Thermal and economic performance of MPCM-enhanced AAC bricks combined with an auxiliary heater plate in cold and freezing climates: A numerical investigation

Abstract

This study is the first to numerically evaluate the thermal performance of MPCM-enhanced autoclaved aerated concrete (AAC) bricks combined with an auxiliary heater plate for passive space heating in cold and freezing climates. A two-dimensional finite-volume CFD model with time-dependent outdoor boundary conditions and an apparent-heat-capacity formulation for phase change is developed and implemented in a custom C++ solver. The effects of MPCM volume fraction (φ = 0, 4, 8, 12%) and heater-plate heat flux (q″_hp = 0, 50, 100, 150 W/m²) are examined over a 24 h cycle with outdoor temperature varying between −15 and 15 °C. Indoor surface temperature (T_is), indoor heat flux (q_is), MPCM melting fraction (MF), and daily power consumption (DPC) are employed as performance indicators. For q″ = 100–150 W/m², φ = 8–12% reduces peak T_is by about 1–2 °C and peak q_is by roughly 15–25%, while raising minimum values and delaying the peak by 1 h. At these heater powers, DPC drops from about 0.31–0.34 kWh/m² for plain AAC to 0.24–0.28 kWh/m² (0–30% saving) with MPCM, demonstrating the potential of the proposed AAC–MPCM–heater configuration for peak-load mitigation and energy-efficient envelope design in cold climates. Moreover, over a 40-year service life, the techno-economic analysis shows that 4 vol% MCPCM delivers the highest returns, with NPV = $11,689–$15,970 and IRR = 13.55–17.45% across q’'=0–150 W/m².

Introduction

Reducing reliance on fossil-fuel energy for maintaining stable indoor temperatures has become increasingly important as greenhouse-gas emissions drive global warming and intensify climate variability^1–3. Conventional heating and cooling systems, which depend heavily on fossil fuels, contribute substantially to atmospheric carbon accumulation, further amplifying the very temperature fluctuations they are designed to mitigate^4,5. This feedback mechanism increases the long-term energy demand of buildings and accelerates environmental degradation. Therefore, lowering fossil-fuel consumption in the building sector is essential not only for improving energy efficiency but also for mitigating climate impacts and promoting more sustainable indoor thermal management strategies^6–8. One promising approach to reducing this dependence on fossil-fuel heating and cooling is the incorporation of advanced building materials capable of regulating temperature passively^8–10. Among these, thermally smart bricks enhanced with phase-change materials (PCMs) have attracted significant attention due to their ability to store and release latent heat as outdoor conditions fluctuate^11–14. By buffering temperature fluctuations, PCM-integrated bricks help maintain a more stable indoor environment without continuous mechanical intervention, thereby lowering overall energy demand^15,16. Such materials represent a practical and scalable strategy for improving building thermal performance while supporting broader efforts to decrease greenhouse-gas emissions and enhance sustainability in the built environment. In recent years, numerous studies have evaluated the thermal performance of thermally smart bricks (TSBs) enhanced with various PCMs under different climate conditions^17–21. In one investigation²², adding PCM to lightweight wall systems made a big difference: the peak heat flux was cut by 66.4 %, and the transfer of heat through the wall was pushed back by more than 5 hours. The best phase change temperature range also depended on which way the wall was facing, 20–30 °C for east and south orientations, and 18–28 °C for west and north, showing that PCM can be tuned to improve thermal performance based on wall direction. Meng et al.^23,24 shown that improving PCM-based thermal energy storage requires both faster heat transfer and better control of when and where stored heat is released. For spherical encapsulated PCM, increasing copper-foam fin thickness up to 15 mm can achieve 67% faster discharging and ~35% faster charging, while preserving > 97% of the PCM volume and increasing cycle efficiency to ~83%. At the building-envelope scale, a dynamic rotating PCM layer can release heat directly indoors during winter, producing an indoor-directed heat flow on the order of −22 to −80 W m⁻², although it may reduce thermal release and storage capacity by ~33.8–34.8% compared with a static configuration. Taj et al.²⁵ mixed eutectic organic PCMs into clay bricks and tested them both in the lab and in real buildings to assess thermal behavior, structural performance, and energy savings. They reported clear gains: indoor air temperatures were lowered by about 4–5.5 °C, the indoor temperature swing dropped by 32%, the heat-flow response was delayed by up to 150 minutes, and heat flux through the walls decreased by roughly 25–30% compared with standard bricks. Abdulmunem et al.'s²⁶ introduced a bio-based phase change material (BPCM) derived from stearin of sheep tail-fats (SSTF) for sustainable building-envelope thermal energy storage, evaluated through numerical and experimental melting analyses in a rectangular cavity. The authors showed that natural convection dominates heat transfer during melting because SSTF has relatively low thermal conductivity, leading to non-uniform melting. Adding a small amount of carbon nanotubes (0.03%) slightly increases thermal conductivity and improves performance, accelerating melting by 11% and increasing melt velocity by 8.7%, while enhancing heat transfer and storage rates by 13.7% and 7.5%, respectively. Yousef et al.²⁷ conducted numerical analyses of buildings made with hollow bricks, with and without PCM, for eight Mediterranean locations and for various melting temperatures and building types. Their findings indicate that PCM can lower cooling energy demand by as much as 56% in North-East Mediterranean climates (with an optimal melting point around 26 °C), but yields minimal benefits in the much hotter South-East Mediterranean regions.

