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12 

 

 

 

Article 

Exploring the impact of nano-enhanced phase 

change materials on Trombe wall efficiency 
Nazlıcan Meco1, Coskun Firat2* 

Istanbul Technical University, Energy Institute, Istanbul, Turkiye 

A R T I C L E   I N F O 
 

Article history: 
Received 14 January 2025  
Received in revised form 
25 February 2025 
Accepted 07 March 2025 
 
Keywords: 
Trombe wall, Nano-enhanced phase change 
materials (NePCM), Energy efficiency, Thermal 
energy storage, Finite element method simulation 
 
*Corresponding author 
Email address:  
coskun.firat@itu.edu.tr 
  
 
DOI: 10.55670/fpll.fuen.4.2.2 

A B S T R A C T 
 

A novel Trombe wall design that incorporates highly thermally conductive 
materials along with nano-enhanced phase change material is presented. 
Performance analysis is conducted using finite element method simulations. A 
comparative study of NePCM and PCM in a room with a Trombe Wall revealed 
minor differences in thermal performance during January, February, and 
December, but a significant discrepancy in March due to higher solar radiation 
levels. The enhanced latent heat storage capability of NePCM contributed to a 
more sustained temperature increase during periods of intense solar radiation. 
Over seven months, NePCM demonstrated a 16% higher average energy gain 
compared to PCM, attributed to its improved thermal conductivity and heat 
transfer efficiency. These findings indicate that nano-enhanced phase change 
materials are more effective than their non-nano counterparts. The results 
indicate a substantial impact of the system, raising room temperatures to 22°C 
during the day and resulting in significant energy savings.  
 

 
1. Introduction  

Historically, numerous researchers have sought new 
energy sources in response to global energy crises. In this 
context, extensive studies have been conducted on alternative 
fuels and solutions that can replace fossil resources. To 
achieve sustainable development, countries require a reliable 
supply of clean and safe energy that minimizes environmental 
impacts [1]. Consequently, the exploration of renewable 
energy sources has become a crucial area of focus. This 
increasing interest in renewable energy has attracted 
considerable attention. Turkey, in particular, emphasizes the 
development of domestic and renewable energy sources, in 
line with the goals set forth in the National Energy Policy of 
2017. As a testament to this commitment, Turkey has risen to 
the fifth position in Europe and twelfth globally in terms of 
installed renewable energy capacity. By the end of 2022, 
renewable sources accounted for 54% of Turkey's total 
installed energy capacity [2]. The global energy crisis and the 
urgent need for sustainable solutions have driven intensive 
research into renewable energy sources. Turkey, endowed 
with significant solar potential, has emerged as a key player 
in the renewable energy landscape. This study examines 
Turkey's impressive growth in solar energy, particularly in 
Istanbul, a city characterized by unique weather conditions. 
By analyzing statistical data from the International 
Renewable Energy Agency [3] and national energy ministries 
[4], this research investigates the critical role of solar energy 

in residential heating within the specific context of Istanbul. 
The building sector is responsible for 30-40% of global 
energy consumption, with nearly half of this energy allocated 
to heating and cooling systems to maintain indoor comfort 
[5,6]. This significant energy usage contributes substantially 
to global greenhouse gas emissions, highlighting the urgent 
need for reduction strategies. The United States aims to 
decrease building energy consumption by 70% by 2020 as 
part of federal policy initiatives [7], while China has set 
ambitious targets to cut energy usage in new constructions by 
50% [8]. Furthermore, rising fossil fuel consumption and 
electricity demand underscore the necessity for more 
efficient building practices. Addressing these challenges is 
essential for mitigating environmental impacts and 
promoting sustainable energy practices. Various methods 
utilizing solar energy are implemented in construction, 
including passive walls with solar facades, natural ventilation 
systems, architectural solar roofs, solar chimneys, and 
Trombe walls [9,10]. Passive heating and cooling systems 
capture solar radiation and ambient temperature variations 
to store energy, which is then released into indoor spaces at 
optimal times. Trombe walls represent a pioneering approach 
in passive solar technology, effectively harnessing solar 
energy to provide space heating in buildings for several 
decades. These thermal mass walls, typically composed of 
masonry or concrete, absorb sunlight through a glass facade 
and subsequently release the stored heat into the interior 

 

 

Future Energy 

Open Access Journal 

https://doi.org/10.55670/fpll.fuen.4.2.2 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

