## 1 Introduction
(2016) [7] showed an increase of 5.23% in thermal conductivity of graphene-water nanocomposite, prepared using surfactant, when the volume concentration of nanoparticles is changed from 0.05% to 0.1%, and a 14.56% enhancement was observed when the volume concentration increased by three times. [PERSON] et al. (2014) [8] inferred that the latent heat of composite PCMs is lower than that of base material for both melting and freezing and the maximum changes are 3.56% and 3.82%, respectively. The thermal conductivity of graphene-water nanocomposite is found to be higher when compared with that of the metal oxide nanoparticles and is lower when compared with that of pure metallic nanoparticles. However, the use of pure metallic nanoparticles in fluids causes stability problems. Hence, [PERSON] et al. (2016) [9] suggested that instead of using a high-volume concentration of metal oxide and pure metal nanoparticles, a low-volume concentration of graphene can be used as the heat transfer fluid to enhance thermal conductivity. [PERSON] et al. (2015) [10] treated graphene nanoparticles with concentrated nitric acid to avoid the use of surfactants. A maximum thermal conductivity enhancement of \(\sim\)230% was measured in lauric acid treated with the acid graphene nanoinclusions for 1 vol %. As a result of the ever-growing demand for energy, there is a need for energy storage in PCMs. The PCMs are usually encapsulated in containers/capsules. Different researches have used different geometrical shapes for the capsules such as cylinders, spheres, pyramids, cones, rectangles, and cuboids with different materials like stainless steel, aluminum, copper, polypropylene, and polyolefin for numerical and experimental studies. The material selection was based on the property of the PCM used and the potential applications [11; 12; 13; 14; 15; 16]. [PERSON] et al. (2001) [17] studied the freezing properties of water in a circular cylinder kept horizontally. During the initial phase of freezing, an annular ice layer started growing on the surface of the cylinder at a higher rate. This was followed by the asymmetric ice layer at a medium cooling rate and finally an instantaneous ice layer growing over the whole region at a low cooling rate. [PERSON] et al. (2008) [PERSON] et al. (2008) performed an analytical analysis in the freezing and melting process of different PCMs encapsulated in a cylindrical capsule. The presence of heat generation enhanced the freezing time whilst also hastening the melting time. Total freezing time was subject to Stefan's Number and heat generation parameters, whereas complete melting time depended on equivalent thermal conductivity. Nanotechnology is being used in many applications to provide more efficient energy transfer. The application of nanocomposites in heat exchanging devices appears promising with these characteristics. In this context, the use of nanoparticles in water provides a scope for performance improvement in thermal storage for an ice bank tank. The main objective of this work is to study the freezing and melting characteristics of graphene-water nanocomposite in a vertical cylindrical capsule and compare it with base fluid. Graphene has been widely used in many applications since its discovery by [PERSON] et al. [PERSON] et al. (2008) because of its structure i.e., a single-atom-thick sheet of hexagonally arrayed sp\({}^{2}\)-bonded carbon atoms. Graphene possesses remarkable thermophysical properties due to its large specific surface area (50-750 m\({}^{2}\)/g) and extremely high thermal conductivity (3000-5000 W/m K) [PERSON] et al. (2008); [PERSON] et al. (2009); [PERSON] et al. (2010); [PERSON] et al. (2011); [PERSON] et al. (2012); [PERSON] et al. (2013); [PERSON] et al. (2014); [PERSON] et al. (2015); [PERSON] et al. (2016); [PERSON] et al. (2017); [PERSON] et al. (2018).