In addition to pure passive thermal systems, Active PCM systems (also called latent heat–assisted active thermal storage) combine the latent buffering of PCMs with a supplementary heat source, such as electric heating elements, radiant floor circuits, or embedded heaters^28–30. This approach has been explored in PCM-enhanced radiant/underfloor heating, where PCM integration increases thermal storage capacity and can shift or smooth heating demand while maintaining comfort. More recent concepts also integrate electrically charged PCM storage directly into building components (e.g., bricks/plates) to address heating needs in cold climates by actively storing heat during charging periods and releasing it later. In this context, the present work, which couples MPCM-integrated AAC bricks with an auxiliary heater plate, is best positioned as a hybrid active–passive system, where the PCM provides passive thermal regulation while the heater plate enables controlled thermal input when required^31,32.

Moreover, to enhance the thermal performance of PCM-enhanced TSBs, the PCM is incorporated in micro- or nano-encapsulated form, which effectively prevents leakage during melting and solidification^33–38. Encapsulated PCM bricks have become a prominent component of high-performance building envelopes in both residential and commercial sectors, particularly in climates with large day–night temperature swings and growing cooling loads^39–42. Vicente⁴³ experimentally examined masonry walls incorporating PCM macrocapsules and showed that these systems substantially damp indoor temperature oscillations and extend the time lag, confirming their effectiveness for passive temperature regulation and reduced energy use. Abdulhossein et al.⁴⁴ embedded 5 and 10 PCM capsules into conventional bricks and evaluated the resulting wall performance; the configuration with 10 capsules decreased heat flux by 34%, increased stored thermal energy by 50%, and lowered the interior surface temperature by more than 3 °C relative to a reference wall. Maleki et al.⁴⁵ formulated a plasterboard containing nano-encapsulated PCM produced via miniemulsion polymerization and comprehensively characterized its thermal behavior. Their findings indicate that the nano-PCM significantly enhances latent heat storage, mitigates indoor temperature swings, and improves thermal comfort compared with standard plasterboards. Hassan et al.⁴⁶ numerically modeled clay hollow blocks and cement layers incorporating nano-encapsulated PCM using a detailed PDE-based framework that more accurately represents latent heat effects than simplified models. Their simulations reveal that increasing NEPCM content up to 10% delays the peak inner-surface temperature, narrows Tis to 23.3–26.6 °C, and reduces heat flux by 13%, alongside a maximum 16% reduction in Pd, highlighting the strong potential of nano-PCM systems for adaptive, energy-efficient envelopes. Nassr et al.⁴⁷ used CFD together with a techno-economic analysis to assess bricks containing PCM capsules under varying boundary conditions. They reported that the encapsulated PCM performs most effectively for indoor temperatures of 20–24 °C and outdoor temperatures of 25–31 °C, delivering notable cooling-load reductions, while the economic study predicted long-term savings of $415k–$444k over a 30-year period and an internal rate of return well above the discount rate, making PCM-enhanced bricks a financially attractive green-building solution. Additionally, controlling energy consumption during peak heating and cooling periods is essential to mitigate grid overload and reduce operational costs. Peak demand typically occurs when outdoor temperatures are most extreme. To effectively manage these critical periods, in addition to using TSBs, other supplementary components such as heaters are required. Overall, to address the existing gaps in this field, this study, for the first time, investigates a hybrid active–passive PCM-based thermal management system enhanced with pentadecane as a PCM under cold and freezing climatic conditions. To manage peak energy demand during critical periods, a heater plate with varying power levels is integrated with the brick system. In addition, to enhance the thermal storage capability and ensure leakage prevention, the PCM is encapsulated within polymethyl methacrylate (PMMA) shells. A CFD framework based on the FVM is employed to examine the effects of micro-encapsulated PCM (MPCM) volume fraction and heater plate power on the thermal performance of buildings incorporating TSB components. The thermal behavior of the proposed system is evaluated using key indicators, including indoor surface temperature (T_is) and its temporal variation, indoor heat flux (q_is), MPCM melting fraction, and daily power consumption (DPC). Additionally, by conducting a techno-economic analysis using NPV and IRR, we present the economic benefits of this hybrid active–passive thermal regulation structure.

