Extended surfaces, also known as fins are used commonly for heat transfer enhancement in energy storage and thermal management problems. A fin may improve the rate of heat transfer by offering greater surface area. While the performance of a fin in a single-phase ambient such as air is well-understood, relatively lesser work is available on fin performance, including parameters such as fin effectiveness and efficiency, when embedded in a phase change material (PCM). A key theoretical challenge in such analysis is the transient nature of the phase change problem that must be combined with transient diffusion and phase change in the fin. This work presents theoretical analysis of phase change heat transfer between a base wall and a PCM in presence of a fin. The processes of thermal diffusion in the fin, thermal diffusion and phase change in the PCM are combined using perturbation analysis of a problem with time-dependent boundary condition. Results are found to be in good agreement with numerical simulations. Expressions for fin effectiveness and fin efficiency as functions of time are derived. The impact of various problem parameters such as fin geometry, material and the Stefan number on fin performance is analyzed. Expressions for efficiency and effectiveness of an array of equally-spaced fins are also derived. It is shown that while a fin provides additional surface area for enhanced melting of the PCM, transient diffusion in the fin may limit the benefit of the fin, especially at small times. On the other hand, fin performance at large times is limited by slow phase change in the PCM. Results presented here improve the fundamental understanding of PCM and fin based thermal management. Expressions for fin effectiveness and efficiency derived in this work offer useful tools for designing and improving the performance of practical fin and PCM based thermal management systems.
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