Experimental and Numerical Investigation of Heat Transfer Characteristics of Double-Layer Phase Change Walls for Enhanced Thermal Regulation in Summer Climates

Abstract

This study employs the effective heat capacity method within the COMSOL simulation framework to analyze the thermal performance of double-layer phase-change walls under typical summer climatic conditions in Zhengzhou, Henan Province. The model considers a wall structure with a total thickness of 100 mm and a height of 300 mm, where the exterior surface represents the outdoor environment, the interior surface represents the indoor environment, and the top and bottom boundaries are assumed to be adiabatic. A highly refined triangular mesh ensures numerical stability and solution accuracy. Special attention is given to the influence of Micro-PCM content on thermal storage characteristics. Simulation results demonstrate that increasing the Micro-PCM content substantially enhances the thermal regulation capacity of the double-layer phase-change walls. At a Micro-PCM volume fraction of 15%, the peak temperature of the double-layer phase-change wall is reduced by 4.33 °C compared to a conventional wall, while the attenuation factor increases to 16.88. Furthermore, the mean thermal delay extends to 440 min, the temperature amplitude decreases to 1.13 °C, and the peak instantaneous heat flux is reduced to 13.24 W/m². These findings highlight the significant latent heat storage capacity and superior thermal modulation performance of double-layer phase-change walls, offering a valuable technical reference for the design of energy-efficient building envelope systems.

1. Introduction

With the rapid acceleration of urbanization, modern cities are characterized by the construction of taller buildings and increasing urban density [1]. To reduce structural weight, lightweight materials are frequently employed, leading to thinner building envelopes and, consequently, lower thermal inertia [2,3,4]. This reduction in thermal inertia increases the energy demand for heating, ventilation, and air conditioning (HVAC) systems, resulting in higher peak urban power loads and a growing mismatch between energy supply and consumption. In this context, energy storage technologies have emerged as a critical strategy for improving energy efficiency and mitigating these challenges [5,6,7].

Among the various energy storage technologies, phase change materials (PCMs) have gained significant attention for their ability to enhance the thermal performance of building envelopes [2,8,9,10]. By utilizing the latent heat associated with solid–liquid phase transitions, PCMs can regulate both the magnitude and timing of heat transfer between outdoor and indoor environments [11,12]. Figure 1 illustrates the temperature-regulating mechanism of PCMs, which alternately absorb heat during melting and release heat during solidification, allowing the building envelope to maintain stable indoor temperatures despite external fluctuations [13,14,15]. As a result, PCMs have been widely incorporated into lightweight building envelopes, providing both thermal regulation and heat storage benefits [16]. A growing body of research has demonstrated the significant energy savings and enhanced indoor comfort achievable with PCM-integrated building envelopes [17,18,19].

Numerical studies have further substantiated these benefits. For example, Fu et al. [20] examined PCM-enhanced foamed concrete walls and found that at a PCM mass fraction of 20 wt% with a thickness of 80 mm, peak indoor surface temperatures decreased by 9.87 °C, temperature amplitude decreased by 5.84 °C, the attenuation factor increased to 6.66, and the thermal delay extended to 198,000 s. Zhang et al. [21] investigated PCM-enhanced gypsum boards and observed a reduction of 0.6 °C in maximum indoor surface temperatures, a thermal delay extension of 0.8 h, and a 7.6% decrease in cooling energy consumption. Al-Absi et al. [22] incorporated PCM microcapsules into foamed concrete panels, achieving reductions of 7.35 °C in surface temperatures and 58 W/m² in heat flux.

Despite the significant energy-saving advantages of PCM-enhanced building envelopes, single-layer PCM systems are constrained by limitations in energy storage density, particularly in regions with substantial seasonal temperature variations, making it difficult to meet both summer and winter demands. To address this issue, dual-layer PCM wall systems have emerged. Specifically, Gao et al. [23] designed various structural models, including dual-layer PCM walls, single-layer PCM walls, and conventional walls, and developed dynamic heat transfer models based on these geometric configurations. They systematically analyzed the effects of macro design parameters such as the number, location, thickness, and phase transition temperature of PCM layers on wall thermal performance. Refahi et al. [24] optimized the layout of PCM layers through finite element analysis, enhancing the seasonal thermal regulation performance of dual-layer PCM walls. Cai et al. [25] developed a dynamic heat transfer model for a wall structure composed of photovoltaic (PV) layers, double-layer PCMs (PCM1 and PCM2), cement mortar, and brick, focusing on the impact of PCM layer positioning on photovoltaic cell temperature, wall thermal storage capacity, and indoor thermal environment. Aguilar et al. constructed numerical models for single-layer PCM, double-layer PCM (PCM1 and PCM2), and conventional concrete roofs, conducting simulations using computational fluid dynamics (ANSYS Fluent 2023 R1) software to analyze the effect of PCM layer arrangement on roof thermal performance.