Problem and configuration definition

One of the main challenges in heating and cooling buildings is maintaining and controlling indoor temperatures within an acceptable comfort range, particularly under cold and freezing climatic conditions. The reason for selecting a PCM with a melting temperature of 10 °C is that, although the indoor air temperature is maintained at 18 °C, the interior wall surface temperature in winter can be much lower due to the large indoor–outdoor temperature gradient (e.g., 18 °C indoors versus −15 °C outdoors) and may remain only a few degrees above 0 °C. Therefore, choosing an MCPCM with a melting range around 10 °C targets the actual wall/surface temperature window to reduce heat loss by buffering the wall temperature, rather than aiming to raise the indoor air temperature to 18 °C. For this reason, as shown in Figure 1, a passive heating configuration is proposed that combines MPCM-enhanced autoclaved aerated concrete (AAC) bricks with varying MPCM volume fractions (ϕ = 0, 4, 8, and 12%) and an auxiliary heater plate operating at different heat flux levels ( = 0, 50, 100, and 150 W/m²) under climatic conditions characterized by T_min = −15 °C and T_max = 15 °C. The heater plate functions as an auxiliary element to regulate energy consumption during peak demand periods rather than serving as the primary heating source. The geometric dimensions of the system, length (L), width (W), and height (H), are presented in Fig. 1 and are 600 mm, 200 mm, and 150 mm, respectively. The core component of the passive thermal system is the AAC brick integrated with MPCM material. AAC bricks are lightweight, porous building materials whose properties are governed by their cellular microstructure. They exhibit compressive strengths of approximately 2–6 MPa and an elastic modulus of 1–3 GPa, while offering favorable thermal performance with low thermal conductivity in the range of 0.09–0.20 W/m.K. These combined characteristics make AAC bricks suitable for building applications where thermal insulation and energy efficiency are of primary importance. To enhance the thermal performance of AAC bricks, this study integrates pentadecane PCM, encapsulated within a PMMA shell, into the AAC matrix. Pentadecane is an organic phase change material widely used for thermal energy storage due to its suitable melting temperature near indoor comfort conditions. It offers high latent heat capacity and stable phase transition behavior, enabling effective attenuation of temperature fluctuations in building envelopes. In addition, pentadecane exhibits good thermal reliability and chemical stability over repeated melting–solidification cycles, making it suitable for long-term passive thermal regulation applications. Moreover, the PMMA shell serves as a protective encapsulation component that prevents leakage of the PCM during the melting–solidification process. It provides adequate mechanical integrity and chemical compatibility with cementitious matrices, ensuring stable incorporation within AAC bricks. In addition, PMMA offers good thermal stability and transparency, allowing reliable thermal cycling without degradation of the encapsulated PCM. All important thermophysical characteristics of AAC brick, pentadecane as PCM, and PMMA shell are listed in Table 1.

Fig. 1.

Schematic of the proposed MPCM-enhanced AAC integrated with a heater plate.

Table 1.

Thermophysical properties of the MPCM-modified AAC component ^1,46,48–52.

Properties	AAC	Pentadecane	PMMA
	400	768	1185
	0.1	0.15	0.2
	1000	2070	1466
	-	208	-
	-	10	-

Fundamental equations and assumptions

The accuracy of any CFD analysis strongly depends on the appropriate selection of governing equations and boundary conditions, as these define the physical processes represented in the numerical model. The chosen conservation laws, constitutive relations, and turbulence or radiation models must reflect the dominant transport mechanisms in the system; otherwise, important phenomena may be neglected or incorrectly captured. Likewise, boundary conditions specify how the computational domain exchanges mass, momentum, and energy with its surroundings, so unrealistic assumptions at inlets, outlets, or walls can significantly distort the predicted flow and thermal fields. In order to strengthen the reliability of the CFD simulations, this study introduces time-varying boundary conditions that more faithfully reproduce the dynamic heat exchange between the indoor and outdoor environments, an aspect that has frequently been simplified or omitted in earlier works. In the adopted model, the inner surface of the MPCM-enhanced AAC brick, coupled with a stacked heater plate operating at different imposed heat fluxes (), is assumed to transfer energy to the indoor air purely by convection, as expressed in Equation (1) ^46,48–54. As shown in Eq.1, the heater plate is modeled as a constant heat-flux boundary condition applied continuously over the 24-hour simulation period. By contrast, the outer surface of the MPCM-enhanced AAC is subjected to a combined thermal loading that encompasses absorbed solar radiation, convective interaction with the ambient air at prescribed temperatures (−15 and 15 °C), and long-wave radiative emission. Together, these contributions define the external thermal boundary condition and are formulated in Equation (2) ^46,48–54. The individual terms entering this boundary description, including the maximum solar irradiance and the outdoor temperature profile, are specified in Equations (3–5), while all relevant parameters and thermophysical properties are compiled in Table 3^46,48–54.

1

2

3

4

5

Table 3.

The value of required parameters for Techno-economic analysis^56–59.

Parameter	Value	Parameter	Value
House width	15 m	Discount rate	1.2%
House height	3 m	Number of windows	2
House length	15 m	Number of doors	1
Window area	4 m2	Lifespan	40 years
Door area	4 m2	MCPCM price (PMCPCM)	3500 $/m3
Electricity price (Pele)	0.12 $/kWh

To construct a numerically efficient model while retaining the key thermal response of MPCM-improved AAC bricks, a number of simplifying but physically reasonable assumptions are adopted. The bulk thermophysical properties of the AAC and cementitious matrix, including density (ρ), thermal conductivity (k), and specific heat capacity (C_p), are taken as temperature-independent over the simulated range. This widely used approximation reduces computational effort and has been shown to introduce only minor errors in similar building-energy applications. The MPCM component is assumed to be homogeneously distributed within the AAC, so the composite is treated as an effective continuum rather than resolving its detailed microstructure. Volume changes associated with PCM melting and solidification are neglected because they are small and constrained by the capsule shell, and thermally induced deformation of the AAC is not considered, as mechanical effects are beyond the scope of this work. These assumptions are consistent with common practice in thermal energy-storage modeling and allow the transient heat-transfer problem to be written in terms of effective thermophysical properties for the MPCM-improved AAC. The resulting energy equation (Equation 6) describes the temporal variation of stored thermal energy on the left-hand side and the diffusive heat flux through the composite, expressed via its effective thermal conductivity, on the right-hand side^46,48–54.

