S-shaped Research Articles

Monocytes to lymphocytes multiplying platelets ratio as an early indicator of acute kidney injury in cardiac surgery with cardiopulmonary bypass: a retrospective analysis.

The monocyte-to-lymphocyte multiplying platelets ratio (MLPR) is a novel systemic inflammatory marker, deriving from the monocyte-to-lymphocyte ratio (MLR). However, the link between MLPR and acute kidney injury following cardiac surgery (CSA-AKI) with cardiopulmonary bypass (CPB) has not been investigated yet. We comprehensively explored the potential linear and nonlinear relationship between MLPR or MLR and CSA-AKI. Data of patients who underwent cardiac surgery with CPB between December 2018 and April 2021 were retrospectively collected at Fuwai Hospital, Beijing, China. MLPR was defined as monocyte count (×109/L)×1000/(lymphocyte count (×109/L)×platelets (×109/L)). MLR was defined as monocyte count (×109/L)/lymphocyte count (×109/L). Logistic regression and restricted cubic spline (RCS) were used for linear and nonlinear analysis. The primary outcome was postoperative AKI within 48 h of after cardiac surgery. Of the 2420 patients screened, 2387 eligible patients were enrolled in the final analysis; the mean age was 54.7years, and 1501 [62.9%] were men. The incidence of AKI was 25.8%. Logistic regression showed that MLPR (odds ratio [OR]=1.31, 95% confidence interval [CI]: 1.16-1.48, p<.001) and MLR (OR = 3.06, 95% CI: 1.29-7.29, p=.012) were independent risk factors for AKI. Moreover, in the RCS model with adjustment for age (median: 56), female sex, and history of diabetes, a significant statistical difference was detected between preoperative MLPR, MLR, and AKI (p for non-linearity <.001). The subgroup analyses revealed similar results. The study revealed a nonlinear relationship between MLPR and MLR with AKI. MLPR exhibited a J-shaped curve, and MLR showed a favorable S-shaped curve in relation to AKI. Particularly, MLPR emerges as a promising clinical composite index for early CSA-AKI prediction. These findings emphasize the significance of MLPR as a valuable tool in clinical practice for timely identification and management of CSA-AKI.

Moisture sorption isotherm and thermodynamic analysis of egg powders dried by foam-mat-assisted refractance window drying.

In the designed study, the moisture sorption isotherm and thermodynamic properties of refractance-window-dried egg white powder (EWP), egg yolk powder (EYP) and whole egg powder (WEP) were determined. The adsorption isotherm of egg powders was classified as type II, giving a sigmoidal shape. Peleg showed the highest goodness of fitting for egg powder. The monolayer moisture content of egg powders varied between 0.02 and 0.09 g g-1. According to the thermodynamic analysis, an increase in moisture content led to a decrease in net isosteric heat of sorption (qst), and the highest decrease was observed in EWP. The qst of EWP was calculated as 18 637 kJ mol-1, while it decreased to 3104 kJ mol-1 at 0.2 g g-1 moisture content. Like qst, sorption entropy decreased from 52.07 to 7.14 J mol-1 K-1 with increasing water activity (aw) for EWP. Increasing temperature caused a decrease in spreading pressure and was higher in EWP samples. Increasing moisture content and temperature also decreased Gibbs free energy level. Moisture sorption isotherm (MSI) is used to predict the amount of bound water in a material at a specific relative humidity and temperature. To inhibit chemical and microbiological spoilage, the drying process must continue until the monolayer moisture content is reached. In this study, the monolayer moisture content of powdered eggs for safe storage was demonstrated by MSI. Additionally, by determining the thermodynamic functions of egg powder, valuable information was obtained related to predicting the energy requirement in drying processes. © 2024 Society of Chemical Industry.

Impact of proficiency in the transcatheter aortic valve implantation procedure on clinical outcomes: a single center retrospective study

BackgroundWe used transcatheter aortic valve implantation (TAVI) procedure time to investigate the association between surgical team maturity and outcome.MethodsAmong patients who underwent TAVI between October 2015 and November 2019, those who had Sapien™ implanted with the transfemoral artery approach were included in the analysis. We used TAVI procedure time and surgery number to draw a learning curve. Then, we divided the patients into two groups before and after the number of cases where the sigmoid curve reaches a plateau. We compared the two groups regarding the surveyed factors and investigated the correlation between the TAVI procedure time and survey factors.ResultsNinety-nine of 149 patients were analysed. The sigmoid curve had an inflection point in 23.2 cases and reached a plateau in 43.0 cases. Patients in the Late group had a shorter operating time, less contrast media, less radiation exposure, and less myocardial escape enzymes than the Early group. Surgical procedure time showed the strongest correlation with the surgical case number.ConclusionThe number of cases required for surgeon proficiency for isolated Sapien™ valve implantation was 43. This number may serve as a guideline for switching the anesthesia management of TAVI from general to local anesthesia.