May 2025| Volume 04 | Issue 02 | Pages 12-22 

Journal homepage: https://fupubco.com/fuen 

 
ISSN 2832-0328 

mailto:coskun.firat@itu.edu.tr
https://doi.org/10.55670/fpll.fuen.4.2.2
https://fupubco.com/fuen


N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

13 

 

space. Despite their potential, the thermal performance of 
Trombe walls can be hindered by various factors, including 
heat loss through conduction and convection, as well as their 
dependency on direct sunlight exposure. The well-established 
Trombe wall functions similarly to a solar thermal collector; 
it consists of a large wall with an external glazing area that 
stores solar energy within its mass for later use, particularly 
after sunset. Other passive systems include solar chimneys, 
unglazed transpired solar facades, and green walls—all 
designed to effectively harness natural energy sources. 
Trombe walls are also known as thermal or storage walls [11]. 
Trombe walls come in various forms, including classic 
Trombe walls, aquatic Trombe walls, water Trombe walls, 
zigzag Trombe walls, composite Trombe walls, solar 
compound walls, and the widely utilized PV Trombe wall [12]. 
In existing literature, the Trombe wall stands out as one of the 
most extensively studied passive systems with numerous 
configurations explored. In traditional designs, openings are 
integrated into the solid wall to enable air circulation. During 
winter months, circulation occurs internally; conversely, 
during summer months, an external connection is established 
to enhance ventilation rates [13]. A study by Abbassi et al. 
[14] examined the effectiveness of Trombe walls in Tunisia's 
climate and found that a 4 m² wall could reduce annual 
auxiliary heating energy needs by approximately 50%, while 
an 8 m² version could achieve a remarkable 77% reduction. 
Similarly, Bojic et al. [15] studied a residence in Lyon, France, 
demonstrating that a south-facing Trombe wall could 
decrease yearly heating consumption by up to 20%. These 
studies collectively highlight the versatility and efficiency of 
Trombe walls across various climates, making them a focal 
point for research in passive energy systems. Hu et al. [16] 
investigated the use of Venetian blinds placed between 
glazing and thermal mass walls and emphasized how blind tilt 
angles significantly influence natural convection within the 
air gap.  

Likewise, Hong et al. [17] focused on optimizing Venetian 
blinds integrated into Trombe walls; their findings indicated 
that an optimal distance of 9 cm between the blinds and glass 
was effective with a 14 cm air gap. Duan et al. [18] explored 
placing an absorber plate within the middle of the air gap 
rather than on the thermal mass wall surface; they 
demonstrated that this configuration outperformed 
conventional Trombe walls regarding both energy efficiency 
and interpretative aspects. Innovative designs for Trombe 
wall systems have also been explored. Rabani et al. [19] 
developed a Trombe wall that captures solar irradiation from 
eastern, western, and southern directions while covering half 
of the south-facing wall; this cost-effective system provided 
satisfactory thermal comfort due to its reduced surface area. 
Shen et al. [20] conducted a comparative analysis between 
classical and composite Trombe walls and highlighted 
superior performance for composite designs under cold and 
overcast weather conditions. Li et al. [21] researched thermal 
efficiency in PCM-integrated Trombe wall systems through 
comparative experiments conducted during summer months 
in hot and humid regions of China; results indicated that PCM-
integrated designs exhibited better heat insulation properties 
compared to standard building envelopes and traditional 
Trombe wall designs. Recent advancements in materials 
science have introduced nanoparticles and phase change 
materials (NePCMs) as promising solutions to enhance the 
thermal efficiency of Trombe walls. Nanoparticles can 
significantly improve thermal conductivity, while PCMs are 
capable of increasing thermal storage capacity by absorbing 
and releasing heat during phase transitions. The integration 

of these materials into building energy systems has attracted 
increasing attention due to their potential to enhance energy 
efficiency, reduce carbon emissions, and improve occupant 
comfort. However, despite the growing interest in NePCMs, 
there remains a substantial gap in research regarding their 
application in Trombe walls specifically. This study aims to 
address this gap by investigating the incorporation of 
NePCMs into Trombe wall systems to enhance their energy 
efficiency. Through a theoretical analysis of thermal 
performance, this research seeks to contribute valuable 
insights into passive solar heating technologies and building 
energy efficiency strategies. 