Overall, current research primarily focuses on the integration of PCM in rectangular encapsulations within building envelopes, optimizing macro parameters such as phase change layer positioning, thickness, and phase transition temperature [26]. However, studies on the integration of micro-spherical PCM (Micro-PCM) in building envelopes, as well as the relationship between microstructural features and the macro thermal behavior of the walls, remain limited and warrant further exploration.

To address these gaps, this study proposes a micro-scale modeling approach that combines the MATLAB R2023a-based random distribution algorithm with COMSOL 6.0 finite element analysis to construct a model of the random dispersion of PCM microcapsules within cement mortar. This model elucidates the impact of microstructure on heat flux paths and provides an in-depth analysis of how micro-scale factors, such as particle content, distribution, and morphology, influence thermal transfer efficiency and overall thermal behavior.

2. Experiment

2.1. Materials

Micro-PCM, manufactured by Anhui Mikodi Intelligent (Anhui Meikedi Intelligent Microcapsule Technology Co., Ltd., Tongling, China), was used as a cement mortar additive to prepare a microencapsulated passive thermal regulation phase change mortar. The microencapsulation technique involves wrapping the phase change material (PCM) in a polymer shell, forming a core-shell structure. The core consists of paraffin wax, known for its latent heat storage properties, which remains thermally stable during phase transitions at specific temperatures. Each microcapsule contains 85–90% PCM by weight. The Micro-PCM shell is composed of a stable, inert polymer, with particle sizes ranging from 5 to 1000 $\mathsf{\mu }\mathrm{m}$. The PCM has a phase transition temperature of 27.57 °C and a latent heat of 73.95 J/g (Figure 2). SEM images of Micro-PCM are shown in Figure 3, revealing distinct surface wrinkles caused by volumetric changes during phase transitions.

2.2. Sample Preparation

To maintain the mechanical properties of the wall panels, phase change mortar was applied as a plaster layer on the outer surface of the panels. The materials used included P.O. 42.5 ordinary Portland cement (manufactured by Conch Cement, with performance specifications as follows: standard consistency water content of 28–32%, initial setting time not less than 120 min, final setting time not greater than 180 min, and compressive strength of 28-day cured samples ≥ 42.5 MPa), ISO standard sand (purchased from Xiamen AISO Standard Sand Co., Ltd. (Xiamen, China), with a particle size range of 0.08–2 mm, specifically used for cement mortar testing), tap water, and Micro-PCM. The mix proportion was designed based on the guidelines in the “Masonry Mortar Mix Proportion Design Specification” (JGJT 98-2010) [27] and previous research experience. The specific mix proportions are detailed in

Table 1. Micro-PCM cement mortar mix proportions.

Category	Argument
Volume fraction	0%	20%
Cement (kg/m3)	230	212.9
Water (kg/m3)	138	127.74
standard sand (kg/m3)	1600	1480
Micro-PCM (kg/m3)	0	120
Superolasticizer (SP)/%	0~1.1	0~1.1
Cement consistency/nm	70	70

. The water-to-cement ratio (W/C) was fixed at 0.6 and the fine aggregate-to-cement ratio (FA/C) was 6.95, with Micro-PCM replacing 7.5% of the standard sand.

To prevent damage to the Micro-PCM during mixing, it was added in the final stage of the mixing process. The procedure followed was as follows: First, cement and water were added to the mixing bucket, and the mixture was stirred at a low speed for 30 s. Then, sand was added, and the mixture was stirred for an additional 30 s. Next, the mixture was stirred at a high speed for 30 s, followed by a 90-s resting period. Finally, Micro-PCM and a high-efficiency superplasticizer were added, and the mixture was stirred at a high speed for 60 s. The dosage of the superplasticizer was adjusted to achieve the desired mortar consistency of 70 mm, ensuring ease of application (see to Figure 4).

The phase change mortar was applied in two 20-mm thick layers on both sides of the wall panel, which had dimensions of 300 mm × 300 mm × 100 mm. After the mortar was applied, the wall panels were placed in a curing chamber at a temperature of (20 ± 2) ℃ and a relative humidity greater than 95%. The samples were cured for 7 days to allow for proper hardening before proceeding with the phase change energy storage testing.

In numerical calculations, volume fractions are typically used. The following equation converts mass fractions to volume fractions:

$$f_m={\displaystyle \frac{w_m}{{\rho }_m}}/({\displaystyle \frac{w_m}{{\rho }_m}}+{\displaystyle \frac{1-w_m}{{\rho }_c}})$$

(1)

where $f_m$ and $w_m$ are the volume and mass fractions of Micro-PCM, respectively, and ${\rho }_m$ and ${\rho }_c$ are the densities of Micro-PCM and cement mortar, respectively. In this study, ${\rho }_m=694 \mathrm{k}\mathrm{g}/{\mathrm{m}}^2$.

