## 1 Introduction  
Drug and food safety have become more important issues with a growing population and demand in recent years. In order to extend and ensure the shelf-life of pharmaceutical drugs or food, it is very important to keep their temperature at a given range through the storage and transportation processes. Such a temperature-controlled supply chain is called cold chain. Large quantities of drugs or food are normally transported by refrigerated trucks, while small quantities are delivered by containers. There are at least 1 million refrigerated road vehicles and 400,000 refrigerated containers worldwide [1]. They run on a vapor compressor that is driven by electric or fuel energy, and release amounts of greenhouse gas. It was reported that the cold chain is responsible for approximately 2.5% of global greenhouse gas emissions when considering both direct and indirect effects [2]. Thermal energy storage based on phase change materials (PCMs) is an advanced energy technology that has recently attracted increasing interest in cold-chain systems. PCMs are able to absorb or release amounts of thermal energy during the phase transition process, maintaining the internal temperature in an acceptable range. Many studies have indicated that the energy savings can be achieved by utilizing PCMs in cold-chain systems. For example, [PERSON] et al. added PCM into the insulation layer of a refrigerated truck trailer. The inclusion of the paraffin-based PCM in the standard trailer walls was studied as a heat transfer reduction technology. An average reduction of 16.3% in total heat transfer from the exterior to the refrigerated truck was achieved by adding PCM to the insulation foam of the trailer walls [3]. [PERSON] et al. developed an innovative refrigeration system incorporating PCM to maintain refrigerated trucks at the desired thermal conditions. The PCM storage tank was charged by a refrigeration unit when stationary and provides cooling when in service. An analysis showed that delivery of refrigerated products can be made with a PCM system having a weight that is comparable to that of an on board conventional refrigeration system, with less than half of the energy cost [4]. [PERSON] et al. integrated an external PCM layer with a refrigerated container envelop to reduce and displace the heat flux phase caused by the external climatic conditions. It was found that a PCM-added layer helps to store the incoming heat load at a constant temperature during the melting phase. A reduction on peak heat transfer rate of 5.55% and 8.57% during two experimental days was observed in comparison with the reference [5]. [PERSON] et al. presented the first numerical investigation of the energy behavior of a refrigerated container envelope that was fitted with PCMs. An organic PCM named RT35 HC manufactured by Rubitherm(r) Technologies GmbH in Berlin in Germany, which has a melting peak temperature of 35 \({}^{\circ}\)C, was found to perform best on a typical summer day in Milan, Ancona, and Palemo. It was observed that the heat load peak was reduced by 20% and the peak was delayed for 2-3 h [6]. The above-mentioned studies focus on the trucks or containers having a refrigeration system. However, insulated containers integrated with PCMs are also an attractive alternative for cold-chain systems. Such containers do not use any conventional refrigerators, but a thermal energy storage of PCMs to control the internal temperature. The PCMs are normally preconditioned when stationary and provide cooling or heating when in service. The temperature-controlled time is mostly within 48 h due to the limited thermal capacity of PCMs and the poor insulation of the containers. For example, the company EMBALL'ISO in Saint-Georges-de-Reneins in France provides a packaging comprising a cardboard box, six vacuum insulation panels, and six PCM briquettes [7]. This packaging is normally used for an isothermal transportation up to 48 h at extreme temperatures.