1.1 Trombe walls 
A typical unvented Trombe wall consists of a south-

facing masonry structure with a thickness ranging from 10 to 
40 cm. The exterior surface of this wall is coated with a dark, 
heat-absorbing material and is covered by one or two layers 
of glass. These glass layers are spaced 2 to 5 cm away from the 
masonry wall, creating a small air gap between them. When 
sunlight enters through the glass, the dark surface absorbs 
heat, which is then stored within the wall and gradually 
conducted inward through the masonry. Using high-
transmission glass enhances the solar heat gains captured by 
the masonry. Additionally, incorporating patterned glass can 
serve as an architectural feature that obscures the view of the 
dark concrete wall from outside while still allowing light to 
pass through. Trombe walls are architectural components 
designed for passive solar heat absorption, storage, and 
distribution. Typically made from high-mass materials such 
as concrete or stone, these walls collect solar radiation during 
the day and slowly release it into the interior at night, 
providing consistent and sustainable heating. However, their 
successful implementation relies on various factors, including 
orientation, thermal properties, and local climate conditions. 
The efficiency of Trombe walls across different scenarios has 
attracted interest from both researchers and building 
professionals. Different configurations are employed to adapt 
Trombe walls for various climates, purposes, and seasons, as 
illustrated in Figure 1 [22]. 

Several types of Trombe walls exist, including classic and 
modified designs, zigzag Trombe walls, solar water walls, 
solar trans walls, solar hybrid walls, Trombe walls with phase 
change materials (PCM), composite Trombe walls, fluidized 
Trombe walls, and photovoltaic (PV) Trombe walls [23]. A 
conventional Trombe wall, also known as a standard Trombe 
wall, features glass and an air gap that separates it from the 
outdoor environment [24]. The concept of the Trombe wall 
was first patented by Edward Morse, an American engineer, 
in 1881 but gained widespread recognition thanks to Felix 
Trombe and architect Jacque Michel [25], leading to its 
common designation as a Trombe wall. Figure 2  shows a PV-
Trombe wall equipped with photovoltaic cells that enhance 
thermal comfort while contributing to electricity generation 
[26]. 

1.2 Solar radiation in Istanbul 
Turkey has a vast land area well-suited for capturing 

solar energy, attributed to its favorable geographical position. 
The country lies between latitudes 36° and 42° N. Historical 
data gathered by the Turkish State Meteorological Service 
from 1971 to 2000 indicates a significant solar potential 
across the nation. On average, Turkey has 2,573 hours of 
sunshine annually (approximately 7 hours per day) and an 
average total radiation of 1,474 kWh/m² per year (or about 4 
kWh/m² daily). Figure 3 illustrates the global irradiation 
levels for Turkey [27].  



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

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Figure 1. Operating schemes: non-ventilated solar wall (a); Trombe wall in winter mode with air thermo-circulation (b); Trombe wall in 

summer mode with cross ventilation [22] 

 

 

 

Figure 2. Schematic diagram and photograph of PV-Trombe wall for winter heating [26] 

 

 

Figure 3. Global irradiation levels for Turkey [27] 



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

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With a population exceeding 80 million, Turkey is facing 
a rising demand for energy, leading to a continuous increase 
in energy consumption. In 2022, Turkey's per capita energy 
consumption reached 3,360 kWh [28]. According to the 
Turkey Energy Efficiency Development Report, 
approximately 20% of the country's energy and around 22% 
of total electricity consumption is utilized in households. Of 
this energy usage, about 60% is allocated to heating in 
buildings [29]. The average cooling requirement for a typical 
building in Istanbul is approximately 33.52 kWh/m² per year, 
while the heating requirement is around 84.49 kWh/m² per 
year [30]. Alarmingly, over 75% of this energy is currently 
supplied through imports, a figure that continues to rise 
annually. Therefore, it has become increasingly urgent to 
diversify energy sources by focusing on both domestic non-
renewable and renewable resources. Among these 
alternatives, solar energy stands out as a crucial option with 
significant potential that remains largely untapped in Turkey. 
The nation has an average of 200 sunny days each year, 
providing a solid foundation for developing a comprehensive 
solar energy strategy. The primary objective of this research 
is to evaluate the performance of a Trombe wall system 
integrated into a room within Istanbul. Located at a latitude 
of 40.58° N, longitude of 29.05° E, and an elevation of 39 
meters, Istanbul is one of Turkey's most densely populated 
urban areas in the northwestern part of the country.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4 presents data on global solar radiation and 
sunshine hours for Istanbul. In Istanbul, the average annual 
global solar radiation is recorded at 1,612 kWh/m² per year, 
with an average annual sunshine duration of 2,446 hours. 
These values are relatively low compared to many other cities 
in Turkey. To promote solar energy utilization, the Istanbul 
Metropolitan Municipality's Geographic Information System 
(GIS) Directorate has developed the Istanbul Solar Energy 
Potential Map. A snapshot from this map is shown in Figure 5 
[31]. 