6

7

8

9

ρ_eff and C_p,eff were determined using a volume-fraction–based averaging approach that incorporates the MPCM content (ϕ). In contrast, evaluating k_eff requires a more rigorous formulation, as this property is highly sensitive to the geometry and spatial distribution of the PCM cores encapsulated within the PMMA shell. The subscript “eff” represents the homogenized value of each thermophysical parameter. To account for these microstructural influences, the Hamilton–Crosser model was employed, which incorporates particle morphology along with the conductivity contrast between the MPCM inclusions and the surrounding AAC matrix. The corresponding expressions for calculating these effective properties are presented below, based on the thermal characteristics of both the MPCM composite and the matrix phase (m)^46,48–54. Because each MPCM particle contains both a Heptadecane core and a surrounding PMMA shell, evaluation of its thermophysical characteristics requires a composite-based formulation rather than a single-material assumption. The , , and of the microcapsule must reflect the combined influence of these two constituents. To accomplish this, the mass ratio between the PCM and the PMMA shell (w = 0.45) is adopted as the governing parameter for assembling the bulk properties of the encapsulated particle. This ratio enables the thermal contributions of the core and shell to be proportionally integrated, producing representative effective values for , , and . The governing relations used to compute these properties are presented in the subsequent equations^46,48–54, where the subscripts “c” and “shell” distinguish the PCM core from the PMMA shell within the MPCM structure.

The effective density (ρ_eff) and specific heat capacity (C_p,eff) of the MPCM-enhanced AAC are evaluated by a volume-fraction–based mixing rule that explicitly accounts for the MPCM volume fraction (ϕ). In contrast, the effective thermal conductivity (k_eff) requires a more refined treatment, since it is strongly influenced by the geometry and spatial arrangement of the encapsulated PCM particles. Throughout this work, the subscript “eff” denotes the homogenized value of each thermophysical property. To incorporate microstructural effects on k_eff, the Hamilton–Crosser effective-medium model is adopted, which includes both particle morphology and the conductivity contrast between the MPCM inclusions and the surrounding AAC matrix. The corresponding expressions for ρ_eff, C_p,eff, and k_eff are given in the following equations and are formulated using the thermal properties of the matrix phase (m) and the MPCM additive^46,48–54. Each microcapsule consists of a Heptadecane core surrounded by a PMMA shell, so the properties of the MPCM phase (ρ_MPCM, C_p,MPCM, k_MPCM) must be obtained from a composite relation rather than assumed as a single-material value. This is achieved by using the mass ratio between the PCM and the shell (w = 0.45) as the weighting parameter when assembling the bulk capsule properties. The thermal contributions of the core (“c”) and shell (“shell”) are therefore combined in proportion to this ratio, yielding representative effective values for ρ_MPCM, C_p,MPCM, and k_MPCM. These effective capsule properties are then introduced into the Hamilton–Crosser framework to determine the overall thermophysical behavior of the MPCM-improved AAC, as summarized in the governing equations^46,48–54.

10

11

12

13

During the phase-change interval, the specific heat of the PCM core, C_p,c, no longer represents purely sensible heat storage; it also embeds the latent heat absorbed or released as the material melts or solidifies. This temperature-dependent behavior is essential for accurately capturing the thermal response of the MPCM, because the effective heat-storage capacity rises sharply near the melting temperature. In this study, C_p,c​ is therefore modeled as a temperature-dependent, or “apparent,” specific heat that combines the baseline sensible heat capacity with a distributed latent-heat term spread over the phase-change temperature range. This approach reproduces the progressive absorption and release of energy as the PCM transitions between solid and liquid states, rather than treating the transformation as an instantaneous event. The mathematical expression used to calculate C_p,c​ follows the formulation reported Table 2 in Refs.^46,48–54.

14

Table 2.

Specification of heat-transfer constraints and surface characteristics applied in the computational framework^1,46,48–52.

Parameter	Amount and unit
Indoor convective heat transfer coefficient ()
Indoor temperature ()
The absorptivity of the block’s surface ()	0.4
Outdoor convective heat transfer coefficient ()
The emissivity of the block’s surface ()	0.9
Stefan-Boltzmann constant ()
Maximum solar irradiance ()

Simulation approach, mesh study, and validation process

CFD offers a powerful and cost-effective approach for examining heat transfer in advanced building materials when experimental studies are constrained by cost, duration, or uncontrolled conditions. In this work, the thermal response of MPCM-enhanced AAC is analyzed using the conjugate heat transfer solver chtMultiRegion from foam-extend 4.1, a C++ finite-volume solver that enforces energy conservation across the heterogeneous solid domain and explicitly models PCM phase change. The transient temperature field is obtained by discretizing the energy equation over a control-volume mesh of the brick–heater assembly. Time integration uses a first-order explicit Euler scheme with a sufficiently small time step for stability, while the diffusive term is spatially discretized via a second-order central-difference scheme, balancing accuracy and computational cost. These numerical choices provide an efficient, robust framework for capturing time-dependent thermal storage and release in MPCM-based building components under realistic, time-varying conditions.

