Thermal and Phase-Change Wave Propagation and Velocities Subject to Shrinking Core Phenomena for Melting and Freezing Packed-Beds of Encapsulated Phase-Change Materials

Abstract

Th is research focuses on heat transfer between a fluid and a packed - bed comprised of encapsulated phase - change materials (PCMs). The objective of this work is to develop and validate models that can be used to predict the propagation of melting and freezing fronts and sensible heat fronts as a heated or cooled fluid is injected into the packed - bed . To achieve this objective, an analytical model was developed to study sensible a nd phase - change thermal wave propagation with respect to time and spatial variation along a 0.356 m axial bed length, with a 0.023 m 2 cross - sectional area, under low temperature test conditions between 15 to 50 °C, for time intervals ranging from 5 to 18 h ours. Model results exhibit classical thermal wave forms in the sensible heat transfer regime, exponential variations in temperature near the phase - change front, and lagging thermal wave velocities for partially frozen or melted conditions. Time - scales for complete melting or freezing were identified for both a range of low Biot numbers (0.001 to 1), and high Biot numbers (1 to 1000) conditions through the development of a shrinking core model applicable to phase - change within the capsules. To validate this model and to further investigate the thermal characteristics of the system , a bench - scale fluidized packed - bed test system was developed with air used as the heat transfer fluid. Charging operations required preheating the bed supply air, while discharging operations required cooling the air prior to delivery at the bed. Temperature data support the mathematical models used to predict the behavior of thermal and phase-change fronts advancing through the bed during melting and freezing processes. Test data allowed an accurate assessment of the time of arrival for the phase-change wave front at each known temperature transducer location and thus quantify the velocity of both the melting and freezing fronts. Velocities of isotherms in the partial phase-change region were also identified. The temperatures and measured velocities were used to determine some unknown properties of the commercial encapsulated PCM product such as phase-change temperature, specific heats, and fraction of capsule mass comprising the PCM material. Thus, the analytical predictions represented the data very well. Temperature profiles under sensible heat transfer conditions were well represented by the classic diffusion-dispersion equation. Temperature data near the phase-change fronts show an exponential temperature profile, but significant air-to-capsule heat transfer limitations are apparent very near the front. The estimated timescale for complete melting obtained from the shrinking core model was in a reasonable agreement with what was observed in the experiments. In addition to the exploration and validation of models for thermal and phasechange wave behaviors and temperature distributions across the bed, exergy of the bed was evaluated based on direction of flow and exergy efficiencies were estimated for two different flow arrangements, namely parallel and counter flow. Exergy efficiencies were uniform for both arrangements under test conditions in which sensible heat transfer occurred. Test results reveal that for parallel flow through the bed, where both charging and discharging occur from the bottom or the top inlet, as opposed to counter flow, in which the bed is charged and discharged through opposite inlets, longer charging times and more uniform discharge temperatures are characteristic of parallel flow arrangements.