and policymakers looking to reduce energy consumption and improve the sustainability of buildings. In conclusion, the results of this study support the use of PCM in building design as an effective strategy for reducing energy consumption and greenhouse gas emissions in buildings. Further research is needed to investigate the cost-effectiveness of using PCM in buildings design and to explore the potential for their widespread implementation.


Introduction
The building sector is one of the leading sectors in energy consumption and carbon dioxide (CO 2 ) emissions, with a share of about 30% at the world level [1].Buildings in Montenegro have a share of about 45% in total energy consumption and about 75% in electricity consumption [2].
The largest share of energy used in buildings is spent on space heating and cooling.European and world trends are moving towards the total cessation of greenhouse gas emissions, to stop the harmful consequences of global warming.Considering the share that the building sector has in the overall energy consumption and in accordance with various regulations on the minimum energy efficiency requirements of buildings, it is essential to drastically reduce the energy needed for space heating and cooling.
As one of the potential methods that could be used to reduce the energy consumption necessary for space heating and cooling in buildings is the application of phase changing materials (PCM).PCMs can be of organic or inorganic origin and can have different physical properties and melting points.The principle by which PCMs can help reduce energy consumption in buildings is based on the fact that they change their aggregate state at temperatures that are approximately equal to the temperatures at which people feel comfortable.While in a phase change process, temperature of PCM materials cannot change IOP Publishing doi:10.1088/1742-6596/2766/1/012226 2 so heat flux cannot get through the elements of the building envelope on which the PCM materials are placed.
This paper presents a study of the impact of using some commercially available PCM materials on energy consumption in a residential building in the climatic conditions of Podgorica.Podgorica is a city with mild winters and hot and dry summers.The energy required for space cooling in buildings on an annual basis is generally greater than the energy required for space heating in the climatic conditions of Podgorica.Cooling peak loads are also generally higher than heating peak loads, so the focus of this paper is on the energy required for space cooling.Building models were created in a way to incorporate PCM in form of a panel, and simulations were done with five different types of PCM, five different thicknesses and three different positions (outside, inside and middle of building envelope).

Materials and methods
EnergyPlus software [3] was used for the purpose of this analysis.EnergyPlus is one of the leading energy analysis software in the building sector.The energy model of the building from EnergyPlus was applied to the residential building in the climatic conditions of Podgorica.

Mathematical model
Mathematical model that EnergyPlus uses to calculate heat transfer through walls and other opaque surfaces which have integrated PCM materials is presented in this subsection.An implicit formulation of some interior node in the wall using fully implicit first order in time could be written as: i) Where   -specific heat of the material,  -density of the material,  -node temperature, ∆calculation time step, ∆ -finite difference layer thickness,   -thermal conductivity for interface between node  and node  + 1,   -thermal conductivity for interface between node  and node  − 1, and subscripts and superscripts  -node being modeled,  + 1 -adjuctent node to interior of construction,  − 1, adjuctent node to exterior of construction,  + 1 -new time step,  -previous time step.
Four types of nodes are used: nodes on the surface of the wall that are in contact with the internal air, nodes on the surface of the wall that are in contact with the external air, nodes in the interior of the material and nodes that are at the boundary between two layers of different materials.The spatial step between two nodes is calculated in the first iteration according to the following equation: Where  is the thermal diffusivity of the material.The actual number of nodes is chosen by rounding the value obtained when dividing the length of the wall layer and the length of the spatial step from the previous equation.After this, the actual length of the spatial step is obtained by dividing the length of the material layer by the actual number of nodes.
Since the calculations are performed by an implicit method and a system of equations needs to be solved, the Gauss-Seidel iteration scheme is used to update the new temperatures of the nodes in the structure.Due to the stability of the solution, relaxation is used: Due to the iteration scheme, the enthalpy value in the calculation nodes is updated in each iteration and these values are used to form a variable specific heat of the material if some kind of PCM material is being calculated.The specific heat update of the nodes is calculated via the following equation: If the used PCM has variable heat transfer coefficient dependent on the temperature of the material itself, the actual heat transfer coefficient can be calculated as: where  0 is the thermal conductivity of the material at 20°C, and k1 is the coefficient of change in the thermal conductivity of the material per 1°C.In order to calculate the thermal conductivity of the material in the interface node between two materials, it is necessary to perform linear interpolation, so the following equations are used for the final calculation: The heat flux passing through the nodes bordering the external or internal air is equal to the heat flux passing from the node to the air, that is   =   .For all other nodes, the heat flux passing through them can be expressed as:

Case study
The case study was made for a typical residential, multifamily building in Montenegro built after 2011.User energy consumption profiles were taken from the Montenegrin national software for energy certification of buildings [4].Building layout was reconstructed on the basis of MEEC data on the number of floors, ceiling height, thickness of the mezzanine structure, and the surface area of walls, windows, roof, ground floor.According to the user profile for the building, all the activities are set from 6 am to 10 pm.The number of people is set to be 1 person / 20 m 2 , and the sensible heat load per person is 70W.Cooling set point is at 26 °C.Electric equipment loads are set to be at constant level of 1.7 W/m 2 .The electrical power of the lighting is set to 2.9 W/m 2 .The set point for daylighting control is 200 lux at a height of 80 cm.An overview of the building envelope surface areas is given in Table 1 Not counting the PCM, the walls are set to be four-layered.Looking from the outside, the first layer is 2 cm thick plaster, then 5 cm thick thermal insulation, 19 cm thick brick and last layer is 2 cm thick plaster again.Overall heat transfer coefficient for this wall construction is 0.6 W/m 2 K.This type of wall construction is standard in Montenegro.Heat transfer coefficient for windows was set to 2 W/m 2 K, and solar heat gain coefficient (SHGC) to 0.62.The roof construction consists of tiles, sheet metal, 7 cm thick thermal insulation and wooden construction.Overall heat transfer coefficient for roof is 0.4 W/m 2 K.
For simulations with PCM materials, commercially available materials manufactured by Rubitherm [5] were selected.Simulations were done for 5 different materials with melting temperatures close to the temperature at which people feel comfortable.Thermal properties of selected PCM materials are given in Table 2: Simulations with selected PCM materials were performed for five different PCM layer thicknesses: 1 cm, 1.5 cm, 2 cm, 2.5 cm and 3 cm.In addition to combinations of PCM material types and thicknesses, simulations were performed for 3 different placements of PCM layer in building envelope: outside, middle (between thermal insulation and the main structural material) and inside placement.

Results and discussion
The results of the calculation of the annual energy consumption required for cooling, with different variants of the thickness and position of the selected PCM materials, and comparison of best results for each thickness against case with no PCM incorporated are given in the following figures:  From the figures above, it can be seen that in most cases it is best to put the PCM material on the outside of the wall regardless of the thickness of the layer and the type of PCM material, which is in agreement with the findings of other authors [6], if the goal is to reduce the energy consumption required for cooling.Also, it can be seen that with an increase in the thickness of the PCM material layer, there is a decrease in the energy required for cooling, but this reduction in energy consumption is not linear and the percentage difference compared to the previous layer thickness also decreases.The percentage reductions in energy consumption required for cooling compared to the case when there is no PCM are respectively 9.15% 11.21% 12.82% 13.75% 14.88% if right type and placement of PCM are chosen.These percentages already represent a significant saving in the total energy required for cooling, but if we consider that the cooling load of the building coming from the external walls and roof is about 30 GJ per year when no PCM is installed, just by placing a layer of PCM material with a thickness of 3 cm, the heat load coming from the walls and roof alone can be reduced by about 83%.In the case of a building with a smaller wall-to-window area ratio, using windows with a lower SHGC coefficient and a lighter user profile of the building, the impact of using PCM could be much higher and on the total energy used for cooling.
Although it is shown that the use of PCM can drastically reduce the energy consumption required for cooling, it is necessary to carry out a detailed analysis of the cost-effectiveness of this measure in relation to other possible measures for cooling load reduction.

Conclusion
This paper presented a study on the utilization of PCMs in residential buildings emphasizes their potential to drastically reduce cooling loads in climate conditions similar to Podgorica.Employing five different PCM materials with varying thicknesses and placements, a significant decrease in annual cooling demands was achieved.Material-specific performance, thickness impact, and strategic placement on the exterior of building envelopes emerged as critical considerations.While findings of this study highlight the promise of PCM integration, a crucial next step involves assessing the costeffectiveness of these technologies.A comprehensive economic analysis, factoring in material costs, installation expenses, and long-term operational savings, will inform the practicality and widespread adoption of PCM applications.In conclusion, our study contributes valuable insights to sustainable building practices, showcasing the potential of PCM materials for substantial reductions in residential cooling loads.As we move forward, a focus on cost-effectiveness will be paramount to realizing the broader goal of energy-efficient and environmentally conscious residential structures.

Figure 1 Figure 1 .
Figure 1.Layout of the case study building

Figure 2 .Figure 3 .
Figure 2. Annual cooling load for different positions and melting temperature of a 1 cm thick PCM layer Figure 3. Annual cooling load for different positions and melting temperature of a 1.5 cm thick PCM layer

Figure 4 .Figure 5 .Figure 6 .Figure 7 .
Figure 4. Annual cooling load for different positions and melting temperature of a 2 cm thick PCM layer Figure 5. Annual cooling load for different positions and melting temperature of a 2.5 cm thick PCM layer

Table 1 .
: Overview of the building envelope surface gross area