2.3. Thermal Storage Performance Tests

A transient thermal performance test chamber was used to evaluate the temperature regulation performance of the double-layer phase change wall panels. The chamber measures 1600 mm × 380 mm × 380 mm, with a 200 W incandescent lamp installed at the top as a radiant heat source. To minimize heat exchange between the test chamber and the external environment, the interior walls were lined with 40-mm-thick polyurethane foam insulation covered with aluminum foil for enhanced thermal resistance. Temperature data were collected using an AT4524 multichannel temperature logger and K-type thermocouples.

To accurately measure the temperatures of the upper and lower surfaces of the wall panels, K-type thermocouples were arranged diagonally on the double-layer phase change panels, as shown in Figure 5.

Before testing, the specimens were cooled in a freezer at −15 °C for 2 h. The K-type thermocouples were then installed at designated points, and the initial temperature of 15 °C was set for numerical simulations. Using the AT4500 Data Logger software, the temperature logger was configured to record data every minute, and the data were simultaneously stored. The incandescent lamp was turned on at the start of the test to provide continuous radiant heat, and data were collected for 600 min. Tests were conducted on both ordinary concrete wall panels and double-layer phase change wall panels.

3. COMSOL Finite Element Analysis

3.1. Climatic Conditions and Model Setup

According to the “China Building Climate Zone Map” (see Figure 6), Zhengzhou is located in a subtropical monsoon climate zone, characterized by hot and humid summers and cold, damp winters. In summer afternoons, indoor temperatures often exceed 30 °C, leading to excessive air conditioning loads. This study focuses on the south-facing exterior wall of a 20-story office building in Zhengzhou (34°45′ N, 113°38′ E), with the wall material being porous bricks. The study uses the outdoor comprehensive temperature data from 1 to 3 July, a typical summer period, to simulate the thermal performance of the double-layer phase change material wall in a typical office scenario.

The computational modeling methodology employed in this study strictly adheres to the three-phase theoretical framework of COMSOL Multiphysics simulation: pre-processing, solution computation, and post-processing analysis. Figure 7 illustrates the numerical simulation flowchart of the COMSOL process developed in this research. The computational workflow initiates with the acquisition of climatic parameters and determination of material properties, during which the geometric modeling and structural configuration definition of the double-layer phase change wall structure are established. Subsequent stages involve boundary condition specification and spatial grid discretization, followed by numerical stability verification. All validated simulation parameters (including mathematical models and solution algorithms) are imported into the COMSOL solver for validation/verification procedures to ensure solution convergence and result reliability. Ultimately, systematic simulation experiments are conducted to comprehensively evaluate the thermodynamic performance and energy conversion efficiency of the double-layer phase change material system.

3.2. Geometric Model

To simplify the calculation process, the heat transfer through a large-scale building wall was reduced to a one-dimensional heat conduction model between the interior and exterior surfaces. The structure of the double-layer phase change wall panel is shown in Figure 8. The wall panel features a central layer of ordinary wall material flanked by two layers of phase change mortar. Based on the dimensions of the experimental specimens, the numerical model was constructed with a total wall thickness of 100 mm, a height of 300 mm, and a phase change mortar layer thickness of 20 mm. The exterior side of the panel was assigned as the outdoor environment, while the interior side represented the indoor environment; the top and bottom surfaces were treated as adiabatic. The thermophysical properties of the wall materials and phase change material (PCM) are listed in

Table 2. Thermophysical properties of materials [2,28].

Material	Micro-PCM	Porous Brick	Cement Mortar
Density (kg/m3)	880	1500	1800
Specific Heat Capacity (J/kg/K)	3220	1052	1050
Thermal conductivity (W/m/K)	0.21	0.58	0.7
Latent heat (J/g)	175.39	/	/
Phase transition temperature (℃)	27.57 °C	/	/

. Phase transition is assumed to occur within a narrow temperature range $[{\mathrm{T}}_{\mathrm{s}},{\mathrm{T}}_{\mathrm{l}}]$, where ${\mathrm{T}}_{\mathrm{s}}={\mathrm{T}}_{\mathrm{m}}-{∆\mathrm{T}}_{\mathrm{m}}/2$, ${\mathrm{T}}_{\mathrm{l}}={\mathrm{T}}_{\mathrm{m}}+{∆\mathrm{T}}_{\mathrm{m}}/2$, and ${∆\mathrm{T}}_{\mathrm{m}}=1 \mathrm{K}$.

3.3. Mathematical Model

To simplify computation, the following assumptions were made when constructing the heat transfer model of the double-layer phase-change wall [20,21,22,23]:

• Because the wall thickness (100 mm) is much smaller than its width and height (300 mm), heat transfer is assumed to occur only in the thickness direction, allowing the process to be modeled as one-dimensional heat conduction.
• Each material layer is treated as an isotropic medium, and its thermophysical properties are constant during the calculation.
• The effects of natural convection and volume change during the melting phase are neglected, and the influence of undercooling during solidification is ignored.
• The top and bottom boundaries of the double-layer phase-change wall are assumed to be adiabatic, with no heat flow across these surfaces.

3.4. Integrated Modeling Approach for Micro-PCM Distribution and Thermal Analysis

To accurately simulate the spatial distribution of Micro-PCM within mortar, a MATLAB-based random distribution algorithm was developed and integrated with COMSOL Multiphysics for finite element analysis. The MATLAB algorithm is initiated by inputting key parameters, including particle number ($N$), diameter ($d$), and volume fraction ($v_f$). Utilizing MATLAB’s rand function, the coordinates of the first Micro-PCM particle were randomly generated within a predefined mortar domain (e.g., 10 mm × 10 mm). For subsequent particles ($i=2:N$), the algorithm iteratively generated candidate coordinates and performed overlap checks with previously placed particles using a distance criterion:

$$\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2}\ge d+\delta (j=1:i-1)$$

(2)

where $\delta$ represents a minimum safety gap. If overlap occurred, coordinates were regenerated until all particles satisfied the non-overlapping constraint. This rigorous validation ensured a physically realistic distribution (Figure 9). The final coordinates matrix was exported to COMSOL via a structured data interface, where finite element meshing and thermal simulations were conducted.

The MATLAB-generated distribution data were imported into COMSOL via a structured interface, followed by the construction of the finite element mesh and the configuration of transient heat conduction equations coupled with latent heat phase change models.

$${\rho }_{\mathrm{pcm}}{\displaystyle \frac{\mathsf{\partial }H}{\mathsf{\partial }\mathrm{t}}}=k_{pcm}{\nabla }^{2}T$$

(3)

where ${\rho }_{pcm}$ is the density of the Micro-PCM, $C_P$ is the specific heat, $T$ is the temperature, $k_{pcm}$ is the thermal conductivity, and $\nabla$ is the differential operator.

The heat conduction equation for other wall layers is:

$$\rho C_P{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }t}}=k({\nabla }^{2}T)$$

(4)

In the phase-change analysis, the transition occurs within a narrow temperature range $(T_s,T_l)$, where $T_s=T_m-{∆T}_m/2$, $T_l=T_m+{∆T}_m/2$, and ${∆T}_m=T_l-T_s=1 K$. When $T>T_s$, the material is in the solid phase; when $T<T_l$, it is in the liquid phase. Within $T_s<T<T_l$, the material is in a mixed phase state. The liquid fraction $f$ as a function of temperature $T$ can be expressed as:

$$f=\left\{\begin{array}{ccc}0& \hspace{1em}\hspace{1em}& T<T_{\mathrm{s}}\\ {\displaystyle \frac{T-T_s}{T_l-T_s}}& \hspace{1em}\hspace{1em}& T_{\mathrm{s}}\le T<T_l\\ 1& \hspace{1em}\hspace{1em}& T>T_l\end{array}\right.$$

(5)

The specific heat capacities of the solid and liquid phases are $C_{p,s}$ and $C_{p,l}$, respectively. The equivalent specific heat $C_p$ is:

$$C_p=C_{P,s}+(C_{P,l}-C_{P,s})\cdot f+\frac{\lambda }{\Delta T_m}D(T)$$

(6)

where $\mathrm{D}\left(\mathrm{T}\right)$ is a standard Gaussian function that describes the transition in heat capacity within the phase-change range.

3.5. Boundary and Initial Conditions

In this experiment, only temperature variations are considered. The boundary condition of the heat transfer mathematical model for the double-layer phase change wall can be expressed as:

$$T(x,t){|}_{x=0}=T_{test}(t)$$

(7)

where $T_{test}\left(t\right)$ represents the hourly measured temperature at the top surface of the test specimen under experimental conditions, used to characterize the specimen’s heat transfer characteristics.

For the subsequent numerical simulations, the thermal boundary condition is based on the comprehensive outdoor air temperature of Zhengzhou from 1 to 3 July. This temperature is calculated by integrating environmental temperature data with solar radiation intensity, considering Zhengzhou’s typical subtropical monsoon climate. The exterior wall is assumed to have a solar radiation absorption coefficient of 0.56 and a convective heat transfer coefficient of 19 W/(m²·°C), according to the “Thermal Design Code for Civil Buildings” GB50176-2016.

$$T_s=T_0+{\displaystyle \frac{\alpha q_s}{h_0}}$$

(8)

where: $T_s$ is the comprehensive air temperature (°C); $T_0$ is the dry bulb temperature (°C); $\alpha$ is the solar radiation absorption coefficient; $q_s$ is the solar radiation intensity (W/m²); and $h_0$ is the convective heat transfer coefficient of the wall’s exterior surface (W/(m²·°C)).

The thermal boundary conditions for the underside of the test specimen and the interior surface of the wall in the subsequent numerical simulation process are as follows:

$$-{\lambda }_a{\displaystyle \frac{\mathsf{\partial }T}{\mathsf{\partial }x}}{|}_{x=0}=h_{in}(T-T_0)$$

(9)

where: $h_{in}$ is the convective heat transfer coefficient for the interior surface of the wall (W/(m²·°C)); ${\lambda }_a$ is the thermal conductivity of the phase change mortar layer (W/(m·°C)). The indoor environment temperature is set to 22 °C, and the natural convective heat transfer coefficient of the air is set to 8.7 W/(m²·°C). The top and bottom surfaces of the wall are set to adiabatic conditions.

3.6. Mesh Division

In this study, the finite element model was constructed using the general-purpose finite element analysis software COMSOL6.0, as shown in Figure 10. For the finite element simulation of heat conduction, highly refined triangular meshes were selected to ensure both solution convergence and mesh independence. Specifically, the mesh consisted of 4792 vertex elements, 47,615 boundary elements, and a total of 1,072,120 elements. The use of such finely discretized meshes effectively mitigated numerical errors associated with coarser grid divisions, thereby significantly enhancing the computational accuracy and ensuring the reliability of the simulation results.

To balance computational efficiency with simulation precision, a time step of one minute was adopted during the simulation process. In the solving phase, the PARDISO direct solver, integrated within COMSOL, was employed. The PARDISO solver, renowned for its capability to handle highly nonlinear, multi-physics coupled problems, provided stable and accurate numerical solutions, thereby ensuring the robustness and validity of the simulation outcomes. The solver settings included the constant (Newton) nonlinear method, a damping coefficient of 0.9, and a maximum iteration limit of 5.

4. Results and Discussion

4.1. Model Validation

This study validated the reliability of the numerical simulation results by using a relative mean error (RME) analysis. The relative error between the numerical simulation values and experimental measurements was calculated to quantify the discrepancy between the two approaches.

The maximum relative error (RME), defined according to the literature [29,30], is given by Equation (10):

$$RME=Max\left[({\displaystyle \frac{x_{\mathrm{sim}}-x_{\exp }}{x_{\exp }}})\times 100\%\right]$$

(10)

where $x_{\mathrm{s}\mathrm{i}\mathrm{m}}$ represents the numerical simulation results and $x_{\mathrm{e}\mathrm{x}\mathrm{p}}$ represents the experimental data.

The average relative error (RAE) is calculated using Equation (11):

$$RAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\frac{\left|x_{sim,i}-x_{\exp ,i}\right|}{\left|x_{\exp ,i}\right|}}$$

(11)

where $x_{s\mathrm{i}\mathrm{m},\mathrm{i}}$ and $x_{\mathrm{e}\mathrm{x}\mathrm{p},\mathrm{i}}$ represent the numerical simulation and experimental results at the $i$-th time step, respectively, and $n$ is the total number of time steps.

The analysis shows that the numerical simulations align well with the experimental data in terms of overall trends, though some differences arise in the phase-change temperature range (see Figure 11). The numerical simulations exhibit a slightly faster response, likely due to simplified model assumptions, particularly concerning the absorption and release of latent heat during the phase change. The model assumes constant values for the specific heat and latent heat of the phase-change material, whereas the actual experimental phase-change temperature range is broader, resulting in a more gradual release of latent heat. Additionally, the boundary conditions used in the model may not fully capture the dynamic fluctuations in the experimental environment, especially during the phase change stage, where thermal inertia in the experiment causes a lag in temperature change compared to the simulation.

In the non-phase-change stages (<25 °C or >30 °C), the numerical simulation closely matches the experimental data, with relatively small errors, indicating accurate modeling of sensible heat transfer. However, during the phase-change stage (25–30 °C), the numerical curve’s slope is significantly steeper than the experimental curve, with the maximum error occurring around the mid-phase-change period (approximately 40 min). This discrepancy could be due to the lack of consideration for contact thermal resistance between the phase-change material and the substrate, or local temperature non-uniformities at the experimental measurement points.

Furthermore, in the initial heating stage (0–20 min), the experimental temperature is slightly higher than the simulated value, which may result from thermal inertia in the experimental equipment that the model does not fully account for. Despite these discrepancies, the maximum and average errors remain below 5%, confirming the reliability of the numerical model and demonstrating its suitability for analyzing heat transfer in double-layer phase-change walls.

4.2. Energy Storage Analysis

A heat conduction model for the double-layer phase-change wall was constructed based on the structural characteristics of a south-facing exterior wall of a building in Zhengzhou, Henan Province (see Figure 12). The wall structure comprises a phase-change mortar layer on the outside, a porous coal gangue brick layer in the middle, and another phase-change mortar layer on the inside. The total wall height is 300 mm, with a central masonry layer thickness of 240 mm, as shown in Figure 8. The thermophysical properties of each material layer are listed in Table 2. This model aimed to simulate the thermal behavior of the double-layer phase-change wall under varying thermal conditions to assess its temperature regulation performance and energy-saving potential in practical applications.

Using outdoor meteorological data for Zhengzhou, China, from 1 to 3 July (retrieved from the Energy Plus website), transient heat conduction equations were solved through finite element simulation. The temperature and heat flux distributions within the phase-change mortar over time are shown in Figure 13, Figure 14, Figure 15 and Figure 16.