Mesh-independence verification is a basic quality check in CFD because the spatial discretization of the domain can strongly affect the predicted fields if the grid is too coarse. A properly designed grid study demonstrates that the main output quantities are governed by the underlying physics rather than by numerical artifacts associated with the cell size. This is typically done by refining the mesh in several steps and monitoring the evolution of target variables until further refinement produces only marginal changes, indicating that discretization errors have been reduced to an acceptable level. In the present work, mesh sensitivity was assessed by tracking the maximum indoor surface temperature (Max T_is) for the MPCM-improved AAC brick at ϕ = 12% and heater plate with heat flux of 150 W/m² ( W/m²). As shown in Fig. 2, five meshes containing approximately 60,000, 80,000, 100,000, 120,000, and 140,000 elements were analyzed. The results indicate that Max T_is becomes practically unchanged once the mesh size reaches about 120,000 elements, and any differences beyond this resolution are negligible. This grid level was therefore adopted for all subsequent simulations as a compromise between computational efficiency and numerical accuracy.

Fig. 2.

Mesh convergence analysis based on the maximum T_is results.

Validation process is a critical step in CFD because it tests whether the numerical model can reproduce measured thermal behavior under comparable conditions, rather than merely solving the equations in a mathematically consistent way. By comparing simulation outputs with independent reference data, one can assess the suitability of the governing equations, thermophysical properties, and boundary conditions used in the analysis, and thus determine whether the predicted fields are physically credible. In this work, the validity of the numerical framework is examined by comparing the computed indoor heat flux (q_is)​ at ϕ=10% and t=8h with the benchmark results reported by Hassan et al.⁴⁶. The present configuration and the reference case share similar geometrical features and identical external thermal loads, providing a consistent basis for comparison. Although Hassan et al. employed a slightly different PCM-embedding strategy and considered somewhat higher ambient temperatures, the overall heat-transfer mechanisms and boundary interactions remain closely aligned, allowing the dataset to serve as a meaningful validation target. The comparison, performed for outdoor temperatures of 5, 10, 15, 20, and 25 °C, shows good agreement between the predicted and reference heat-flux trends (Fig. 3-a), thereby supporting the robustness and physical reliability of the proposed CFD model. In addition, to strengthen the credibility of our manuscript, we compared the indoor surface temperature predicted by our model with the experimental measurements reported by Thongtha et al.⁵⁵, who investigated AAC bricks with PCM-contained conical holes. Based on Fig. 3-b, an acceptable agreement is observed.

Fig. 3.

Model validation through comparison of the predicted (a) q_is with Hassan et al.'s data as a function of ambient temperature and (b) inside temperature with Thongtha et al.'s work.

Results and Discussions

As previously mentioned, this study uses MPCM-enhanced AAC bricks with different MPCM volume fractions (φ = 0, 4, 8, and 12%) together with a heater plate operating at various heat fluxes (= 0, 50, 100, and 150 W/m²) to control indoor temperature in cold and freezing climates. The heater plate helps to reduce energy consumption during peak load periods. To evaluate the thermal performance of this structure, the results of T_is, q_is, melting fraction of MPCM (MF%), and DPC are presented.

According to Fig. 4, for all four cases, the indoor surface temperature (T_is)​ of the MPCM-enhanced AAC follows a sinusoidal-type variation, but the amplitude and phase of the response depend strongly on both the heater power () and the PCM volume fraction φ. When the heater plate is not used (=0 W/m²), T_is​ is mainly driven by the outdoor boundary, and increasing φ progressively damps the temperature fluctuation around the daily minimum and maximum of T_is. The MPCM-improved AAC (φ = 4, 8, and 12%) curves also show a slight delay in the time at which the peak T_is​ occurs, reflecting the additional thermal inertia provided by latent heat storage in the microcapsules. For example, for cases with =150 W/m², the minimum values of T_is happen at t= 6h, t=8.5h, and t=10h for φ = 4, 8, and 12%, respectively. On the other hand, using moderate internal heating (=50 and 100 W/m²) shifts the entire T_is​ profile upward and highlights the role of the PCM. For both heat-flux levels, the cases with φ = 4%, 8%, and 12% reach lower maximum indoor surface temperatures than the plain AAC brick, yet stay warmer at the minimum. In other words, the MPCM bricks simultaneously cut the peaks and lift the valleys of the temperature profile. As the heater power rises from 50 to 150 W/m², the curves for higher PCM contents become smoother and less steep around the maximum, showing that a larger fraction of the input energy is temporarily absorbed in the phase-change interval rather than immediately transmitted to the indoor side. At the highest heater power (=150 W/m²), the system approaches a strongly heated regime in which the differences between PCM loadings become most pronounced. The reference wall (φ=0%) and the low-PCM case (φ=4%) show the largest peaks in T_is​, while the φ=8% and 12% configurations limit the maximum indoor surface temperature and yield a more gradual rise and fall over the day. This indicates that, under high internal , higher MPCM fractions are more effective at moderating temperature extremes, although the curves converge once the PCM approaches full melting and its additional storage capacity is temporarily exhausted. Overall, the figure demonstrates that combining MPCM with internal heating can substantially change the indoor thermal response, with optimal benefits obtained at intermediate–high PCM volume fractions.

Fig. 4.

Results of the Tᵢₛ for plain and MPCM-modified AAC at different MPCM volume fractions under various heater-plate : a)0 W/m², b) 50 W/m², c)W/m², and =W/m².

