**4. Highlights of Reviewed Work**

A summary of the 131 reviewed studies targeted at improving the performance of LHTESS, realized through inserting fins with high values of TC to improve heat transfer, are presented in Table 1. Specifically, the container shape, the imposed boundary conditions, phase-change mode (melting (charging) and/or solidification (discharging)), PCM, fin material, geometry and orientation and the adopted methodologies/techniques are summarized. The importance of geometrical parameters (similar to [15]) and operational factors on the characteristics of phase change conversion in melting and solidification modes are noted. Introducing fins is viewed as a significant geometrical modification to enhance the effective TC of PCM. Adding fins will enhance the thawing and freezing rates, shorten the charging and discharging times, realize uniform and stable operating temperature and assist safe operation of the heat sink. Moreover, design parameters of the fins (number, length, thickness and orientation) influence the performance of LHTESS to different degrees. It was found that the number of fins (or fin-pitch) and fin length have stronger effects on the system performance compared to that caused by fin thickness and fin orientation. On the other hand, insertion of fins will restrain natural convection, which is well-known to play an important role on thawing. Therefore, interacting but opposing influences of enhancement of the effective TC and simultaneous suppression of buoyancy should be decided by the designer through selecting the optimum location and orientation of planned fins.












not available; NF = number of fins; RU = Rectangular unit or test cell; S = solidification;

ThC =

thermocouple.

 SH = sensible heat; *Tm* = melting temperature; *Tw* = wall temperature;

#### **5. Classification of Similar Work (Themes), Performance Indicators and Challenges**

Similar to [17], which discussed 75 fin-assisted LHTES systems dating back to 1966, the reviewed studies here [20–150] were classified and summarized in Table 2. Themes of "*Rectangular cuboid thermal storage units* and *shell and tube heat exchangers"* are the broadest groupings, whereas a few outliers are listed separately. In studies with the theme of "Rectangular cuboid storage systems with horizontal/vertical/other types of fins in contact with PCM", phase transition was activated on a boundary subjected to a constant heat flux, constant wall temperature, heat transfer fluid stream(s) or jet-cooling, whereas HTF stream(s) initiate phase transition in the shell and tube heat exchangers, for which AF/LF are in direct contact with PCM. Given the variety of configurations, fin/PCM materials, lack of widely accepted thermophysical properties, etc., the widely sought-after correlation:

Efficiency = f(PCM properties, shape, boundary conditions, fin type/material, etc.)

does not exist at this time.

**Table 2.** Classification of the reviewed studies [20–150] on fin-assisted LHTESS based on similarity of work (theme); listing of the abbreviations other than those used in Table 1 are summarized at the bottom of the table.


CS = cross-section; H = HTF; JA = jet arrays, P = PCM, VIA = varying inclination angles. Terms such as HPH refer to the order of the constituents encountered moving away from within the unit to the outside.

Researchers have sought improved performance of LHTES units through shortening charge/discharge time periods, in connection with the sacrificed PCM, due to introducing fins. Adoption of simple planar fins has diminished over the years, while more complicated shapes, such as branching arrangements, crosses and Y-shapes, etc., are being reported, at times with the aid of the constructal theory. However, the fundamental challenge of utilizing high TC fins remains the promotion of conducting pathways with minimum distance that connect the high and low temperatures of a heat storage system.

#### **6. Concluding Remarks**

Analytical, computational and experimental investigations focused on improving the performance of LHTES systems that utilize generally metal-based high TC fins/extended surfaces were reviewed. A variety of PCM, including capric-palmitic acid, chloride mixtures, dodecanoic acid, erythritol, fluorides, lauric acid, naphthalene, nitrite and nitrate mixtures, paraffins, potassium nitrate, salt hydrates, sodium hydrate, stearic acid, sulfur, water and xylitol, covering *Tm* in the range of −129.6 to 767 ◦C, have been reported. Freezing and thawing within various TES vessel geometries and heat exchange operating conditions were studied. The unifying findings/observations of these studies are:


Whereas simple planar fins are still being studied, more complicated shapes (e.g., branching arrangements, crosses, Y-shapes, slanted, dendritic, snowflake-shapes, arrowshapes, helical, varied honeycomb cells, etc.) are being explored, at times with the wider adoption of the constructal theory. Promoting short conducting pathways linking the high and low temperatures of the storage system through innovative approaches still remains the ultimate challenge.

**Author Contributions:** Conceptualization, J.M.K.; Methodology, J.M.K.; Formal Analysis, J.M.K.; Investigation, W.Y., D.J. and J.M.K.; Writing—Original Draft Preparation, W.Y., D.J. and J.M.K.; Writing—Review & Editing, W.Y., D.J. and J.M.K.; Visualization, W.Y.; Supervision, J.M.K.; Project Administration, J.M.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Presented data in the form of graphs/tables were taken with permission from original publications.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **List of Symbols**


#### **Abbreviations**