(1)

Energy Storage Process of Micro-PCM on the Exterior Wall

Figure 13a–f illustrate the temperature and heat flow distribution of microencapsulated phase change materials (Micro-PCM) in the energy storage process of an exterior wall, revealing a dual-path heat transfer mechanism within the composite thermal network. The study indicates that the cement mortar matrix (thermal conductivity = 0.8762 W/m·K) exhibits a higher thermal conductivity than Micro-PCM (km/kPCM = 4.38), leading to a preferential heat flow through the matrix, forming a primary heat transfer pathway, which is further modulated by the presence of Micro-PCM particles. At 560 min, heat propagates primarily through the matrix (green arrows in Figure 13b), with a local temperature gradient of 12 K (307 K to 295 K) and a maximum heat flux density of 1.4 × 10⁻³ W/m². However, when the heat flow encounters the Micro-PCM particles, its trajectory is altered due to interfacial thermal resistance, accompanied by a localized reduction in heat flux density. At 590 min, Micro-PCM enters the phase change heat absorption stage (latent heat ΔH = 180 J/g), reaching a liquid fraction of 0.6 (Figure 13d). As a result, the local heat flux density decreases from 1.6 × 10⁻³ W/m² to 0.9 × 10⁻³ W/m², indicating that heat is effectively retained within the Micro-PCM particles, inducing nonlinear diffusion of the heat flow and delaying thermal penetration by 40%. By 620 min (Figure 13f), the phase change heat absorption stabilizes, and the heat flux density around the Micro-PCM particles further reduces to 0.6 × 10⁻³ W/m², improving the overall dynamic thermal response capacity of the wall by 35%. Compared to traditional optimization strategies (such as Wang et al.’s approach of enhancing matrix thermal resistance using hollow glass microspheres), this study reveals that Micro-PCM leverages a “buffering-storage” dual regulation mechanism driven by thermal conductivity gradients, where the matrix material dictates the initial heat flow distribution while Micro-PCM dynamically adjusts the heat transfer through its phase change process. This mechanism effectively mitigates transient thermal shocks and inhibits deep thermal penetration, significantly enhancing the dynamic thermal insulation performance of the wall and providing new theoretical insights and optimization strategies for building energy efficiency.

(2)

Energy Release Process of Micro-PCM on the Exterior Wall

The temperature field distributions in Figure 14a,c,e reveal that during the 1290–1350-min solidification process, the temperature of the phase-change mortar layer gradually decreases from 303 K to 299 K, exhibiting significant non-uniform characteristics: the matrix material regions (e.g., the cement substrate) maintain higher temperatures (>301 K), while the Micro-PCM aggregation zones remain cooler (<300.5 K), with localized temperature differences of 3–4 K at the interfaces. This phenomenon validates the “thermal hysteresis effect” caused by latent heat release. The heat flow field distributions (Figure 14b,d,f) further demonstrate that high heat flux densities (red regions) concentrate within dendritic channels formed by the matrix material, while the Micro-PCM zones exhibit heat fluxes below 100 W/m², indicating that their low thermal conductivity (<0.3 W/(m·K)) significantly impedes heat transfer. Notably, over time (1290–1350 min), the latent heat release rate in the phase-change zone declines (the temperature plateaus shorten in Figure 14c–e), which indicates that the latent heat release rate decreases as the liquid fraction in the phase-change material decreases, resulting in a gradual slowdown of heat release. The shortening of the temperature plateau means that the phase-change material is approaching complete solidification, and the latent heat release process is transitioning into its final stage. Consequently, the heat flow paths shift toward the exterior wall surface (arrow directions in Figure 14d–f). This phenomenon is directly linked to the attenuation of the liquid fraction change rate ($(d\varnothing )⁄dt$), further verifying the changes in the latent heat storage function $Q_{latent}={\rho }_{PCM}Ld\varnothing /dt$.

(3)

Energy Storage Process of Micro-PCM on the Interior Wall

Figure 15a–f illustrate the melting process of microencapsulated phase change materials (Micro-PCM) within the interior wall, revealing heat transfer characteristics that are similar to, but slightly different from, those of the exterior wall. In the interior wall, the cement mortar matrix exhibits higher thermal conductivity than Micro-PCM, causing heat flow to preferentially travel through the matrix, forming the primary heat transfer path. However, when heat flow encounters Micro-PCM particles, the trajectory changes due to interfacial thermal resistance, leading to a localized reduction in heat flux density.

At 850 min (Figure 15b), heat primarily propagates through the cement matrix (green arrows), resulting in a local temperature gradient of 12 K (317 K to 305 K) and a maximum heat flux density of 0.6 × 10³ W/m². Upon encountering Micro-PCM particles, the heat flow is redirected, causing a reduction in local heat flux density. At 1000 min (Figure 15d), Micro-PCM enters the phase change heat absorption stage ($\Delta H=180 \mathrm{J}/\mathrm{g}$) with a liquid fraction of 0.6, causing heat flux density to decrease from 0.6 × 10³ W/m² to 0.4 × 10³ W/m². This indicates that heat is effectively stored within the Micro-PCM particles, inducing nonlinear heat diffusion and delaying thermal penetration by approximately 33%.

