Multi-scale composite models for the effective thermal conductivity of PCM-concrete Pania Meshgin, Yunping Xi ⇑ Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, USA highlights  An analytical model was developed to predict the effective thermal conductivity of concrete with phase change materials.  Multi-phase, multi-scale internal structural models were combined with generalized self-consistent model.  The model unveiled that the configuration of the internal structure for the PCM phase is very important.  The PCM phase must be considered as a thin shell matrix in the model for predicting the effective thermal conductivity.  Physically, the PCM can effectively block the heat flow and thus reduce the thermal conductivity. article info Article history: Received 21 January 2013 Received in revised form 23 May 2013 Accepted 17 June 2013 Available online 31 July 2013 Keywords: Composite Concrete Generalized self-consistent model Phase change material Thermal conductivity abstract Encapsulated phase change materials (PCMs) were used in concrete to improve thermal properties of the concrete, called PCM-concrete. This paper presents the predictions of the effective thermal conductivity of PCM-concrete using different composite models, such as the parallel, the series models, Maxwell model and Generalized Self-Consistent (GSC) model. Multi-phase, multi-scale internal structural models were developed and combined with GSC model to predict the effective thermal conductivity of PCM-con- crete. It was found that the configuration of the internal structure for the PCM phase is very important. The PCM phase needs to be considered as a matrix (a thin shell), which can effectively block the heat flow and thus reduce the thermal conductivity of PCM-concrete. The GSC model with the suggested internal structure model can predict the effective thermal conductivity of PCM-concrete. The prediction agreed with test data quite well, and the prediction is within the upper and lower bounds. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Composite materials are engineered materials made of two or more constituent phases with significantly different physical, ther- mal, or mechanical properties, which remain distinct on a specific scale. Multi-phase composite materials exhibit a remarkably com- plex microstructure. For example, when encapsulated phase change materials (PCMs) are added in Portland cement concrete to enhance the thermal storage capacity of the concrete, called PCM-concrete, the resulting composite is a multi-phase composite material. It is composed of regular components of Portland cement concrete and the encapsulated phase change materials. Regular concrete itself is a multi-phase composite material composed of coarse aggregates, fine aggregates, and cement paste, where the ce- ment paste is also a multi-phase composite material composed of hydration products of the Portland cement (gel and crystals) and pores. The internal structure of regular concrete (the mixture of aggregates and cement paste) is in the centimeter scale, the inter- nal structure of cement paste is in the micrometer scale, and the size of encapsulated PCM is in the range of millimeters and micrometers. Therefore, PCM-concrete can be considered as a mul- ti-scale and multi-phase composite. Predicting the behavior of multi-scale and multi-phase compos- ite materials is a challenging task. Over the years, many composite models have been developed for this purpose [1–5]. In the case of two-phase composites with a perfectly aligned internal structure, exact models already exist. Among these models are the parallel model and the series model. For a two-phase composite with spherical inclusions, various methods can be used to estimate the effective behavior of the composite material, including Maxwell approximation and Self-Consistent approximation (SC), etc. For two-phase composites with random internal structure, it is not possible to obtain exact solutions; thus the bounds on the effective properties have been developed such as Wiener–Voigt bounds (the parallel and the series models mentioned above) and the 0950-0618/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2013.06.068 ⇑ Corresponding author. Address: University of Colorado at Boulder 428 UCB, Room: ECOT 547, USA. Tel.: +1 (303) 492 8991; fax: +1 (303) 492 7317. E-mail addresses: Pania.Meshgin@Colorado.edu (P. Meshgin), Yunping.Xi@ Colorado.edu (Y. Xi). Construction and Building Materials 48 (2013) 371–378 Contents lists available at SciVerse ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat