Study of Nusselt Number Evolution in PCM Shell-and-Tube Configuration Mohammed Bechiri and Kacem Mansouri 1 Introduction To study the fluid flow through tubes constructed with phase change materials, researchers usually use experimental cor- relations to represent the Nusselt number evolution along the tube. Rieger et al. (1982) presented a numerical study of melting around a horizontal cylinder embedded in phase change material. Lacroix (1993) developed a theoretical model to predict the transient behavior of a storage unit made up of cylindrical tubes of phase change material (PCM), with a heat transfer fluid (HTF) circulating inside the tubes in laminar and turbulent regimes. Zhang and Faghri (1996) presented a semi-analytical solution of latent heat energy storage system consisting of a hollow cylinder of phase change material (PCM). The PCM melting was studied using the Approximate Integral Method. The local Nusselt number correlation used in laminar and turbulent regimes was given by Kays and Crawford (1993). Ismail and Abugderah (2000) studied numerically the transient phase change phenomena in a thermal energy storage system consisting of vertical tube. Trp (2005) treated a latent ther- mal energy storage system consisting of tubes enveloped by a phase change material. El-Qarnia (2009) developed a theoretical model based on energy equations to predict the thermal behavior and performance of a solar latent heat storage unit (LHSU) consisting of a series of identical tubes embedded in the phase change material PCM. Tao and He (2011) established a model of two physical and mathemat- ical dimensions for a tube bundle storage unit enveloped by a phase change material. Through the literature we find that the correlations used are mostly valid for the cases of temperature or heat flux imposed at the wall. Then, our study came to elaborate a valid correlation for the cylindrical tube with PCM wall. 2 Problem Description The thermal storage unit consists of cylindrical tubes of phase change material, traversed by heat transfer fluid cir- culating in one direction. Figure 1 shows the studied storage module. The heat transfer fluid (HTF) circulating inside the tube by laminar forced convection is subjected to a constant inlet temperature. With the enthalpy method, the governing energy equation is written for the entire PCM region, including solid and liquid phases and interface, assuming that the density in the liquid and solid phases is the same. In this case, the math- ematical model is formulated in cylindrical and resolved using the finite element method. 3 Results and Discussion Paraf fin was used as a latent heat storage material and water as heat transfer fluid. Paraf fin is a chemically stable and non-toxic material; it has a high latent heat storage capacity at low melting/solidification temperatures. In Fig. 2, the transient variation of the Nusselt number along the tube is presented for different axial positions. We can see that the Nusselt number keeps the same evolution whatever the tube thickness R 2 , except that there is a time lag. This lag is related to the PCM melting and saturation times, since the increase in R 2 increases the melting time. The transient evolution of Nusselt number passes through three distinct phases, at the flow beginning the Nusselt number increases quickly with time until the PCM begins its Melting. At this point, the Nusselt number takes a constant M. Bechiri (&) Department of Mechanical Engineering, Faculty of Science and Applied Sciences, University of Oum-El-Bouaghi, Oum El Bouaghi, Algeria e-mail: bechiri_med@yahoo.fr M. Bechiri Á K. Mansouri Energy and Mechanical Engineering Laboratory, University M. Bougara, 35000 Boumerdès, Algeria e-mail: manskac@yahoo.fr © Springer International Publishing AG 2018 A. Kallel et al. (eds.), Recent Advances in Environmental Science from the Euro-Mediterranean and Surrounding Regions, Advances in Science, Technology & Innovation, https://doi.org/10.1007/978-3-319-70548-4_311 1079