2. Methodology 

2.1 Material selection 
n-Octadecane, a paraffin-based organic phase change 

material (PCM), was selected for the present study due to its 
advantageous properties for industrial applications. The key 
factors influencing this choice include: 
• Thermal Comfort Range: n-Octadecane has a phase change 

temperature that closely aligns with the optimal range for 
thermal comfort in indoor environments. This 
characteristic allows it to effectively absorb and release 
thermal energy within a temperature range conducive to 
human comfort. 

• High Thermal Conductivity: Compared to other organic 
PCMs, n-Octadecane exhibits relatively high thermal 
conductivity. This property facilitates efficient heat 
transfer both within the material and between the PCM and 
its surrounding environment. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

 

Figure 4. Monthly averaged daily global solar radiation and sunshine duration hours in Istanbul [27] 

 

 

Figure 5. Istanbul Solar Energy Potential Map [31] 

 



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

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• Latent Heat Storage Capacity: n-Octadecane possesses a 
significant latent heat of fusion, enabling it to store a 
substantial amount of thermal energy per unit mass during 
its phase transition. This maximizes its potential for energy 
storage. 

In the study, n-Octadecane (C₁₈H₃₈) was chosen as the 
primary PCM due to its melting point of 28°C, which is well-
suited for maintaining thermal comfort in occupied spaces. 
This property allows n-Octadecane to effectively store and 
release thermal energy within the desired temperature range. 
To enhance the PCM's performance the nano-enhancement 
expandable graphite (EG), a carbon-based compound, was 
selected for its compatibility with n-Octadecane. Both 
materials share graphite as a common source, ensuring 
chemical compatibility and minimizing potential adverse 
interactions within the composite. 

2.2 Trombe wall construction 
The Trombe wall was designed with two essential 

components: 
• Highly Thermal Conductive Encapsulation: The outer layer 

was constructed using pyrolytic graphite, a highly ordered 
form of graphite known for its exceptional thermal 
conductivity (approximately 1800 W/m·K in-plane). This 
high conductivity ensures efficient heat transfer from the 
solar-heated exterior surface to the PCM layer within the 
wall. 

• Energy Storage Substance (PCM): The core of the Trombe 
wall consisted of the PCM layer containing n-Octadecane, 
with or without nano-enhanced EG for comparative 
analysis. During daylight hours, the PCM absorbed thermal 
energy from the sun-heated pyrolytic graphite and 
released it back into the room as temperatures dropped, 
thereby providing passive heating during colder periods. 

2.3 Room construction 
The surrounding room walls were constructed from 

concrete, selected for its robust thermal mass, which helps 
regulate fluctuations in room temperature. Additionally, a 
glass window was incorporated into the design to allow direct 
solar radiation onto the Trombe wall, optimizing its potential 
for thermal gain. Detailed properties of the materials used in 
this system are summarized in Table 1 for reference.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The subject of this study is a small room with an 
approximate area of 15.5 m², which includes four external 
walls, a roof, and a ground floor. A window is situated on the 
south side, adjacent to the Trombe wall (TW). The 
configuration of the room featuring the Trombe wall is 
depicted in Figure 6, showcasing a unique setup regarding 
both its placement and operational mechanism. The TW is 
constructed from a highly thermally conductive material 
(pyrolytic graphite) and utilizes phase change material (PCM) 
for energy storage. This innovative design presents several 
advantages, making it an intriguing subject for examinations. 
Firstly, it does not include any ventilation gaps, setting it apart 
from other types of Trombe walls documented in the 
literature. Secondly, it functions as a hybrid system that 
allows the wall to transfer heat into the room while storing 
some energy in the PCM for use during nighttime. The 
dimensions and configuration of the TW considered in the 
calculations are shown in Figure 7. The thermal and 
mechanical properties of the materials used in the TW are 
summarized in Table 2. Although the Trombe wall is primarily 
intended for use during the eight cold months in Istanbul, 
analyses and calculations were conducted for all twelve 
months. Weather and solar data specific to Istanbul for each 
month are detailed in Table 3.  

