Investigations on the functional modes of a thermal energy storage system for sustainable steam cooking application - an experimental study

ABSTRACT Steam cooking using parabolic trough collectors is a well-established sustainable technology. The augmentation of a thermal energy storage (TES) system with such a sustainable system will make the technology completely reliable on the renewable energy source. However, there are limited research findings to improve the thermal performance of the TES heat exchangers by adopting non-structural and non-elemental modifications. In this article, experimental studies have been performed on a TES shell and tube heat exchanger that could be envisaged for steam cooking applications. Erythritol was used as the phase change material. The heat exchanger was operated in two modes: progressive and impulsive. From the observations, the performance of the impulsive mode was better than the progressive mode. The impulsive mode of functionality witnessed a 32% decrease in the charging duration, 2.5% increase in the energy stored and 50% increase in the charging rate in comparison to the progressive mode.


Introduction
An array of parabolic trough collectors (PTCs) is an evidenced energy source for direct steam generation by utilising solar energy (Pal and Kumar 2021).PTCs could be conveniently applied for steam cooking whenever mass cooking is required (Motwani and Patel 2019).But, the main disadvantage of using such a system is the non-continous availability of the solar energy source and hence, this source of thermal energy cannot be utilised during off-sunshine hours.Hence, this paves the way for a thermal energy storage (TES) system that could store excess energy during sunshine hours and could release the accumulated energy during off-sunshine hours.Though this proposition is conceptually ideal, the empirical knowledge on the functionality of such systems is limited.It was identified that phase change materials (PCMs) will be suitable for the purpose to act as thermal storage media.But, substantial PCMs and TES systems, when employed in its native form, i.e. without any specific design and elemental modifications, require heat transfer enhancements either physically or chemically (Ibrahim et al. 2017;Sadeghi 2022).Concerning the heat transfer enhancement in PCM-based TES systems, it was identified that the heat transfer enhancement techniques in contemporary practice could be categorised into physical structural modifications, elemental modifications and encapsulation techniques.Notable physical structural modification techniques include adopting extended surfaces and fins, utilising cascaded systems and inducing metal matrices (Sarbu and Dorca 2018).Elemental modifications include inducing additives that would improve crucial PCM thermo-physical parameters, such as thermal conductivity, nucleation parameters, etc. (Chen et al. 2022;Liang and Chen 2018;Wen et al. 2022).Furthermore, encapsulation techniques enhance the thermal performance by enclosing the PCM in a shell such that the surface area of heat transfer increases (Benner et al. 2022;Cao et al. 2022;Huo et al. 2021).For instance, Selvnes, Allouche, and Hafner (2021) had experimentally investigated the effect of pillow plates in a heat exchanger for thermal energy storage and had evidenced positive outcomes.In another research, Al-Mudhafar, Nowakowski, and Nicolleau (2020) had performed performance enhancement studies on a TES system utilising a webbed tube heat exchanger.Elmaazouzi et al. (2020) performed a numerical experimentation with coaxial heat exchanger with fins and explored the temperature and enthalpy developments.Further, Horibe et al. (2015) had investigated on the effect of perforation partition plate on the phase change behaviour of a PCM erythritol, and had observed that there was a significant effect owing to the incorporation of the plate.Further, Khan, Khan, and Ghafoor (2016) had discussed about multiple structural incorporation techniques such as addition of longitudinal or axial fins, circular fins, using multitube configurations, finned rectangular and cylindrical containers, inserting carbon fibre chips and brushes, utilising the PCM in the form of spherical balls to enhance the thermal performance of TES systems.Kanimozhi et al. (2014) had reported that there was heat transfer enhancement when vertical fins were employed between two isothermal planes.The researchers had reported that employing fins had increased the conductive as well as the convective heat transfer.
On the other hand, concerning the non-structural modifications (elemental modifications and encapsulations), a research study conducted by Rahmanila, Rahman, and Ismail (2022) had asserted the superior storage efficiency of form-stabilised PCM to conventional paraffin-based PCMs.In the aforementioned research, high-density polyethylene and styrenebutadiene were reported to be utilised as the supporting materials.Furthermore, in another research work conducted by Liu et al. (2021), the researchers had reported that the addition of 3 wt.% of Al/C hybrid nano-particle to Na 2 SO 4 10H 2 O base PCM had improved the thermal conductivity of the base PCM by 26.41%.Furthermore, the researchers had also reported an improvement in the stability of the base PCM.Further, it was interesting to note that, researchers also ponder to integrate structural and nonstructure modifications.For instance, a research study by Gupta, Mishra, and Singh (2022) had reported that the utilisation of a vertical undulated wall and the augmentation of a multi-walled carbon nano-tube enhanced base PCM had improved outcomes in the melting duration.The researchers had utilised n-octadecane as the base PCM.
From the literature review, it was identified that substantial heat transfer enhancement techniques modify the functional operation of either the TES system or the PCM, i.e. the heat transfer enhancement techniques either involve structural modifications or altering the elemental composition (through additives or fillers).Either of the options involve artificially induced operations, and researches that have been conducted with an aim to enhance the thermal performance of the PCM, solely with the functional modes, without any of the aforementioned artificial inducements, have been hardly reported.Hence, it was identified that there is a research gap that could be bridged by devising strategies and techniques to perform heat transfer enhancement through nonstructural and non-elemental modifications.Furthermore, as discussed in the preceding passages, the steam cooking application is required to be operated primarily utilising the available solar energy.Limited availability of solar energy, i.e. during the sunshine hours, forces this technology to incorporate a TES design such that the PCM utilised is charged within the sunshine hours.This makes the charging duration a priority, and hence, the charging duration must be optimised for harnessing maximum benefits.Inducing high thermal conductivity additives to the base PCM is a viable option to reduce the charging duration.But there are reported evidences that an increase in the thermal conductivity of PCMs reduces the latent heat of fusion of the PCMs (Felix, Rajagopal, and Kumaresan 2022).Hence, this research study was conducted to bridge the research gap through a functional mode study involving no structural and elemental modifications.
Adopting shell and tube heat exchangers is a more common practice, as it is simple in construction and in operation.As far as the shell and tube heat exchangers employed for the TES systems are concerned, only limited modifications (structure and non-structural) are feasible for performance enhancement.For instance, in a research on shell and tube heat exchanger (Gasia et al. 2017), the utility of finned and nonfinned tubes was studied and the performances were compared.The study had reported a better performance for the finned case.In another study, Mahdi et al. (2021) had performed numerical investigations on different tube configurations with lauric acid as the PCM.In the investigations, the researchers had reported that there was a 76% reduction in the melting duration by utilising an arc array configuration instead of a conventional array configuration.In another research work carried out by Wołoszyn, Szopa, and Czerwiński (2021), the researchers had reported a reduction in the PCM melting duration by 76% when a combined helical, conical shell design and spiral fins were employed instead of a conventional vertical configuration.Hence, it was identified that the aforementioned research gap has its impact on shell and tube heat exchangers as well.
It was further identified that a PCM erythritol is more appropriate to be utilised for the intended steam cooking application (Felix, Rajagopal, & Kumaresan 2021).The key thermo-physical properties of erythritol identified from literature are presented in Table 1.In this study, erythritol was considered as the PCM of interest and a shell and tube heat exchanger was designed and fabricated, and the performances of two different functional modes were studied in operation.In this study, the operational functional modes were selected and designed such that there were no structural modifications to the conventional shell and tube heat exchanger.Further, erythritol was desired to be utilised in its native form without any elemental modifications.The methodology adopted for this study and the impended outcomes are discussed in the succeeding sections.

Study design
In this study, erythritol was utilised as the PCM.An experimental setup that could test 70 kg of the PCM was fabricated.The experimental setup was fabricated at Greenera Energy India Private Limited, Coimbatore.Erythritol with 99% purity was procured from RR enterprises, Coimbatore.The experimental procedure was then carried out in two charging modes: progressive and impulsive charging modes.The process where the PCM is allowed to completely melt from its ambient temperature is termed as 'charging'.Then, the comparative arguments were studied based on the empirical observations and the most optimal charging mode of operation was inferred.Further, to envisage this PCM for long-term applicability, the thermal endurance behaviour of the PCM erythritol was also studied through a thermal cycling analysis and the results have been recorded.

Design of the experimental setup
The PCM was designed to be housed inside a shell and tube heat exchanger and the heat exchanger was supplied with a steam source from a 6 kW electrical boiler.A detailed schematic of the experimental layout and the temperature observation plan is presented in Figure 1.It could be noted from Figure 1a that a closed circuit was designed for the experimental observation.During the charging mode, the boiler was designed to supply steam to the upper pass of the heat exchanger.The heat exchanger was designed to be of a two-pass configuration with the PCM statically housed within the shell and steam passing through 63 tubes.The heat exchanger was designed in such a way to allow only completely condensed steam to leave the exchanger.This was intended to harness the maximum possible latent heat energy from the supplied steam source.During the discharge mode, the heat exchanger was designed to receive water at 2 bar at the lower pass and steam was extracted from the upper pass exit.The heat transfer area of heat exchanger was designed to be 4.5 m 2 .The total length of the heat exchanger (excluding headers and pass transits) was designed to be 1 m.Further, glass wool possessing a thermal conductivity of 0.0343 W m −1 K −1 (Jeon et al. 2017) was utilised to insulate the heat exchanger.The critical radius of insulation was estimated to be nearly 50 mm.Further, to validate the reliability of the glass wool insulation, the surface temperature was visualised periodically utilising a thermal camera.The thermal images recorded are presented in the supplementary material.
From Figure 1b, it could be observed that a total of 18 temperature probing locations were planned in three consecutive planes.Each plane consisted of 6 temperature sensors diametrically spaced.The first measurement plane was designed to be located 0.4 m from the header of the exchanger and the consecutive planes at 0.2 m from the preceding one.The first plane alone was located at a longer distance owing to the location of the flange designed to fill the PCM.PT100 temperature sensors with a range of 0-250°C were utilised for the experimental study.The sensors, being platinum resistance type had incertitudes of � 0.3°C in their measurements.A photograph of the fabricated experimental setup is presented in the supplementary material.

Experimental procedure adopted
Any notable experimental study involving PCMs will consist of a charging mode (C.M.) and a discharging mode (D.M.).This current study improvises the conventional practice.The experiments conducted in this study were grouped under two broader modes viz. the progressive mode and the impulsive mode.In the progressive mode of study, the entire study duration was compartmentalised further into a C.M., a pre-discharge mode (P.D.M.) and a D.M.The key feature of the progressive mode is that the boiler and the heat exchanger was directly coupled since the commencement of the experiment.Thus, as the boiler started generating steam (in C.M.), it was progressively supplied to the heat exchanger.The C.M. was followed by a P.D.M.In P.D.M., water was supplied to the heat exchanger and the heat exchanger exit was closed such that the water boils and the generated steam was accumulated inside the heat exchanger itself.This was intended to harness the maximum possible heat that has been stored in the PCM.The P.D.M. was followed by a D.M. where steam was made to exit and the steam supply was observed.
On the contrary, the impulsive mode was compartmentalised further into a pre-impulsive mode (P.I.M.), a C. M., a P.D.M. and a D.M.In the P.I.M., the boiler was isolated from the heat exchanger until a boiler steam temperature of 140°C was attained.Then the steam at 140°C (4 bar) was impulsively supplied to the heat exchanger.In the C.M., the impulsive steam was utilised to heat the PCM.The functionality of P.D.M. and D. M. remained the same for both impulsive and progressive modes.In this study, the temperature history (T-history) of the PCM was observed for the two modes.In this study, the quantity of heat energy stored at the end of charging (Q st ) was estimated by adopting the mathematical formulation presented in Equation.1.
In the aforementioned equation, 'm' represents the quantity of the PCM, 'T pm ' represents the peak melting temperature, 'T e ' represents the end temperature, 'C ps ' represents the specific heat of the PCM in the solid phase and 'C pl ' represents the specific heat of the PCM in the liquid phase, 'γ' represents the liquid fraction and 'λ' represents the latent heat of fusion of the PCM.In this study, the magnitudes of C ps , C pl and λ were estimated through a differential scanning calorimetry (DSC) analysis on the PCM.A detailed description on the outcomes of the DSC analysis is provided in the succeeding sections.Furthermore, to estimate the instantaneous mean liquid fraction ðγÞ of the PCM, the mathematical model presented by Shmueli, Ziskind, and Letan (2010) was adopted.
The mathematical model is presented in Equation.2.
In the aforementioned equation, 'T om ' represents onset of melting temperature and 'T em ' represents the end melting temperature.Further, the charging rate was estimated by adopting the mathematical formulation presented in Equation.3.Further, the charging mode efficiency was estimated by adopting the mathematical formulation presented in Equation.4.
In the aforementioned equation, the quantity of heat energy supplied through the steam was estimated through the temperature of the steam supply, mass of the steam supplied and its phase transition enthalpy (at that temperature).Further, during the discharge, the heat energy extracted as steam output and as residual hot water was estimated.The discharging efficiency was estimated by adopting the mathematical formulation presented in Equation.5.Ultimately, the overall efficiency was estimated as a product of the charging and discharging efficiencies. where, The key difference between the progressive mode and the impulsive mode was that, in the progressive mode, steam was supplied continuously since the boiler was powered.This gave rise to a gradual increase in the inlet steam temperature through which the PCM was charged.But, unlike the progressive mode, in the impulsive mode, the boiler was allowed to generate steam upto 140°C and only then that steam was supplied to the heat exchanger.This study was adopted envisaging the applicability of this technology for the intended solar thermal application.
In real-time, when PTCs are connected to the TES heat exchanger, by default, PTCs will give rise to a progressive steam supply as it is dependent on the solar radiation.Hence, a choice of whether to allow the PTC integrated system to operate in the default progressive mode or to design it to be impulsive has to be pre-defined.Hence, this study will pave the way to work out a decision for this kind of operation.

Incertitude analysis
An incertitude analysis for the experimentation is necessary to investigate the reliability limits of the quantifiable outcomes.It was taken note that γ depends on the temperature and Q st depends on temperature, γ and λ and hence an explicit incertitude analysis was required to be carried out.It was noted that the temperature incertitude for the temperature outcomes from DSC analysis were � 0.1°C.Further, the mass estimation had an incertitude of � 0.001 g.From peer literature (Anish et al. 2021;Niyas et al. 2017;Senthil 2020), it was identified that Kline and McClintok's method is the most favourably adopted incertitude estimation method for PCM research.The mathematical formulation adopted for this estimation is presented in Equation.7 (Niyas et al. 2017).In the formulation 'N' represents the dependent functions and 'u' represents the independent variables.
By adopting the aforementioned formulation, the incertitudes in the estimation of the energy stored accounts to � 3.78%, charging rate accounts to � 5.14%, energy extracted accounts to � 2.67% and the overall efficiency accounts to � 3.54%.The estimated incertitudes were satisfactory and hence the outcomes were deemed to be reliable.

Post-cycling thermal characterisation study
It was desired to study the thermal endurance of the PCM and address any degradation of the PCM in the long run.To perform this study, the DSC technique was adopted.A sample of erythritol before subjecting it to thermal cycling, and another sample of erythritol after 50 thermal cycles were subjected to DSC analysis using a Perkin Elmer Pyris 6 equipment.The DSC thermogram was plotted and utilising the thermogram, key thermal characterisation parameters such T om , T pm , T em and λ, were recorded.The specific heat magnitudes utilised for Equation.1 were also estimated through the implications of the DSC thermogram.The results were then compared for reason.

Experimental observations and its implications
The progressive mode observations are presented in Figure 2. From the figure, it is evident that the PCM had completely melted and there was a steady rise in the PCM temperature during the C.M. and an abrupt fall in the PCM temperature during the D.M.The impulsive mode observations are presented in Figure 3. From the figure, it is apparent that the impulsive steam from the boiler had been well utilised for charging the PCM.Also, in both of the modes, it was observed that the bottom zone's temperatures were higher than the top zone's temperatures.This was because the steam source entered through the upper pass and then proceeded through the bottom pass.In the upper pass tubes, the steam had been comparatively in motion, whereas in the lower pass tubes the steam was nearly static, as the temperature controlled exit valve placed had allowed the steam to pass only if it had completely condensed.Hence, the steam present in the bottom zone had more potential to release its latent heat than the steam in the upper pass.Also, in both cases, plane B had a faster temperature development than the other planes.This was also because of the same factor.Plane B, being in the middle portion of the heat exchanger witnessed a higher temperature development.Further, from Figure 2(d) and from Figure 3(d), it could be observed that a clear demarcation between the sensible and the latent heat phases does exist.The liquid fraction model adopted validated the reliability of the experimental observations as the contours of energy stored in the PCM go on par with the liquid fraction contour.Furthermore, the liquid fraction plot in both the cases indicated that complete melting of the PCM was achieved.
However, a comparative study had to be made to discuss the strengths and weaknesses of each mode of functionality.A comparison between the major inferences of the two modes has been presented in Table 2.The outcomes inferred were estimated by adopting the mathematical formulations presented in the preceding sections.From the table, it could be observed that there had been only a marginal difference between the overall efficiencies of both the modes.The progressive mode had a marginally higher efficiency than the impulsive mode.But, the key factor to be noted is the charging duration.A 32% reduction in the charging time was achieved by employing the impulsive mode.Despite the impulsive mode having a comparatively lower charging mode efficiency than the progressive mode, the higher quantity of steam discharge had surpassed this factor.The discharge rate of steam had also improved when the impulsive mode was employed, and this had contributed to a marginally higher discharge efficiency in the impulsive mode.From application perspective, this quantum of reduction in the charging duration is highly appreciable as the application requires the entire quantity of the PCM to be charged within the sunshine hours.From the performances of both of the modes, it was apparent that the impulsive mode had performed in a superior way than its counterpart.Further, from the steam cooking perspective, this mode of operation could be designed in such a way that the steam generated from the PTCs could be stored in an interim steam drum (conventional practice for steam systems) and could be impulsively allowed to charge the PCM  after the impulsive pressure is reached in the steam drum.Thus, this facility could serve as an accumulator to manage any inconsistencies in the solar steam supply.This is also a benefit that could be envisaged when this mode of operation is scaled-up for the application.
As utilising a steam drum is a usual practice for steam systems, this practice does not induce any other special structural modification to the system.Further, the reliability of adopting a functional modification (rather than elemental or structural modifications) could only be validated on a comparative note.Hence, the benefits achieved through functional modifications (in this current study) have been compared with benefits achieved by adopting other methods (from literature reports).A comparison has been presented in Table 3. From the outcomes, it is apparent that the benefits reaped through adopting this proposed functional modification are on par with several other peer research studies.

Thermal cycling on erythritol and post-cycling thermal characterisation
From an applicability perspective, the research objectives will not be fulfilled until the long-term performance of the PCM is not addressed.Hence, the thermal cycling performance of the PCM was observed intricately.Figure 4 presents a comparison of the magnitudes of T om , T pm , T em and λ before and after 50 thermal cycles.It could be observed from the magnitudes that there were no significant degradations in the melting temperature components, but there was a 15% reduction in the λ magnitude.The endothermic DSC thermogram obtained is presented in the supplementary material.Comparing the outcomes from this current study to peer research reports, it was noted that Sharma et al. (Sharma et al. 2020) had reported that there was a 8.4%, 9% and 9.3% decrease in the melting enthalpy after 3000 thermal cycles, when 1-Dodecanol, 1-Hexadecanol and Table 3.A comparison between the outcomes in this current study and literature reports.

Source
Enhancement method Key quantifiable benefits Zağlanmış, Demircan, and Gemicioğlu (2022) Modifications in the inlet temperature of the heat transfer fluid (HTF), mass flow rate of the HTF and pipe sequencing.
In the study RT-50 PCM had been utilised and water was utilised as the HTF.
Nearly a 35% decrease in the charging duration with an increase in the HTF inlet temperature.Nearly a 20% decrease in the charging duration through pipe sequence modifications.Anish et al. (2021) Modifications in the HTF inlet temperature and flow rate.
A 30% decrease in the charging duration with a 10°C increase in the HTF inlet temperature (at 2.5 lpm and 3.5 lpm) and a 37% decrease in the charging duration at 3 lpm.Senthil (2020) Vertical orientation of the TES heat exchanger.PCM utilised was KNO 3 -NaNO 3 .
Average temperature of the PCM 3.5% more than in horizontal orientation and charging duration 12.5% faster than in horizontal orientation.Govindaraj, Panchabikesan, Denkenberger, Ramalingam (2017) Orientation of fins for spherically encapsulated PCMs.A 22% and a 42% reduction in the charging duration when a orthogonal fin configuration was utilised in comparison to a circumferential fin and a no fin configuration respectively.Paria et al. (2015) Modifications in the inlet flow rate of the HTF.58% reduction in the charging duration by increasing the Reynold's number of the flow from 1000 to 2000.

Current study
Functional modification through progressive and impulsive modes.
A 32% reduction in the charging duration when impulsive mode was adopted.A 25% increase in the discharging rate, a 2.5% increase in energy stored and a 50% increase in the charging rate.1-Octadecanol were utilised as base PCMs respectively.In another study on organic binary PCMs (Mengjie et al. 2017) involving compositions of capric acid, lauric acid, myristic acid and palmitic acid, the researchers had reported a decrease in the latent heat of fusion under thermal cycles.Hence, it was inferred that a decrease in the latent heat of fusion upon thermal cycling is inevitable.
A comparison between the current study and literature findings is presented in Table 4.The latent heat loss per thermal cycle was desired as the metric of comparison as multiple research works had reported outcomes for different cycles.A uniform metric would suffice from a validation perspective.From the table, it could be inferred that the outcomes of this current study are similar to that of the compared literature.This validates the reliability of the thermal characterisation study and further asserts that the latent heat loss experienced in this study is convincing and within limits.Hence, the PCM erythritol could be envisaged for long-term utility.

Conclusion
A reduction in the charging duration of the PCM erythritol housed in a shell and tube heat exchanger was desired.Such a reduction is necessary as the PCM is required to be charged within the sunshine hours and the TES system is envisaged for steam cooking utilising solar thermal source.The experiments were conducted with 70 kg of erythritol and by supplying steam at 140°C to the TES system.The real-time PTC system has been envisaged to be delivering steam to the application at 140°C.This could be achieved by supplying the steam that goes through a boiler before reaching the cooking application.The variation in solar insolation has not been taken into consideration, but that could be taken care by supplying the output steam from the PTC system through the LPG boiler before supplying it for the cooking application.The experimental study was conducted in two modes: progressive and impulsive.From the experimental observations, it was observed that there was a reduction in the charging duration by 32% when the impulsive mode was employed.Further, from the experimental observations, the following minor inferences were also inferred.
(1) It was observed that there was a 2.5% increase in the energy stored by the PCM when the impulsive mode was adopted.This phenomenon could be ascribed to the impulsive thermal load that acted upon the PCM.
(2) The increase in the energy stored during the impulsive mode was accompanied by a considerable decrease in the charging duration and that had caused a 50% increase in the charging rate.
(3) In the impulsive mode, it was observed that, owing to the higher quantum of energy stored, the magnitude of the energy extracted was also comparatively higher, aiding to a higher discharging efficiency.The impulsive mode discharging efficiency was 7.3% higher than that of the progressive mode.
(4) But despite the higher discharging efficiency and a faster charging rate, the overall efficiency of the impulsive mode was 2% lesser than that of the progressive mode.This difference in the overall efficiency was due to the increase in the steam utilisation during the impulsive mode.The impulsive thermal load was accompanied with an increased influx of steam.However, despite this influx, the heat absorption rate of erythritol in the TES exchanger remained constant owing to the material property.This phenomenon had caused the difference in the efficiencies.
(5) The DSC analysis on erythritol sample before and after 50 thermal cycles had revealed that there was a 15% decrease in the latent heat of fusion of the PCM.However, there was no significant degradation in the melting temperatures.The decrease in the latent heat of fusion is acceptable, and hence, the PCM erythritol could be envisaged for longterm applications.
Consolidating the aforementioned arguments, it was inferred that the impulsive mode of functionality could be recommended for solar steam cooking applications.This inference was made as charging duration was desired as the utmost priority.Further, aiding to the arguments, it could be inferred that there has been a significant increase in the quantum of energy stored as well as in the charging rate.It is an agreeable fact that there has been a decrease in the overall efficiency, but if one would consider its magnitude, it could be deemed as insignificant.Further, this modification does not require any customised design installations and elemental modifications.The impulsive mode could be executed by utilising the existing steam drum and a control valve in conventional practice.Hence, the impulsive mode of functionality could be envisaged for TES systems intended for solar steam cooking applications.Further, the implications of this study could also be envisaged for dairy industries, dyeing and bleaching industries, food processing industries, laundry applications and solar desalination

Figure 1 .
Figure 1.Panel (a) presents a detailed scheme of the experimental organisation.Panel (b) presents the scheme of temperature sensors along with a representation of the processes involved during the charging process.The T-history was observed in all of the three planes (A,B,C) containing six sensors each.

Figure 2 .
Figure 2. Panel (a) presents the T-history at all probing locations.Panel (b) presents the mean T-history for plane A, B, C probes individually.Panel (c) presents the mean T-history at the top, and bottom zones and compares it with the mean temperature of the PCM as well as with the steam temperatures.Panel (d) presents the estimated liquid fraction and the energy stored magnitudes.Panels (a)-(d) present the observations for the progressive mode.

Figure 3 .
Figure 3. Panel (a) presents the T-history at all probing locations.Panel (b) presents the mean T-history for plane A, B, C probes individually.Panel (c) presents the mean T-history at the top, and bottom zones and compares it with the mean temperature of the PCM as well as with the steam temperatures.Panel (d) presents the estimated liquid fraction and the energy stored magnitudes.Panels (a)-(d) present the observations for the impulsive mode.

Figure 4 .
Figure 4.The magnitudes of the melting temperatures and the latent heat of fusion before and after 50 thermal cycles.The outcomes were derived from the DSC thermogram presented in the supplementary material.

Table 1 .
Key thermo-physical properties of erythritol.

Table 2 .
Major inferences from the experimental observation.

Table 4 .
Comparison of various thermal cycling researches on erythritol.