Fin design optimization to enhance PCM melting rate inside a rectangular enclosure

Melting characteristics of a phase change material (PCM) inside a rectangular box isothermally heated from the basal surface are investigated. Vertical straight fins are considered for heat transfer enhancement. With the premise of a fixed fin volume percentage (5%), effect of fin spacing (pitch) under a constant fin length is numerically investigated for two different fin materials, namely aluminium and stainless-steel. Then, with fixed fin pitches, optimizations of fin length for those two fin materials are also performed. Results indicate that, for a fin length of 25 mm, the optimal fin pitch (or spacing) is around 7.5-10 mm (or 6.75-9 mm), seemingly irrespective of fin materials. With optimized fin pitch of 10 mm, the best fin lengths for aluminium and stainless-steel are 50 mm (equal to the enclosure height) and 31.25 mm, respectively. The optimal fin length is obviously a function of fin material but, more interestingly, the trends are different for the two materials considered here. That is, for sparse fin distribution, when fin pitch increases, the optimal fin length for aluminium fins increases while the converse is true for a stainless-steel fin under the same condition. For example, with a fin pitch of 40 mm, the optimal fin length for aluminium is 43.75 mm and 50 mm for stainless-steel. To better understand this intriguing behaviour, a theoretical analysis is conducted in parallel. Fin length is optimized using fin effective length theory while optimal value for fin pitch is sought, relying on scale analysis, by minimizing the size of the thermally stratified region formed between two vertical fins. For very short fins, or tall enclosures, a criterion for the optimal tank height is also provided. Theoretical results are compared with numerical and experimental data available in the literature to observe a very good agreement.