temperature distribution to determine the total energy stored in the system. This temperature distribution and therefore the total energy in the TES is influenced by particle size and relative dimensions of the TES. Depending on design constraints the designer will then choose the optimal design variables to maximize the energy density in the TES. The designer may also consider using different PCMs in the same TES to increase the energy density. Nomenclature a Interphase surface area per unit volume A U/\t/2/\x Bf Biot number c Fluid specific heat Effective liquid specific heat cs Effective solid specific heat C D/(l+M0 D ha/St/PCs Do Diameter of vessel containing PCM-laden spheres Ds Diameter of spheres containing PCM E D/3/S-4t/(l+/3/St) f0 Fluid temperature at inlet fi Initial fluid temperature /2 Initial PCM temperature h Heat transfer coefficient Effective heat transfer coefficient hl{ Latent heat of fusion Effective thermal conductivity of quiescent bed K* Axial effective thermal conductivity Kt Fluid thermal conductivity Km Average PCM thermal conductivity L Length of the bed Nu Nusselt number hD/Kt Pr Prandtl number Ap Pressure drop Re Reynolds number t Time △ t Time step T Fluid temperature Tt Inlet fluid temperature T" Fluid temperature of node i and time step n V Fluid velocity △ x Spatial increment Greek Symbols a Quality P K^/^Pc^x2^ E Void fraction p Fluid density Pi Density of liquid PCM T \ + 2A + B+2N~E 0 Temperature of the PCM 0* Melting temperature of PCM
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