 

 
Figure 6. Dimensions and configuration of the analyzed Trombe wall 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 1. Material properties [32] 

Property 
Pyrolytic 
Graphite 

PCM  
(n-octadecane) 

NePCM  
(n-octadecane/EG) 

Concrete Wall Glass Window 

Density (kg/m3) 
2100 814 - 2300 2203 

Specific heat (J/kgK) 
850 2660 - 880 703 

Thermal conductivity 
(W/mK) 

1800 0.36 1.11 1.8 1.38 

Melting point (oC) 
- 28 23 - - 

Latent heat (kJ/kg) 
- 244 196.8 - - 

 



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

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Figure 7. Dimensions of the Trombe wall  

 

Table 2. Properties of TW materials [32, 33] 

Thermal and Mechanical Property 
Pyrolytic 
Graphite 

PCM 
(paraffin) 

Density (kg/m3) 2100 912 

Specific heat (J/kgK) 850 2310 

Thermal conductivity (W/mK) 1800 0.21 

Melting point (oC) - 31.9 

 

Table 3. The weather and solar data specific to Istanbul 

Months 
DNI 

(W/m2) 
Sunshine 

(hrs./day) 

Ambient 
temperature, 

Ta, (oC) 

Wind 
speed, v, 

(m/s) 

h 
(W/m2K) 

Jan 491.33 3.46 6.00 4.81 24 

Feb 493.12 4.43 6.10 4.81 24 

Mar 671.05 5.32 7.70 4.36 22 

Apr 655.18 6.85 12.00 4.03 21 

May 621.95 8.61 16.70 3.97 21 

Jun 549.14 10.51 21.40 4.28 22 

July 516.70 11.17 23.80 4.78 24 

Aug 508.83 10.14 23.80 4.78 24 

Sep 552.55 7.83 20.10 4.92 24 

Oct 609.00 5.22 15.70 4.36 22 

Nov 523.25 3.85 11.70 4.25 22 

Dec 516.89 2.96 8.20 4.83 24 

 

The weather data, including solar radiation (DNI) and 
sunshine hours, were averaged for each day of a specific 
month for these calculations, while convective heat loss due 
to wind was calculated using Equation (1), as described by 
Hong et al. [34]. 

ℎ𝑤𝑖𝑛𝑑 = 5.7 + 3.8𝑣𝑤𝑖𝑛𝑑            (1) 

where 𝑣𝑤𝑖𝑛𝑑  represents wind speed. 
Simulation of the system was performed regarding time 
dependent Finite Element Method. Simulation model is 
calculating the heat load with respect to the effect of the 
conduction, convection and radiation heat transfer rates as 
given below. 

𝑑𝑄 = (𝑞𝑐𝑜𝑛𝑑
′′ + 𝑞𝑐𝑜𝑛𝑣

′′ + 𝑞𝑟𝑎𝑑
′′ )𝑑𝑡          (2) 

In the FEM, the Navier-Stokes equations are used which 
govern conservation of mass, momentum, and energy as 
given trough Eq (3) to Eq (7). 
For the conduction calculations in the system following 
equations are used. 

𝜌𝐶𝑝
𝜕𝑇

𝜕𝑡
+ 𝜌𝐶𝑝𝑢𝛻𝑇 + 𝛻𝑞 = 𝑄          (3) 

𝑞 = −𝑘𝛻𝑇            (4) 

For the laminar flow of air which is Newtonian in the room 
and the gravity calculations, equation below was used.  

𝜌
𝜕𝑢

𝜕𝑡
+ 𝜌(𝑢𝛻)𝑢 = 𝛻[−𝑝𝐼 + 𝐾] + 𝐹 + 𝜌𝑔         (5) 

Where, 

𝜕𝜌

𝜕𝑡
+ 𝛻(𝜌𝑢) = 0            (6) 

𝐾 = 𝜇(𝛻𝑢 + (𝛻𝑢)𝑇 −
2

3
𝜇(𝛻𝑢)𝐼          (7) 

I is the identity tensor, 𝜌 is the density, u is the velocity vector 
, 𝑝 is the pressure, 𝜇 is the dynamic viscosity, 𝐶𝑝 is the specific 

heat capacity at constant pressure, T is the absolute 
temperature, q is the heat flux vector, Q contains the heat 
sources, k is the Thermal conductivity, F is the buoyancy force 
and 𝑔 gravitational acceleration. 
Ambient radiation to the surface was calculated as below. 

