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Sustainability 2018, 10, 191 10 of 32 4. Latent-Heat or Phase-Change Storage LHS materials are known as PCMs due to their property of releasing or absorbing energy with a change in physical state. The energy storage density increases and hence the volume is reduced, in the case of LHS (Figure 2b). The heat is mainly stored in the phase-change process (at a quite constant temperature) and it is directly connected to the latent heat of the substance. The use of an LHS system using PCMs is an effective way of storing thermal energy and has the advantages of high-energy storage density and the isothermal nature of the storage process. The main advantage of using LHS over SHS is their capacity of storing heat at almost similar temperature range. Initially, these materials act like SHS materials in that the temperature rises linearly with the system enthalpy; however, later, heat is absorbed or release at almost constant temperature with a change in physical state. LHS is based on the heat absorption or release when a storage material undergoes a phase change from solid to liquid or liquid to gas or vice versa. The storage capacity Qs, in J, of the LHS system with a PCM medium [17] is given by tm mcpdt+mf∆q+ Qs = mcps(tm −ti)+ f∆q+cpl(tf −tm) (12) where tm is the melting temperature, in ◦C; m is the mass of PCM medium, in kg; cps is the average specific heat of the solid phase between ti and tm, in kJ/(kg·K); cpl is the average specific heat of the liquid phase between tm and tf, in J/(kg·K); f is the melt fraction; ∆q is the latent heat of fusion, in J/kg. For example, Glauber’s salt (Na2SO4·10H2O) has cps ≈ 1950 J/(kg·◦C), cpl ≈ 3550 J/(kg·◦C), and ∆q=2.43×105 J/kgat34◦C. The measurement techniques presently used for latent heat of fusion and melting temperature of PCMs are (1) differential thermal analysis (DTA) and (2) differential scanning calorimeter (DSC) [17]. In DSC and DTA techniques, sample and reference materials are heated at a constant rate. The temperature difference between them is proportional to the difference in heat flow between the two materials and the record is the DSC curve. The recommended reference material is alumina (Al2O3). Latent heat of fusion is calculated using the area under the peak, and the melting temperature is estimated by the tangent at the point of greatest slope on the face portion of the peak. Morrison and Abdel-Khalik [37] developed a model applicable to PCMs in small containers, where the length in the flow direction is L, the cross-sectional area of the material is A, and the wetted perimeter is P. The heat transfer fluid passes through the storage unit in the x direction at the mass flow rate m and with inlet temperature tf,i. The model is based on three assumptions: (1) during flow, axial conduction in the fluid is negligible; (2) the Biot number is low enough that temperature gradients normal to the flow can be neglected; and (3) heat losses from the bed are negligible. An energy balance on the material gives ∂u = λs ∂2ts + UP (tf − ts) (13) where u, ts, λs, and ρs are the specific internal energy, temperature, thermal conductivity, and density of the PCM; tf and U are the circulating fluid temperature and overall heat transfer coefficient between the fluid and PCM; τ is the time. An energy balance on the fluid is ∂tf+ m ∂tf= UP (ts−tf) (14) ∂τ ρfAf ∂x ρfAfcp,f Qs = ti tf tm mcpdt (11) ∂τ ρs ∂x2 ρsAPDF Image | Comprehensive Review of Thermal Energy Storage
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