Detection of periodic peaks in Karenia brevis concentration consistent with the time-delay logistic equation

The logistic equation models single-species population growth with a sigmoid curve that begins as exponential and ends with an asymptotic approach to a final population determined by natural system carrying capacity. But the population of a natural system often does not stabilize as it approaches carrying capacity. Instead, it exhibits periodic change, sometimes with very large amplitudes. The time-delay modification of the logistic equation accounts for this behavior by connecting the present rate of population growth to conditions at an earlier time. The periodic change in population with time can progress from a monotonic approach to the carrying capacity; to oscillation around the carrying capacity; to limit-cycle periodic change; and, finally, to chaotic change.The presence of multiple species and inadequate sampling frequency and spatial coverage hinder the application of the time-delay logistic equation to real-world populations. Blooms of Karenia brevis along the southwest Florida Gulf Coast, however, provide a unique opportunity in that blooms are nearly monospecific and are sampled frequently over a wide geographic region; they are good candidates for testing the time-delay logistic equation. We show that these blooms exhibit peaks in concentration with periods in the range of 40–100 days, consistent with that predicted by the time-delay logistic equation. Cell concentrations in the valleys between the peaks are at least 2–3 orders of magnitude lower than peak values, offering predictable windows of opportunity for potential mitigation efforts.

ОБОСНОВАНИЕ КОНСТРУКЦИИ КРЫТОГО ГРУЗОВОГО ВАГОНА С УВЕЛИЧЕННЫМ ОБЪЕМОМ ГРУЗОВОГО ПОМЕЩЕНИЯ

The market of covered freight cars, as well as existing designs of this car type of domestic and foreign production is analyzed. Promising trends of making innovative designs of freight cars for the transportation of piece and container goods are found out. The original design of a covered freight car with an increased body space due to the use of the space between trucks is proposed. To reduce the complexity of loading and unloading operations, sliding sections of the side walls and roof are provided in the car design. To confirm the compliance of the proposed design with the requirements of regulatory and technical documents, the car was entered into the dimension, checking for automatic coupling at the junction of a straight line and a curve, passage in the coupling of an s-shaped curve and coupling of a straight line and a curve, and a single car along a circular curve of a small radius, as well as passing without self-decoupling of the hump of the sorting slide, the ramp exit of the train ferry. A safety assessment is carried out with regard to rolling the wheel onto the rail and overturning the car in curves. The car dynamic characteristics are found out by mathematical modeling methods. The assessment of the strength of the body load-bearing structure, lifting mechanisms of the floor sections, sliding sections of the roof and side walls is performed using the finite element method implemented in the environment of a specialized software package. The results obtained as a result of calculations and computer modeling confirmed the operability and safety of the proposed design of a covered freight car with an increased loading space.

Modeling the random spreading of fake news through a two‐dimensional time‐inhomogeneous birth‐death process

We consider a two‐dimensional time‐inhomogeneous birth‐death process to model the time‐evolution of fake news in a population. The two components of the process represent, respectively: (i) the number of individuals (say spreaders) who know the rumor and intend to spread it and (ii) the number of individuals (say inactives) who have forgotten the rumor previously received. We employ the probability generating function‐based approach to obtain the moments and the covariance of the two‐dimensional process. We also analyze a new adimensional index to study the correlation between the two components. Some special cases are considered in which both the expected numbers of spreaders and inactives are equal to suitable sigmoidal curves, which are often adopted in modeling growth phenomena. Finally, we provide an application based on real data related to the diffusion of fake news, in which the optimal choice of the sigmoidal curve that fit the datasets is based on the minimization of the mean square error and of the relative absolute error.

Exploring the link: Systemic immune-inflammation index as a marker in endometriosis—Insights from the NHANES 2001–2006 cross-sectional study

Objective The systemic immuno-inflammatory index (SII), a novel immune marker of inflammation, has not been previously associated with endometriosis. The objective of this research is to explore the link between SII and the occurrence of endometriosis. Methods Utilizing data from the National Health and Nutrition Examination Survey (NHANES) spanning 2001 to 2006, we screened and extracted relevant information from the population. Participants missing data on either SII or endometriosis were excluded. We divided the remaining cohort into quartiles based on SII levels: Q1 (SII &lt; 249, n = 848), Q2 (249 ≤ SII &lt; 604.55, n = 847), Q3 (604.55 ≤ SII &lt; 825.35, n = 847), and Q4 (SII ≥ 852.35, n = 848). Multiple linear regression and smooth curve fitting techniques, were to evaluate the non-linear association between SII and endometriosis. Results The study included 3,390 adults aged 20 to 55. Multiple linear regression analysis revealed a significant positive correlation between SII and endometriosis [3.14, 95% CI (2.22, 4.45), P &lt; 0.01]. This correlation was consistent across subgroups defined by marital status, poverty income ratio, BMI, alcohol consumption, and age at first menstrual period. However, the relationship between SII and endometriosis was significantly modified by age, education, and history of pregnancy in the stratified analyses. The curve fitting indicated an S-shaped curve, with an inflection point at SII = 1105.76. Conclusion The SII may serve as a predictive marker for endometriosis risk among women in the United States, offering a potentially simple and cost-effective approach. However, given the cross-sectional design of this investigation, further validation in prospective studies is necessary.

FORECASTING TECHNOLOGY ADOPTION BEHAVIOUR AND AGRICULTURAL PRODUCTION GROWTH

In this paper, we proposed a simple mathematical model for farmers in the Ranchi district to adopt and implement agricultural technologies. We used the Fisher-Pry model, which is a very effective model in the study of technological adoption. The model's output is a Sigmoid curve, or S-shaped curve, that develops exponentially at first, then approximately linearly, and lastly asymptotically. We have studied the models of technology spread using a basic case study and brought in a real-world situation. Mathematically, it is possible to predict that adoption will rise to the number m/2 when 50% of the farmers have adopted the technology, after which it will slow down. In a real-life situation, the point of inflection might occur before or after m/2.We also collected data on some of the food crops, and net irrigated area of Ranchi district from 2011 to 2020, and evaluated it graphically/mathematically. We examined the advantages of technology in agriculture using utility functions, by employing basic scenarios and selecting between different technologies for adoption

Carotid Dolichoarteriopathies: A Comprehensive Overview

Carotid dolichoarteriopathies (CDA) represent a group of morphological abnormalities, with changes in the geometry and tortuosity of the carotid arteries. They were described in 1925 for the first time and were classified in three types according to the angle of torsion, in tortuosity (angle &gt; 90°), coiling (S-shaped curve or loop) and kinking (angle &lt; 90°). The pathophysiology of CDA is controversial and includes congenital mechanisms, genetic factors, connective tissue diseases, acquired mechanisms which can be associated with but not dependent on cardiovascular risk factors, and anomalies of the cervical spine. CDA have been associated with different cardiovascular and cerebrovascular events secondary to hemodynamic abnormalities, thromboembolism and cerebrovascular insufficiency and ischemia. However, the evidence is limited and for some authors they are more of a curiosity than a real predictor of ischemic events. Other studies support the clinical value of the diagnosis and follow-up of CDA and their understanding not only by internists, cardiologists and neurologists, but also by surgeons and otolaryngologists. Several authors proposed different therapeutic strategies to correct CDA, including surgical procedures. However, the indications and management approaches are controversial, and further randomized, multicenter, prospective studies are required to determine the most appropriate course of action. Until then, imaging techniques remain the basis for the etiologic diagnosis of cerebrovascular adverse events when all other causes have been excluded, and close clinical monitoring and follow-up of patients remain key strategies for the prevention of secondary events.

Analysis of self-oscillation stability of a pump-turbine in the S-shaped regions of characteristic curves

Abstract The hydraulic oscillation of pumped-storage power station (PSPS) affects the safe and stable operation of the power station. The S-shaped characteristic curves of pump-turbine may sometimes result in instability in speed-no-load operation. To investigate the instability mechanisms and identify the main factors that affect stability, this paper used the overall matrix method to establish a self-excited oscillation calculation model of a PSPS and analyzed the stability characteristics and influencing factors of the S-shaped regions of the speed-no-load opening. The results show that when the slope of the characteristic curve is negative, the natural frequency attenuation factors of the system are negative, demonstrating stability. When the slope of the characteristic curve is positive, the system remains stable if the slope is large. However, if the slope of the characteristic curve is below a certain value, which may lead to instability. Increasing the inlet valve resistance and appropriately changing the valve layout position can enhance the stability of the system. The damping surge chamber fluctuations have no impact on system stability. The study also found that the stability regions of the S-shaped regions are related to the slope of the characteristic curve, the unit operating discharge, and the value resistance coefficient.

Urbanization inequality: evidence from vehicle ownership in Chinese cities

Unequal outcomes resulting from urbanization can pose a significant challenge to sustainable development. Vehicles are an important urbanization dimension as a critical component of urban infrastructure by providing mobility and accessibility to social services. China’s vehicle ownership (referred to as in-use vehicle stocks) has been growing quickly since 2000, but its per capita stocks are still much lower than that in developed economies. This raises the question of whether and when China’s vehicle stocks will reach a peak level close to that in the developed countries. By analyzing vehicle stocks in 283 Chinese cities during 2001–2018, we have the following findings: (1) vehicle stocks are predominantly distributed in northern and eastern coastal cities and provincial capital cities; (2) inequality in vehicle ownership rates between cities shows a declining trend at both national and region scales; (3) the growth of vehicle ownership rates follows an S-shape curve and most cities are still at the early stage of motorization; (4) China is likely to have a lower saturation level of vehicle ownership rate. These results could help to accurately forecast future vehicle demand in China, estimate the resulting environmental impacts, and explore strategies to achieve carbon neutrality in transportation.

Repeated S-shaped and Σ-shaped bifurcation curves for the one-dimensional non-autonomous Minkowski-curvature problem

We study the multiple existence results of positive solutions concerning one-dimensional non-autonomous Minkowski-curvature problems for certain ranges of a parameter. By providing a sufficient condition, we guarantee repeated S-shaped and repeated Σ-shaped global unbounded continua of positive solutions under superlinear and sublinear nonlinearities, respectively. This result is new even for autonomous cases.

A novel hepatocyte ketone production assay to help the selection of nutrients for the ketogenic diet treatment of epilepsy

The classic ketogenic diet is an effective treatment option for drug-resistant epilepsy, but its high fat content challenges patient compliance. Optimizing liver ketone production guided by a method comparing substrates for their ketogenic potential may help to reduce the fat content of the diet without loss in ketosis induction. Here, we present a liver cell assay measuring the β-hydroxybutyrate (βHB) yield from fatty acid substrates. Even chain albumin-conjugated fatty acids comprising between 4 and 18 carbon atoms showed a sigmoidal concentration-βHB response curve (CRC) whereas acetate and omega-3 PUFAs produced no CRC. While CRCs were not distinguished by their half-maximal effective concentration (EC50), they differed by maximum response, which related inversely to the carbon chain length and was highest for butyrate. The assay also suitably assessed the βHB yield from fatty acid blends detecting shifts in maximum response from exchanging medium chain fatty acids for long chain fatty acids. The assay further detected a dual role for butyrate and hexanoic acid as ketogenic substrate at high concentration and ketogenic enhancer at low concentration, augmenting the βHB yield from oleic acid and a fatty acid blend. The assay also found propionate to inhibit ketogenesis from oleic acid and a fatty acid blend at low physiological concentration. Although the in vitro assay shows promise as a tool to optimize the ketogenic yield of a fat blend, its predictive value requires human validation.

A Sustainable Supply Chain Model with a Setup Cost Reduction Policy for Imperfect Items under Learning in a Cloudy Fuzzy Environment

The present paper deals with an integrated sustainable supply chain model with the effect of learning for an imperfect production system under a cloudy fuzzy environment where the demand rate is treated as a cloudy triangular fuzzy (imprecise) number, which means that the demand rate of the items is not constant, and shortages and a warranty policy are allowed. The vendor governs the manufacturing process to serve the demand of the buyer. When the vendor supplies the demanded lot after the production of items, it is also considered that the delivery lots have some defective items that follow an S-shape learning curve. After receiving the lot, the buyer inspects the whole lot, and the buyer classifies the whole lot into two categories: one is the defective-quality items and the other is the imperfect-quality items. The buyer returns the defective-quality items to the seller after a screening process, for which a warranty cost is included. During the transportation of the items, a lot of carbon units are emitted from the transportation, damaging the quality of the environment. The seller includes carbon emission costs to achieve sustainability as per considerations. A one-time discrete investment is also included for the minimizing of the setup cost of the seller for the next cycles. We developed models for the scenario of the separate decision and for the integrated decision of the players (seller/buyer) under the model’s consideration. Our aim is to jointly optimize the integrated total fuzzy cost under a cloudy fuzzy environment sustained by the seller and buyer. Numerical examples, sensitivity, analysis limitations, future scope and conclusions have been provided for the justification of the proposed model, and the impact of the input parameters on the decision variables and integrated total fuzzy cost for the supply chain are provided for the validity and robustness of this proposed model. The effect of learning in a cloudy fuzzy environment was positive for this proposed model.

Factor reallocation path for low-carbon transformation: A perspective of manufacturing industry ecosystem

The incomplete production factor market induces more factors flowing to industries with lower carbon productivity, highlighting the need for effective factor reallocation to promote low-carbon transformation. Current research is constrained by the dimension of factor endowments, with insufficient attention given to the problem of diminishing marginal benefit of factor input in factor reallocation. By combining the factor flow effect induced by productivity difference with the factor allocation equilibrium effect under diminishing marginal benefit, the factor reallocation path for low-carbon transformation is analyzed using random forest algorithm within a high-dimensional data environment from the perspective of manufacturing industry ecosystem. The results indicate that effective factor reallocation for low-carbon transformation depends on breaking the dual segmentation of factors between regions and industries to facilitate flow of factors from shrub layer industries to canopy layer industries. Adjusting key factor combinations to fall within the optimal equilibrium interval of S-shaped or anti S-shaped partial dependence curves maximizes the marginal benefits of low-carbon transformation. Industries must upgrade their factor endowment structure to accumulate essential carrying capacities that support advanced manufacturing, leveraging the low-carbon transformation dividends of advanced factors inflow and technology spillover. Otherwise, aligning with regional factor comparative advantage to cultivate differentiated characteristic manufacturing industries offers a promising alternative, capitalizing on the low-carbon efficiency premium derived from specialized division of labor.

Detection and Location of High Impedance Fault on the Nigerian 330kV Transmission System Using Artificial Neural Network

The effect of the occurrence of high impedance fault (HIF) in power system networks results to low current signal which cannot be detected by the electrical equipment which results to fire outbreaks. Nigerian power system network has witnessed the occurrence of HIF which has led to fire outbreak in buildings and in minor cases grid collapse. In this paper, the performance of ANN in the detection and location of HIF was studied and determined. The transmission network located in south-south region of the Nigerian 330kV power system network was obtained and modeled in SIMULINK. The line distance was split into six points and implemented in the SIMULINK to obtain the current signals at each point of the lines. The current signals were used as the input data with the split distance utilized as the target to the ANN model. The ANN had three input neurons (each neuron represented the phase current signal), the hidden layer had five neurons with each neuron incorporating log sigmoid curve and the output layer having one neuron which was the split distance. The outcome had the least error deviation value of 0.0118 making the performance of ANN effective in the point location of HIF occurrence on the transmission line.

Simultaneous Reconstruction of Gas Concentration and Temperature Using Acoustic Tomography.

Acoustic tomography utilizes sensor arrays to collect sound wave signals, enabling non-contact measurement of physical parameters within an area of interest. Compared to optical technologies, acoustic tomography offers the advantages of low cost, low maintenance, and easy installation. Current research in acoustic tomography mainly focuses on reconstruction algorithms for temperature fields, while monitoring the composition and concentration of gases is significant for ensuring safety and improving efficiency, such as in scenarios like boiler furnaces and aviation engine nozzles. In excitable gases, the speed of sound exhibits an S-shaped curve that changes with frequency, a characteristic that could be potentially useful for acoustic tomography. Therefore, this study primarily discusses the quantitative calculation of gas concentration and temperature based on the dispersion of the speed of sound. By employing graphic processing and pattern matching methods, a coupled relationship of the dispersion of the speed of sound with gas concentration and temperature is established. The projection intersection method is used to calculate the concentration and temperature of binary and ternary gas mixtures. Combined with the inversion method, a joint reconstruction method for gas concentration fields and temperature fields based on the dispersion of the speed of sound is developed. The feasibility of the proposed simultaneous reconstruction method for temperature and concentration fields is validated using numerical simulations. Additionally, an acoustic tomography experimental system was set up to conduct reconstruction experiments for binary gas concentration fields and temperature fields, confirming the effectiveness of the proposed method.