−𝑛𝑞 = 𝜀𝜎(𝑇𝑎𝑚𝑏
4 − 𝑇4)           (8) 

𝜀 is the emissivity of the surface, 𝜎 is Stefan-Boltzmann 
constant, 𝑇𝑎𝑚𝑏is the ambient temperature, 𝑛 is the surface 
normal vector. 
Phase change interface calculations were performed 
regarding the equations below. In stationary and time-
dependent studies, the temperature is set to the phase change 
temperature, 𝑇𝑝𝑐 , on the interface: 

𝑇 = 𝑇𝑝𝑐            (9) 

In addition, in time-dependent studies, the Stefan condition 
defines the phase change interface velocity 𝑣𝑛 from the 
conductive heat flux jump across the interface, q, the latent 
heat of phase change from solid to fluid, 𝐿𝑠→𝑓, and the solid 

density, 𝜌𝑠: 

𝑣𝑛 =
𝒒

𝜌𝑠𝐿𝑠→𝑓
          (10) 

With, 

𝑞 = −𝑘𝑠𝛻𝑇𝑠 + 𝑘𝑓𝛻𝑇𝑓         (11) 

Where 𝑘𝑠 and 𝑇𝑠 are the solid heat coefficient and 
temperature, 𝑘𝑓  and 𝑇𝑓 are the fluid heat coefficient and 

temperature of PCM.  
A portion of the solar energy entering the room heats the air, 
helping to achieve a comfortable temperature of 22°C. 
Additionally, some of this energy is stored in the Trombe wall 
for use at night. The energy stored within the Trombe wall can 
be calculated using the following equation: 

𝑄𝑇𝑊 = 𝑚𝑇𝑊 × 𝑐𝑇𝑊 × 𝑇𝑇𝑊        (12) 

where 𝑇𝑇𝑊 is the temperature of Trombe wall, 𝑚𝑇𝑊 is the 
total mass, 𝑐𝑇𝑊  is the total specific heat which are calculated 
as below: 

𝑚𝑇𝑊 = 𝑚𝑝𝑔 + 𝑚𝑝𝑐𝑚          (13) 



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

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where 𝑚𝑝𝑔 and 𝑚𝑝𝑐𝑚 are the mass of pyrolytic graphite and 

PCM respectively. 

𝑐𝑇𝑊 = (
𝑚𝑝𝑔

𝑚𝑇𝑊
) × 𝑐𝑝𝑔 + (

𝑚𝑝𝑐𝑚

𝑚𝑇𝑊
) × 𝑐𝑝𝑐𝑚        (14) 

where 𝑐𝑝𝑔  and 𝑐𝑝𝑐𝑚  are the specific heat of pyrolytic graphite 

and PCM respectively. 
The increased temperature, 𝑇𝑟, by the utilization of energy, 
𝑄𝑇𝑊 is given as below:  

𝑇𝑟 = 18 + 𝑄𝑇𝑊 (𝑚𝑎𝑐𝑎)⁄          (15) 

where 𝑚𝑎 is mass and 𝑐𝑎  is specific heat of air. 
The fundamental thermal model for the room-Trombe wall 
system is depicted in Figure 8, providing a schematic 
representation of thermal transfer within the system. 

 
Figure 8. Thermal model for the room-Trombe wall system 

Several assumptions were made based on thermal transfer 
principles: 
• The thermal physical properties used in this model are 

considered constant. 
• Pyrolytic graphite exhibits high thermal conductivity in-

plane but low conductivity through-plane; it is assumed to 
be utilized as an in-plane conductive material. 

Boundary conditions of the simulation model are given 
below. 
• Room is a closed system that has no fluid in or out from the 

system.  
• Outlet temperature and heat flux inlet from solar radiation 

is taken according to the weather data.  
• Initial temperature and pressure of the room is taken as 

18℃ and 1 atm.  
• All the walls of the room except Trombe wall and window 

are insulated.  
• Heat flux from solar radiation is applied to window and 

Trombe wall.  
• No slip condition is applied to the walls.  
• Acceleration of gravity is assumed as constant.  
• Pressure point constraint point is taken the left corner of 

the room. 
• Given the minimal nano-enhancement present in the n-

octadecane/EG composite (NePCM), its density is 
considered equivalent to that of pure n-octadecane. 

3. Results and discussion 

This section presents the simulation results obtained 
from the two-dimensional Finite Element Method (FEM) 
model. The simulations were conducted for the seven coldest 
months of the year: January, February, March, April, October, 
November, and December. The initial simulation utilized 
NePCM, specifically a combination of n-octadecane and 
expandable graphite (EG), yielding promising results. 

Temperature readings for the Trombe wall, PCM, and the 
room were recorded and are illustrated in Figure 9.  

