Investigation of transient heat transfer in multi-scale PCM composites using a semi-analytical model


Under certain operating conditions, the phases of phase change materials (PCM) undergo changes, which induce unique properties, making them important materials for thermal energy storage. The energy needed to bring about the phase change is always the principal factor determining the application of PCMs. Integrating PCMs into building designs has drawn significant research attention as a promising approach for reducing the energy demands for buildings. Considering the transient nature of HAVC systems and the growing need to favorably optimize the PCM size and volume fraction to meet the thermal energy storage requirements for different buildings, it is imperative to study and understand the transient thermal response of PCM.

PCM can be integrated into building materials in many ways. One way is using PCM panels for different composite types. The main drawback of this method is that PCM tends to exhibit low thermal conductivity and poor thermal response, making it impractical for energy storage applications. Notably, increasing the thermal conductivity of PCM systems using different methods requires a thorough understanding of the transient response of the composites, which remains a significant problem considering the inadequacies of the available analytical solution to the problem and the high computational demands of the numerical solution approaches. Thus, developing alternative strategies for designing effective and reliable PCM walls is highly desirable.

Recently, multi-scale analyses of the thermal properties of building materials containing microencapsulated PCM have emerged as an effective alternative for addressing the limitations of the conventional analytical methods. Motivated by the previous findings, Dr. Adam Dobri and Professor Yanwei Wang from Nazarbayev University, in collaboration with Dr. A. Tsiantis and Professor Thanasis Papathanasiou from the University of Thessaly, investigated the transient heat transfer in multi-scale PCM-based composites using a semi-analytical model. They aimed to examine and detail the transient response of composite materials consisting of microencapsulated PCM for potential applications as building materials. Their work is published in the International Journal of Heat and Mass Transfer.

In their approach, the proposed model was based on the assumption that the spherical particles were small and relative to the PCM wall thickness such that each particle was surrounded by time-dependent and spatially uniform matrix temperature at any time instant. A two-temperature model accounting for the interfacial resistance between two phases was utilized. Considering the matrix temperature as the boundary condition, the authors used a semi-analytical expression for the temperature distribution at the particle scale to determine the flow of heat into the particle, thus avoiding the cumbersome and ultimately prohibitive spatial discretization of the micro-scale. The resulting heat equations were then solved using the Method of Lines which efficiently converts the boundary problem into a set of ODEs. Lastly, the constant flux of all conditions commonly associated with PCM walls and structures were simulated using the presented model.

The researchers elucidated the impact of PCM parameters such as interfacial resistance and particle radius on the transition of the thermal management phase, thus providing more details concerning the composites. For instance, the resistances to thermal interference and particle sizes appeared to accelerate the transition. In contrast, an increase in the latent heat or volume fraction appeared to delay the transition. This suggested the importance of long thermal characterization experiments to obtain more accurate results. Cyclic environmental temperature simulations revealed that low PCM volume loadings of 5% could reduce the energy demands of the HVAC system by 15 – 20% during summer.

In summary, the authors reported a new two-temperature semi-analytical model using the analytical solution to avoid discretization at the particle scale for describing transient heating of PCM walls. Additionally, they developed an effective method for estimating the potential energy savings by different PCM-based composite walls under various transient environments. Regarding temperature evolution in hardening concrete by adding microencapsulated PCM, the findings agreed with that of Šavija and Schlangen, who conducted similar experiments using the commercial package FEMMASSE. In a statement to Advances in Engineering, Professor Yanwei Wang stated that the study contributes to the effective utilization of phase change materials for thermal energy storage in buildings.

About the author

T.D. Papathanasiou is Professor of Mechanical Engineering at the University of Thessaly in Greece. He obtained his PhD in Chemical Engineering from McGill University (1991) with specialization in polymer processing and holds MSc and BSc degrees in Chemical Engineering from the University of Calgary (1987) and the National Technical University of Athens (1984). Before joining the faculty at University of Thessaly he has worked with ALCAN Int. R&D, Los Alamos National Laboratories, Imperial College and University of South Carolina. His work and interests involve use of CAD for design of materials and processes, including the effect of complex microstructure on processing and properties.

About the author

Yanwei Wang is Associate Professor of Chemical and Materials Engineering at the School of Engineering and Digital Sciences (SEDS) of Nazarbayev University in Kazakhstan. He is also head of Laboratory of the Computational Materials Science for Energy Applications Lab, Center for Energy and Advanced Materials Science, National Laboratory Astana (NLA). He obtained his MSc (2005) and PhD (2009) from the Technical University of Denmark (2009) with specialization in polymer science and numerical modeling and holds a BEng degree (2003) in Chemical Engineering from Zhejiang University in China. His work and interests focus on macromolecular theory and simulations, composite materials, transport processes, and computational molecular & materials research.


Dobri, A., Tsiantis, A., Papathanasiou, T., & Wang, Y. (2021). Investigation of transient heat transfer in multi-scale PCM composites using a semi-analytical modelInternational Journal of Heat and Mass Transfer, 175, 121389.

Go To International Journal of Heat and Mass Transfer

Adam Dobri (2022). Transient heat transfer in PCM particle-based composites (, MATLAB Central File Exchange. Retrieved May 16, 2022.

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