In vitro antileishmanial activities of hydro-methanolic crude extracts and solvent fractions of Clematis simensis fresen leaf, and Euphorbia abyssinica latex.

As a result of increasing drug resistance, crossover resistance development, prolonged therapy, and the absence of different agents with innovative methods for implementation, the efficacy of recent antileishmanial medications is severely declining. So, it is vital to look for other medications from botanical remedies that have antileishmanial activity. The latex of Euphorbia abyssinica (E abyssinica) and the leaves of Clematis simensis fresen (C simensis) were macerated in methanol (80%). In vitro antileishmanial activity of the preparation was tried on promastigotes of Leishmania aethiopica (L aethiopica) and Leishmania donovani (L donovani) using resazurin assay, and fluorescence intensity was measured. One percent of dimethyl sulfoxide (DMSO) and media as negative control and amphotericin B as positive control were used. Additionally, hemolytic & phytochemical tests of the preparation were done. The mean and standard errors of each extract were evaluated and interpreted for statistical significance using one-way analysis of variance. From sigmoidal dose-response curves of % inhibition, half maximal inhibitory concentration (IC50) values were determined by GraphPad Prism and Microsoft Excel; outcomes were presented as mean ± standard error of mean of triplicate trials. P < .05 was statistical significance. The phytochemical screening of C simensis and E abyssinica confirmed the existence of steroids, phenols, tannins, saponins, alkaloids, terpenoids, flavonoids and glycosides. C simensis possesses antileishmanial activity with IC50 outcomes of 46.12 ± 0.03 and 8.18 ± 0.10 µg/mL on the promastigotes of L aethiopica and L donovani, respectively. However, E abyssinica showed stronger activity with IC50 outcomes of 16.07 ± 0.05 µg/mL and 4.82 ± 0.07 µg/mL on L aethiopica and L donovani, respectively. C simensis and E abyssinica have a less hemolytic effect on human red blood cells at low concentrations. The outcomes from this investigation demonstrated that the preparation of C simensis and E abyssinica indicated significant antileishmanial activity. Therefore, further in vivo assessment of antileishmanial, cytotoxicity activity and quantitative identification of secondary metabolites are highly recommended.

Separation of Perfluorooctanoic Acid from Water Using Meso- and Macroporous Syndiotactic Polystyrene Gels.

Per- and polyfluoroalkyl substances are an emerging class of contaminants that are environmentally persistent, bioaccumulative, and noxious to human health. Among these, perfluorooctanoic acid (PFOA) molecules are widely found in ground and surface water sources. A novel high surface area, meso- and macroporous syndiotactic polystyrene (sPS) wet gel is used in this work as the adsorbent of PFOA molecules from water at environmentally relevant PFOA concentrations (≤1 μg/L) and cleanse water to below the U.S. EPA's 2023 health advisory limit of 4 parts per trillion (ppt). The sigmoidal shape of the PFOA adsorption isotherm indicates a two-step adsorption mechanism attributed to the strong affinity of PFOA molecules for the sPS surface and molecular aggregation at solid-liquid interfaces or within the pores of the sPS wet gel. The adsorption kinetics and the effects of sPS wet gel porosity, pore size, and pore volume on the removal efficiency are reported. The adsorption kinetics is seen to be strongly dependent on pore size and pore volume.

Tracking of the melting front in tube-in-tube latent thermal energy storage heat exchangers

In this study, the shrinking solid regime is investigated in a high aspect ratio tube-in-tube latent thermal energy storage (LTES) heat exchanger by tracking the phase change front evolution. In the setup, water flows through the inner tube as heat transfer fluid (HTF) and the shell contains a paraffin RT35HC as phase change material (PCM). A series of melting experiments have been performed in which the HTF mass flow rate, HTF inlet temperature and initial PCM temperature were varied. During each experiment, the movement of the phase change front was tracked using a camera placed next to the PCM tube. The front position as a function of time follows an S-shape curve. The effect of the operating conditions on the evolution of the phase change front is analysed. It is found that the temperature difference between the HTF and PCM exerts a more pronounced influence on the front position compared to the HTF Reynolds number. Finally, a correlation was developed to determine the temporal evolution of the front position. This research contributes to a deeper understanding of phase change phenomena in LTES systems and the found correlation can be a valuable tool for predicting and optimizing the performance of tube-in-tube LTES heat exchangers.