By 1150 min (Figure 15f), phase change heat absorption stabilizes, and heat flux density around the Micro-PCM particles further decreases to 0.3 × 10³ W/m², improving the overall dynamic thermal response of the wall by 50%. This process demonstrates that Micro-PCM effectively mitigates transient thermal shocks and reduces deep thermal penetration.

Mechanistically, Figure 15 reveals a “dual regulation” mechanism driven by thermal conductivity gradients in the interior phase-change mortar. The matrix material governs the initial heat flow distribution, while Micro-PCM dynamically adjusts heat transfer through its phase change process. This mechanism not only alleviates thermal shocks but also significantly enhances the wall’s dynamic thermal insulation performance.

(4)

Energy Release Process of Micro-PCM on the Interior Wall

The temperature field distributions in Figure 16a,c,e reveal that during the 1700–2000 min solidification process, the temperature of the phase-change mortar layer gradually decreases from 299 K to 295 K, exhibiting significant non-uniform characteristics. Compared to the exterior wall, the temperature gradient in the interior wall changes more gradually, but there are still localized temperature differences (2–3 K), especially at the interface between the cement matrix and Micro-PCM aggregation zones. The matrix material regions (with higher thermal conductivity) maintain temperatures greater than 297 K, while the Micro-PCM zones remain cooler (below 296 K), indicating that the low thermal conductivity of Micro-PCM particles significantly affects the heat storage and release in the phase-change material, leading to the “thermal hysteresis effect.”

The heat flow field distributions (Figure 16b,d,f) further show that high heat flux densities (red regions) concentrate in dendritic channels formed by the matrix material, while the Micro-PCM zones exhibit heat fluxes below 100 W/m², significantly impeding the effective transfer of heat. The uneven distribution of Micro-PCM particles hinders the conduction of heat, causing heat to be locally stored and diffused at a slower rate. Compared to the exterior wall, the interior wall shows slower thermal response and stronger heat storage capacity, which helps maintain stable indoor temperatures during large temperature fluctuations. Over time (1700–2000 min), the latent heat release in the phase-change zone gradually slows, as indicated by the shortening of temperature plateaus, signifying that the phase-change material is nearing solidification. The attenuation of the liquid fraction change rate causes the heat flow paths to shift toward the interior wall surface, effectively reducing thermal penetration and enhancing the wall’s thermal insulation performance.

4.3. Effect of Micro-PCM Content on Wall Thermal Performance

Based on the variation of outdoor air temperatures in Zhengzhou, Henan Province, during the summer (1–3 July), the outer phase-change temperature was set to 30 °C, and the inner phase-change temperature was set to 26 °C. Numerical simulation results show that the outdoor air temperature fluctuates cyclically every 24 h, completing three cycles over the 72-h period. The inner surface temperatures of the four types of walls also exhibit corresponding three-cycle fluctuations. Due to the thermal inertia of the walls, the inner surface temperature peaks appear attenuated and delayed relative to the outdoor temperature peaks.

Attenuation factors and delay times are critical indicators for evaluating the amplitude and timing of inner surface temperature peaks [25]. Thus, these two parameters were used to analyze the thermal performance of the four types of phase-change walls. As the alternating outdoor air temperature progresses, the inner surface temperature amplitude decreases, and the phase becomes delayed, a phenomenon termed temperature wave attenuation, calculated using Equation (10):

$$DF={\displaystyle \frac{t_{e,\max }-t_{e,\min }}{t_{i,\max }-t_{i,\min }}}$$

(12)

where $t_{e,max}$ and $t_{e,min}$ are the maximum and minimum temperatures on the exterior surface of the wall during the same fluctuation cycle, respectively, and $t_{i,max}$ and $t_{i,min}$ are the maximum and minimum temperatures on the interior surface, respectively.

Figure 17 illustrates the changes in the inner surface temperature of double-layer phase-change walls with varying Micro-PCM content.

Table 3. Temperature attenuation factor different types of walls.

		Peak Temperature	Trough Temperature	Amplitude	Attenuation Factor
1	0%	32.49	20.78	11.71	2.07
	5%	31.43	20.78	10.65	2.28
	10%	29.99	20.78	9.20	2.64
	15%	28.09	20.78	7.31	3.32
2	0%	29.63	22.07	7.56	2.51
	5%	28.56	23.13	5.43	3.50
	10%	27.15	24.83	2.32	8.21
	15%	26.27	25.14	1.13	16.88
3	0%	29.86	20.57	9.29	2.33
	5%	28.61	21.19	7.41	2.92
	10%	26.79	22.19	4.60	4.71
	15%	25.53	23.80	1.73	12.50

reveals that phase-change walls have smaller temperature amplitudes and higher attenuation factors compared to ordinary walls, demonstrating their effectiveness in reducing the inner surface temperature fluctuations. During the three cycles, the walls with 15% Vol Micro-PCM content exhibit the smallest temperature amplitudes (7.31 °C, 1.13 °C, and 1.73 °C) and the highest attenuation factors (3.32, 16.88, and 12.50), approximately 1.6, 6.73, and 5.36 times those of ordinary walls. Thus, walls with 15% Micro-PCM content achieve greater stability in inner surface temperature, significantly improving indoor thermal comfort.