As shown in Fig. 5, for all four heater powers, the indoor heat flux q_is​ through the MPCM-enhanced AAC brick follows a clear sinusoidal pattern like T_is curves, but the variation and phase of the curves depend on both the imposed and φ. At =0 W/m², the indoor heat flux q_is​ remains relatively modest and is driven mainly by the outdoor temperature fluctuations. The curves rise to a single maximum value of roughly 15−18 W/m² and then fall back toward zero, with only a short period where the flux becomes slightly negative as the wall releases stored heat to the room. Increasing the MPCM fraction from 0 to 12% does not dramatically change the magnitude of the peak, but it stretches the response over time and shifts the maximum, showing that part of the incoming energy is being temporarily stored in the PCM rather than transmitted immediately indoors similar to T_is curves. By increasing the power of the heater plate up to 50 and 100 W/m², the whole q_is​ profile is lifted and the effect of PCM becomes much clearer. At =50 W/m², the walls with φ=8% and 12% attain lower peak indoor heat fluxes than both the plain AAC and φ=4% configurations, and their flux histories do not exhibit the pronounced low-flux troughs observed in the other cases.

Fig. 5.

Results of the qᵢₛ for plain and MPCM-modified AAC at different MPCM volume fractions under various heater-plate : a)0 W/m², b) 50 W/m², c)100 W/m², and d) 150 W/m².

At 100 W/m², the φ=4% configuration actually produces the largest fluctuation. It reaches the highest peak (around 18−20 W/m2) and then drops close to zero, which means the small amount of PCM saturates quickly. By contrast, φ=8% and 12% achieve the maximum a few watts lower and keep a moderate flux going for longer, which is a much more useful behavior for comfort and load management. The high-power case (=150 W/m²) really exposes the difference between the designs. The plain AAC brick pushes q_is​ into the high-teens to 20 W/m² and keeps it elevated for a large part of the day, effectively dumping heat into the room in a concentrated burst. The φ=4% brick is even more unbalanced. It generates a pronounced early peak followed by a rapid decline, which is precisely the behavior that is undesirable when the objective is to smooth the thermal demand. Only the higher MPCM contents (φ = 8% and 12%) exhibit a favorable response under strong heating, reducing the peak indoor heat flux by several watts per square meter and extending the duration of heat release, thereby converting a brief, intense pulse into a more controlled and manageable flux profile.

In Fig. 6-a, corresponding to the case without auxiliary heating (=0 W/m²), the melting fraction of the MPCM remains zero for most of the day and rises only during a relatively short period around midday. For φ=4%, the MF increases rapidly after about 12 h and reaches a maximum of approximately 21% near t=16 h before returning to zero. Higher MPCM volume exhibits lower peak values under the same boundary conditions. The φ=8% and 12% bricks attain maxima of roughly 15% and 11%, respectively. As expected, the PCM-free brick (φ=0%) shows no phase change (MF = 0%) at all times.

Fig. 6.

Results of the melting fraction (MF) for plain and MPCM-modified AAC at different MPCM volume fractions under various heater-plate : a)0 W/m², b) 50 W/m², c)100 W/m², and d) 150 W/m².

When a heater plate is introduced at =50 W/m² (Fig. 6-b), the additional internal heat input significantly enhances the extent of melting. The φ=4% and 8% configurations now reach peak melting fractions close to 50% between 14 and 17 h, indicating that roughly half of the encapsulated PCM volume participates in the phase transition during the warmest part of the cycle. In contrast, the φ=12% wall still exhibits a substantially lower maximum MF of only about 25%, reflecting the fact that a larger PCM inventory requires more energy to reach comparable melt levels. For =100 W/m² (Fig. 6-c), melting begins much earlier in the day. MF remains at a non-zero value (about 3–8%) even during the morning hours and then sharply increases to a plateau of approximately 50% for all MPCM contents between roughly 13 and 16–17 h. In this area, the main difference among φ= 4%, 8%, and 12% is the timing of the rise and decay, with higher PCM contents exhibiting a slightly delayed but more sustained melting–solidification process. At the highest heater power, =150 W/m² (Fig. 6-d), the MPCM phase is strongly activated throughout the 24-h cycle. All three MPCM-enhanced AAC brick (φ=4%, 8%, and 12%) show appreciable melting fractions (around 8–15%) even at the beginning of the day, followed by a steep increase to nearly complete melting. MF reaches about 50–52% and remains close to this level for several hours between approximately 13 and 17 h. After this plateau, the MF gradually declines but does not immediately return to zero, indicating a prolonged solidification period and thus extended release of stored heat. Taken together, these four subfigures demonstrate that increasing heater power shifts the system from partial, short-duration melting to extensive, long-duration melting, while higher PCM volume fractions primarily influence how early melting starts and how long the material remains within the phase-change interval.

