Latent heat capsulesconsist of a thin-walled

Chapter 7, Problem 7.110

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Latent heat capsulesconsist of a thin-walled sphericalshell within which a solid-liquid, phase-change mate-rial (PCM) of melting point Tmpand latent heat offusion hsfis enclosed. As shown schematically, thecapsules may be packed in a cylindrical vessel throughwhich there is fluid flow. If the PCM is in its solidstate and Tmp?Ti, heat is transferred from the fluid tothe capsules and latent energy is stored in the PCM as itmelts. Conversely, if the PCM is a liquid and Tmp?Ti,energy is released from the PCM as it freezes and heatis transferred to the fluid. In either situation, all of thecapsules within the packed bed would remain at Tmpthrough much of the phase change process, in whichcase the fluid outlet temperature would remain at afixed value To.Phase-changematerial , Tmp, hsfCapsuleShell, DcLvV, Ti Consider an application for which air at atmosphericpressure is chilled by passing it through a packed bed(??0.5) of capsules (Dc?50 mm) containing anorganic compound with a melting point of Tmp?4?C.The air enters a cylindrical vessel (Lv?Dv?0.40 m)at Ti?25?C and V?1.0 m/s.(a) If the PCM in each capsule is in the solid state atTmpas melting occurs within the capsule, what isthe outlet temperature of the air? If the density andlatent heat of fusion of the PCM are ??1200 kg/m3and hsf?165 kJ/kg, what is the massrate (kg/s) at which the PCM is converted fromsolid to liquid in the vessel? (b) Explore the effect of the inlet air velocity and cap-sule diameter on the outlet temperature.(c) At what location in the vessel will complete melt-ing of the PCM in a capsule first occur? Oncecomplete melting begins to occur, how will theoutlet temperature vary with time and what is itsasymptotic value?