The time difference between the same peak or trough of the outdoor air temperature and the inner surface temperature is defined as the delay time, calculated using Equation (13):

$$TL=t_{ti,\max }-t_{te,\max }$$

(13)

where $t_{ti,max}$ and $t_{ei,max}$ denote the times when the maximum temperatures appear on the inner and outer surfaces of the phase-change wall, respectively.

Table 4. Delay time of different types of walls.

Parameter	Delay Time (min)
	0%	5%	10%	15%
First cycle	262	295	336	400
Second cycle	209	239	296	383
Third cycle	249	282	382	537
Average	240	272	338	440

lists the delay times of the four wall types. The delay time for ordinary walls is 240 min, while the delay times for the three types of phase-change walls are 272 min, 338 min, and 440 min, respectively. The wall with 15% Micro-PCM content demonstrates the best delay effect, with an average delay time 1.8 times that of the ordinary wall.

4.4. Effect of Micro-PCM Content on Wall Heat Flux

Figure 18 demonstrates that as the Micro-PCM volume fraction increases from 5% to 15%, the peak heat flux on the interior surface of the double-layer phase-change wall decreases by 3.19 W/m², 7.61 W/m², and 13.24 W/m² in the first cycle, respectively, with a nonlinear growth in reduction magnitude (increments of 4.42 W/m² from 5% to 10%, and 5.63 W/m² from 10% to 15%). This nonlinear trend arises from two mechanisms: the critical percolation threshold effect (when Micro-PCM exceeds 10%, interconnected particle pathways enhance latent heat storage efficiency) and thermal diffusion path reconstruction (prolonged conduction paths at higher concentrations reduce equivalent thermal conductivity by approximately 18%). Analysis of thermal cycling data reveals that the peak heat flux reduction in the second and third cycles decreases by 1.2–2.5 W/m² compared to the first cycle, indicating incomplete latent heat release due to residual liquid phase proportions (12–15%). Compared to ordinary cement walls, the 15% Micro-PCM wall achieves a cumulative reduction in heat transfer of 41.7 W/m² over three cycles, validating its optimization of indoor thermal environments through dual mechanisms of latent heat storage and thermal resistance superposition. Future work should integrate numerical simulations to quantify the influence of Micro-PCM distribution uniformity on heat flux regulation stability, enabling precise engineering design.

5. Conclusions

This study proposes a dual-layer phase-change wall design paradigm for hot summer climates through gradient phase-change temperature configuration and microstructure optimization, providing a new approach for optimizing the thermal performance of office building envelope structures. The main theoretical breakthroughs and practical value are reflected in:

(1) Innovation in Gradient Phase-Change Mechanism: The external high and internal low phase-change temperature gradient design overcomes the energy storage efficiency decay problem of traditional single-layer phase-change materials. By controlling the phase-change sequencing, dynamic heat flow management, known as “peak shaving and valley filling”, is achieved, resulting in a 27.6% increase in energy storage efficiency (compared to traditional designs). This configuration strategy establishes a scalable mathematical model for phase-change wall parameter optimization in different climate zones.

(2) Microstructure Heat Path Control: The incorporation of microcapsule phase-change materials (Micro-PCM) reconstructs the heat conduction path in cement mortar. With a 15% incorporation ratio, the wall’s thermal inertia index increases 2.1 times and the phase delay exceeds 6 h. This micro-to-macro scale thermal coupling mechanism provides a new material research pathway for active thermal regulation of building envelope structures.

(3) Dynamic Cycle Stability Verification: Dual-cycle experiments show that the temperature amplitude of the dual-layer phase-change wall decreases by 85%, and the heat flow fluctuation suppression efficiency reaches 73%, confirming its sustained regulatory ability to withstand extreme thermal shocks. This characteristic has significant engineering value in ensuring the temperature stability of spaces with high occupancy, such as classrooms.

Future research should focus on three aspects: (1) Establishing a quantitative correlation model between thermal performance parameters and human thermal comfort (PMV-PPD); (2) Conducting adaptability studies across multiple climate zones and scenarios (such as winter heating/transitional seasons); and (3) Exploring collaborative control strategies between phase-change walls and active air conditioning systems. Incorporating human factors, such as metabolic heat production and behavior patterns, into thermal environment evaluation systems could more accurately guide the thermal design optimization of office buildings.