 
Figure 9. First simulation temperature data 

The initial room temperature was set at 18°C. In Figure 
9, the blue line represents the average ambient temperature. 
The simulations, which incorporated weather and solar 
radiation data, revealed an increase in room temperature 
over the simulation period. December, January, and February 
recorded the lowest average room temperatures at 19.57°C, 
19.23°C, and 19.40°C, respectively. This increase can be 
attributed to the Trombe wall's high thermal conductivity. 
The heating effect of the Trombe wall extended beyond the 
room itself, resulting in an increase in the temperature of PCM 
as well. The PCM serves as a thermal energy storage medium, 
absorbing heat until the room temperature drops below that 
of the Trombe wall. During these periods, the stored energy 
in the PCM is released to provide additional heating to the 
room. The sunshine duration for each month was factored 
into the simulation, with corresponding temperature 
distributions shown in Figure 10. 

To further investigate the impact of nano-enhancement 
on phase change materials (PCMs), a second simulation was 
conducted using n-octadecane PCM without any nano-
enhanced components. This simulation employed the same 
weather data for Istanbul as used in the NePCM scenario. To 
ensure consistency, the Trombe wall design, room layout, and 
material characteristics were identical to those in the first 
simulation. This approach allows for a controlled comparison 
between NePCM and standard n-octadecane PCM 
performance under identical environmental conditions and 
physical constraints. The primary goal was to isolate and 
evaluate the specific effects of nano-enhancement on the 
thermal behavior of the PCM and its interaction with the 
Trombe wall system. Figure 11 shows the second simulation 
temperature data. 

The results indicated a positive correlation among the 
temperatures of the room, PCM, and Trombe wall. The 
Trombe wall consistently exhibited higher temperatures than 
both the room and PCM, likely due to its superior thermal 
conductivity that facilitates efficient heat transfer from the 
wall to both areas. The months of December (19.56°C), 
January (19.15°C), and February (19.28°C) recorded the 
lowest average room temperatures. This trend can be 
attributed to a combination of lower ambient temperatures 
during these months and an increased thermal demand for 
heating. Overall, these simulations demonstrate how both 
standard n-octadecane and its nano-enhanced counterpart 
perform under winter conditions, highlighting significant 
differences in thermal behavior that could influence future 
designs of passive solar heating systems using Trombe walls. 

 



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

19 

 

 

 

 

 

 

 

 

 

Figure 10. Temperature distribution of the room for the month: (a) January, (b) February, (c) March, (d) April, (e) October, (f) November, 

(g) December 



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

20 

 

The analysis of room temperature data indicated that the 
use of nano-enhanced phase change material (NePCM) 
resulted in a noticeable increase in temperature, especially 
during the colder months as shown in Figure 12.  

 
Figure 11. Second simulation temperature data 

 

 
Figure 12. Room temperature comparison between PCM materials 

While the differences between the NePCM and non-
NePCM scenarios were minimal in January, February, and 
December, March showed the most significant variation. This 
pattern can be attributed to two main factors: 
Increased solar radiation: In March, there was a relatively 
higher level of solar radiation, even though the sunshine 
duration was shorter compared to April. This additional solar 
energy contributed to greater thermal gain in the Trombe 
wall, thereby amplifying the temperature difference 
associated with NePCM. 
Latent heat storage capacity: The latent heat storage 
capacity of NePCM likely played a vital role during this month. 
When solar radiation was high, the PCM absorbed and stored 
thermal energy, which was then gradually released during 
cooler periods of the day or on subsequent days when solar 
input was less available. This ability to act as a latent heat 
buffer allowed for a more sustained increase in temperature 
compared to scenarios that did not utilize NePCM. 

The performance of two different phase change 
materials (PCMs) was examined: n-octadecane (PCM, 
represented by the blue line) and a composite of n-octadecane 
with expanded graphite (NePCM, represented by the orange 
line). The temperature profiles for both materials showed a 
high degree of similarity; however, the NePCM consistently 
recorded slightly higher temperatures as shown in Figure 13. 
The Trombe wall was exposed to solar radiation, allowing for 
an assessment of the effects of both PCM and NePCM. The 
analysis indicated that the average temperature of the 
Trombe wall was slightly higher when NePCM was employed 
as seen in Figure 14. The temperature difference observed 
between the Trombe wall conditions with PCM and NePCM 
closely mirrored the temperature variation between the two 
materials themselves. This suggests that the enhanced 
thermal conductivity of the NePCM, attributed to its nano-