DPC is a critical indicator of both energy demand patterns and the overall efficiency of a building or system. Evaluating power use on a 24-hour basis reveals peak-load periods, off-peak intervals, and load-shifting opportunities, which are essential for designing heating, cooling, and storage strategies that reduce operating costs and prevent overloading of supply infrastructure. Figure 7 summarizes DPC values of the different brick configurations as a function of heater-plate heat flux q’'_hp​. For the plain AAC brick (φ=0%), DPC increases monotonically from about 0.26 kWh/m² at q’'_hp=0 W/m² to roughly 0.29 kWh/m² at 50 W/m², reflecting the direct impact of stronger internal heating on energy demand. Introducing MPCM substantially lowers DPC in almost all cases. At zero heater power, the MPCM-enhanced specimens (φ=4%, 8%, and 12%) cluster around 0.19−0.20 kWh/m², corresponding to a reduction of about 25–30% relative to the plain AAC brick. At q’'_hp=50 W/m², all configurations show similar DPC values (≈0.21 kWh/m2), indicating that the modest auxiliary heating largely offsets the storage advantage of the PCM at this operating point. As heater power increases further, the benefit of MPCM becomes more pronounced again. At q’'_hp=100 W/m², the plain AAC brick consumes approximately 0.32 kWh/m², whereas the MPCM-enhanced bricks lie near 0.24 kWh/m², giving an energy saving on the order of 20–25%. A similar trend appears at q’'_hp=150 W/m², where DPC for the reference brick rises to about 0.34−0.35 kWh/m², while the φ= 4%, 8%, and 12% bricks remain in the 0.26−0.28 kWh/m² range. Among the MPCM-enhanced AAC cases, higher PCM volume fractions provide a slight additional reduction at the highest heater setting, with φ=4 and 8% yielding the lowest DPC. Overall, the results indicate that MPCM integration is particularly effective at cutting daily power consumption under either no-heating or high-heating conditions, whereas its advantage is less pronounced at intermediate heater loads.

Fig. 7.

Results of the DPC for plain and MPCM-modified AAC at different MPCM volume fractions under various heater-plate : a)0 W/m², b) 50 W/m², c)100 W/m², and d) 150 W/m².

Economic assessment of using MPCM-enhanced AAC bricks combined with an auxiliary heater plate

A combined thermal, technical, and economic assessment of MCPCM-integrated thermally smart bricks with an auxiliary heater plate is necessary to evaluate not only how effectively they improve heat regulation, but also whether they are financially viable over the building’s service life. While these bricks can reduce energy consumption by stabilizing indoor temperatures and lowering heating and cooling demands, they typically require higher initial costs for fabrication and installation compared with conventional masonry. Incorporating time-value-of-money metrics, such as net present value (NPV) and internal rate of return (IRR), enables a transparent evaluation of whether the additional upfront investment is justified. This approach supports informed decision-making by balancing sustainability benefits against costs and by identifying the operating and design conditions under which these bricks deliver the strongest economic return. Accordingly, NPV and IRR are calculated as follows^56–59:

15

16

17

18

19

In Eqs. (16–19), TCC represents the overall cost of MCPCM incorporated into the thermally smart brick (TSB). It is determined using the MCPCM unit price (P_MCPCM), the MCPCM volume fraction (φ), and the brick volume (V_con). The symbols A_wall, h_H, W_H, and L_H correspond to the total exterior wall area of the house and the house height, width, and length, respectively. The terms N_win and A_win refer to the number of windows and the window area (or the total window area, depending on how it is defined in the equations), while N_door and A_door similarly denote the number of doors and the door area (or total door area). Lastly, CF indicates the yearly monetary savings, calculated from the reduction in daily electricity consumption and the unit electricity price (P_ele). The input parameters and constant values used in these calculations are summarized in Table 3.

The techno-economic results show a clear dependence of profitability on both the heater-plate heat flux q’' and the MCPCM volume fraction (ϕ). For ϕ=4%, the system consistently delivers the strongest economic performance: NPV increases from $11,689 (q''=0) to $15,970 (q''=150 W/m²), and IRR rises from 13.55% to 17.45%, indicating that higher heater flux improves the lifetime savings enough to outweigh the associated costs. For ϕ=8%, the economics remain positive but weaker; NPV improves relative to q’'=0 (from $9,068 to $11,488 at q’'=100 W/m²) and then slightly drops at q’'=150 W/m² ($11,046), while IRR stays in a narrow band (6.68–7.92%), suggesting diminishing returns at higher flux for this PCM loading.

In contrast, ϕ=12% exhibits the lowest NPV values overall ($5,610–$7,029 across the cases), implying that the higher MCPCM content increases cost faster than it increases the monetized energy benefit under most conditions. The IRR for ϕ=12% is also low and relatively flat (3.97–4.27%) for q’'=0–100 W/m², consistent with the NPV trend. However, the reported IRR of 37.13% at q’'=150 W/m² is not consistent with the surrounding pattern and the corresponding NPV (which is actually the lowest at this ϕ), so it likely reflects either a calculation/typing issue or a special cash-flow assumption for that case; it would be worth re-checking that single value before finalizing conclusions. Overall, based on the combined NPV and IRR trends, ϕ=4% provides the most attractive and robust economic outlook across the tested heat-flux conditions for the long-term horizon Table 4 Table 5.

Table 4.

The results of NPV (in $) as a function of φ and q".

q" (W/m2)	φ = 4%	φ = 8%	φ = 12%
0	11689	9068	6261
50	14993	10976	6866
100	15481	11488	7029
150	15970	11046	5610

Table 5.

The results of IRR (in %) as a function of φ and q".

q" (W/m2)	φ = 4%	φ = 8%	φ = 12%
0	13.55	6.68	3.97
50	16.56	7.66	4.21
100	17.0	7.92	4.27
150	17.45	7.69	37.13

Conclusion

This study examined the thermal and energy behavior of a building envelope that combines MPCM-enhanced AAC with an auxiliary heater plate, a configuration that has not previously been evaluated for cold and freezing climates. The results clearly indicate that the inclusion of MPCM fundamentally alters the thermal response of AAC bricks, particularly under moderate to high heating loads. For heater powers of 100–150 W/m², MPCM volume fractions of 8–12% consistently moderated the indoor response by reducing peak T_is by approximately 1–2 °C and lowering peak q_is by about 15–25% relative to the plain AAC brick. At the same time, minimum temperature and heat-flux levels were elevated and peak occurrence was delayed by roughly one hour, reflecting enhanced thermal inertia and more effective redistribution of heat over time. Lower MPCM content (φ = 4%) was found to be less effective under strong heating, as rapid PCM saturation led to sharper thermal fluctuations rather than smoothing. Analysis of the MF% further clarified these trends. As heater power increased, the system transitioned from short-duration, partial melting to extended phase-change plateaus, with melting fractions approaching 50–52% for several hours at the highest heater setting. This extended melting–solidification cycle explains the observed peak shaving and prolonged heat release at higher MPCM contents. From an energy perspective, MPCM integration yielded substantial reductions in DPC. At zero heater power, DPC decreased from approximately 0.26 kWh/m² for plain AAC to about 0.19–0.20 kWh/m², corresponding to savings of 25–30%. Under active heating at 100–150 W/m², DPC was reduced from roughly 0.32–0.35 kWh/m² to 0.24–0.28 kWh/m², representing a 20–25% reduction. These findings demonstrate that the proposed AAC–MPCM–heater system offers a viable strategy for reducing peak loads and improving energy efficiency in cold-region buildings, with optimal performance achieved at MPCM volume fractions in the range of 8–12%. Additionally, the techno-economic analysis over 40 years shows that ϕ=4% provides the most favorable economics, achieving the highest NPV (up to $15,970) and IRR (up to 17.45%), with performance generally improving as the auxiliary heater flux increases. In contrast, higher MCPCM loadings (ϕ=8% and especially ϕ=12%) yield lower NPVs and IRRs, indicating diminishing economic returns compared with the 4% formulation under the investigated operating conditions.

Abbreviations

TSB

Thermally smart brick

PCM

Phase change material

AAC

Autoclaved aerated concrete

PMMA

Polymethyl methacrylate

TMSB

thermal management smart bricks

MPCM

Microencapsulated PCM

PISO

Pressure-implicit with splitting of operators

CFD

Computational fluid dynamics

FVM

Finite volume method

PDE

Partial differential equation

DPC

Daily power consumption

NPV

Net present value

IRR

Internal rate of return

Nomenclature

Specific heat capacity (J/kg.K)

g

Gravitational acceleration (m/)

k

Thermal conductivity (W/m.K)

W

Brick width (cm)

w

Composite rectangular cubic width (cm)

sh

shell

c

core

V

Velocity (m/s)

K

Permeability ()

p

Pressure (Pa)

h

Convective heat transfer coefficient (W/.K)

T

Temperature (℃)

u, v, w

Velocity vector (m/s)

x, y, z

Cartesian coordinates (m)

t

Time (s)

hp

Heater plate

 

solar irradiance

Greek symbols

ρ

Density (kg/)

μ

Dynamic viscosity (Pa.s)

β

Thermal expansion coefficient (1/K)

λ

Error function

Volume fraction (-)

α

Absorptivity (-)

ϵ

Emissivity (-)

σ

Stefan-Boltzmann constant (W/.)

ε

porosity (-)

Subscript

max

Maximum

min

Minimum

eff

Effective

I

indoor

o

outdoor

env

environment

is

Indoor surface of the TSB

Author contributions

Naif Albelwi: Conceptualization, Formal Analysis, Investigation, Methodology, Software, Validation, Visualization, Resources, Data Curation, Supervision, Project Administration, Writing – Original Draft, Writing – Review & Editing

Funding

This scientific research paper was derived from a research grant funded by Taibah University, Madinah, Kingdom of Saudi Arabia - with the grant number (1160-15-447).

Data availability

The computational framework used in this study is based on the conjugate heat transfer solver chtMultiRegion4PCMFoam from foam-extend 4.1, an open-source CFD platform. The complete simulation case setup, including mesh generation files, boundary condition dictionaries, material property files, and execution scripts, is deposited in Zenodo under the https://doi.org/10.5281/zenodo.19499920. Python scripts for generating time-varying boundary conditions (outdoor temperature, sky temperature, and solar heat flux) and for performing the techno-economic analysis (NPV and IRR calculations) are included in the same deposit, accompanied by detailed README files. The raw numerical output data—including hourly values of indoor surface temperature (Tis), indoor heat flux (qis), MPCM melting fraction (MF), and daily power consumption (DPC) for all simulated cases (φ/alpha = 0, 4, 8, 12% and q″/q = 0, 50, 100, 150 W/m²)—are available from the corresponding author upon reasonable request. All other data supporting the findings of this study are presented in the manuscript and its supplementary materials.

Declarations

Competing interests

The authors declare no competing interests.