engineered structure, significantly influenced both its own 
temperature and that of the Trombe wall. This indicates that 
the nano-enhancement primarily affects the material's energy 
storage capacity rather than its temperature-dependent 
phase transitions. Further analysis revealed a notable 
difference in the amount of stored energy between the two 
PCMs. During the colder months, the NePCM demonstrated an 
average of 16% more stored energy compared to the standard 
PCM. This enhancement can be attributed to the improved 
thermal conductivity and heat transfer capabilities provided 
by the nano-engineered structure of the NePCM, which 
facilitates more efficient absorption and retention of thermal 
energy within the material. Using the stored energy, it is 
possible to adjust the room temperature by approximately 
0.2°C in December; although this change may seem minor and 
not significantly impact nighttime comfort, it is sufficient to 
maintain a pleasant sleeping environment.  

 

 
Figure 13. Temperature comparison between PCM materials 

 

 
Figure 14. TW temperature comparison between PCM 
materials 

4. Conclusion 

This study is confined to a theoretical analysis and 

numerical simulation focused on the thermal performance of 

single-sided Trombe walls utilizing two types of phase change 

materials (PCMs): standard n-octadecane and a nano-

enhanced composite of n-octadecane with expandable 

graphite (NePCM). Through a series of simulations conducted 

over the coldest months of the year, key findings were 

obtained that highlight the advantages of incorporating 

NePCM into passive solar heating systems. The results 

demonstrated that the use of NePCM led to a noticeable 

increase in room temperature, particularly during colder 

months. The contribution of NePCM compare to PCM was 

observed the most in March. This enhancement was 

attributed to two primary factors: the higher solar radiation 

received in March, despite a shorter sunshine duration 

compared to April, and the superior latent heat storage 

capacity of NePCM. The ability of NePCM to absorb and 



N. Meco & C. Firat /Future Energy                                                                                                    May 2025| Volume 04 | Issue 02| Pages 12-22 

21 

 

gradually release thermal energy significantly contributed to 

maintaining comfortable indoor temperatures, even during 

periods of limited solar input. For instance, in December, the 

room temperature rises from 18°C to 19.5°C while consuming 

approximately 71.6 kJ of energy, equivalent to a cost of 0.02 

kWh. This research offers valuable insights into sustainable 

building design practices, equipping architects and engineers 

with crucial information for optimizing passive solar heating 

systems. Ultimately, the study promotes environmentally 

friendly and energy-efficient building designs, supporting 

global efforts to address climate change and reduce 

greenhouse gas emissions. Furthermore, the analysis 

revealed that the average temperature of the Trombe wall 

was slightly elevated when NePCM was utilized, reflecting its 

enhanced thermal conductivity. This characteristic not only 

improved the energy storage capacity of the material but also 

positively influenced the overall thermal performance of the 

Trombe wall system. The findings indicate that integrating 

nano-enhanced materials like NePCM can substantially 

improve the efficiency of passive solar heating systems. By 

optimizing energy absorption and retention, NePCM serves as 

a valuable component in designing more effective and 

sustainable building systems. In conclusion, this research 

underscores the potential of utilizing nano-enhanced phase 

change materials in Trombe walls to enhance energy 

efficiency and occupant comfort. Future studies should 

explore the long-term performance and economic viability of 

these materials in real-world applications, as well as their 

environmental impact, to fully understand their role in 

advancing sustainable building practices. The significance of 

this study lies in its contribution to advancing sustainable 

building design practices. By conducting numerical 

investigations of Trombe walls using finite element method 

simulations, this research aims to provide architects and 

engineers with practical insights for optimizing passive solar 

heating systems. The findings may influence architectural and 

engineering decisions by offering a clearer understanding of 

Trombe wall behavior and their potential role in reducing 

building energy consumption. Ultimately, this study seeks to 

promote environmentally friendly and energy-efficient 

design strategies aligned with global efforts to combat climate 

change and reduce greenhouse gas emissions. 

Ethical issue 
The authors are aware of and complies with best practices in 
publication ethics, specifically concerning authorship 
(avoidance of guest authorship), dual submission, 
manipulation of figures, competing interests, and compliance 
with policies on research ethics. The authors adhere to 
publication requirements that the submitted work is original 
and has not been published elsewhere in any language. 

Data availability statement 
The manuscript contains all the data. However, more data will 

be available upon request from the corresponding author. 

Conflict of interest 

The authors declare no potential conflict of interest. 

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