⚡ electrical engineering

Numerical and Experimental Characterization of Melting Kinetics in Sub- Zero Thermal Energy Storage Units: Influence of Enclosure Geometry

This study combines numerical modeling and experimental validation to demonstrate that rectangular enclosure geometries optimize melting kinetics for rapid thermal discharge in sub-zero energy storage, while triangular shapes hinder convection and cylindrical designs offer the highest predictive accuracy.

Original authors: Ankit Kumar Deshmukh, P.S. Minz, Rohit H. K, Sumit Mehta, Chitranayak Sinha

Published 2026-07-13

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Ankit Kumar Deshmukh, P.S. Minz, Rohit H. K, Sumit Mehta, Chitranayak Sinha

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a giant block of frozen ice cream that you need to thaw out, but instead of a spoon, you're using the shape of the container itself to control how fast it melts. That's exactly what this team of researchers at the ICAR-National Dairy Research Institute did, but with a special "frozen juice" (a 5% saltwater solution) instead of ice cream, and they were testing how different box shapes affect the speed of melting for cold storage units.

Think of the four shapes they tested—rectangular, square, cylindrical, and triangular—as four different race cars. They all started the race at a chilly -15.0°C, and the goal was to see which one could heat up the fastest when placed in a warm room at 30°C.

The Fastest Car: The Rectangle
The rectangular container was the clear winner, zooming ahead of the pack. Because it has flat walls and a high surface area (like a wide-open window letting in a breeze), it allowed the heat to rush in and create swirling currents inside the liquid, just like hot air rising in a room. In just 50 minutes, this rectangular cell managed to heat its contents all the way from -15.0°C to 12.0°C. It hit 0°C (the point where ice turns to water) in just 40 minutes. The researchers found that once the temperature passed a certain "melting band" between -5°C and -2°C, the heat started moving even faster thanks to these natural swirling currents.

The Slowpoke: The Triangle
On the other end of the track, the triangular container was the slowest. Imagine trying to run through a hallway with sharp, pointy corners; you'd get stuck, right? That's what happened to the heat inside the triangle. The sharp points acted like traffic jams, trapping the fluid and stopping the heat from moving around. After the full 50 minutes, the triangular cell was still stuck in the cold, only reaching -0.63°C. It never even fully thawed out! This suggests that if you want something to stay cold for a long time, a triangle is actually a great shape because it holds onto the cold so stubbornly.

The Steady Runner: The Cylinder
The cylindrical shape was the most predictable and smooth. It didn't have any sharp corners to cause traffic jams, so the heat moved in evenly from all sides. While it wasn't as fast as the rectangle, it was very reliable. The computer model used to predict how the cylinder would behave was incredibly accurate, matching the real-world experiment almost perfectly with a score of 0.9826 (on a scale where 1 is perfect). It reached 3.97°C after 50 minutes.

The Middle Ground: The Square
The square container was somewhere in between. It was slower than the rectangle because its symmetry didn't help the heat swirl around as effectively, but it was faster than the triangle. After 50 minutes, it reached just 0.1°C.

Did the Computer Get it Right?
The researchers didn't just guess; they built a digital twin of these containers using Python code and then tested real metal boxes in a lab to see if the computer was telling the truth.

For the cylinder, the computer was spot on, with a tiny error of less than 1°C.
For the rectangle, the computer was still very good, though it got a little less accurate as the melting finished up.
For the triangle and square, the computer struggled a bit more. It tended to guess that the temperature was lower than it actually was, especially in the sharp corners where the math gets tricky. Even so, the computer's predictions were still pretty solid, staying above an accuracy score of 0.85 for all shapes.

The Big Takeaway
The main lesson here is that the shape of your container is a superpower. If you need to cool down milk or food super fast, a rectangular box is your best friend because it lets heat (or cold) move quickly. But if you need to keep something cold for a long time without it warming up too fast, a triangular or square shape acts like a thermal blanket, slowing everything down. The researchers proved that even small changes in design can completely change how a thermal storage unit works, and they have a very reliable computer model to help engineers pick the right shape for the job.

Technical Summary: Numerical and Experimental Characterization of Melting Kinetics in Sub-Zero Thermal Energy Storage Units

Problem Statement
The increasing demand for efficient Thermal Energy Storage (TES) in cold chain logistics, particularly for dairy applications, necessitates container designs that optimize heat transfer rates. While Phase Change Materials (PCMs) are recognized for their high latent heat capacity, the influence of enclosure geometry on melting behavior remains a critical, yet under-explored variable in system design. Existing literature often focuses on enhancing heat transfer through additives or complex finned structures, leaving a gap in the direct comparison of elementary container geometries—specifically triangular and square enclosures—under uniform thermal conditions. This study addresses the need to isolate the effect of shape on melting kinetics to inform the design of portable cooling units.

Methodology
The research employed a dual approach combining numerical simulation and experimental validation to evaluate four distinct cross-sectional geometries: rectangular, square, cylindrical, and triangular.

Experimental Setup: Custom stainless steel (SS-304) containers were fabricated with a consistent internal volume of 148 cm³ (Iso-Volumetric Standard) to isolate shape effects. The PCM used was a 5% sodium chloride (NaCl) aqueous solution, selected for its sub-zero eutectic properties suitable for dairy cold chains. Containers were frozen to an initial temperature of -15°C and subsequently exposed to a 30°C convective environment (h = 9.0 W/m²K). Temperature evolution was monitored using PT-100 sensors at the geometric center and inner walls.
Numerical Modeling: A Python-based simulation utilizing SciPy's solve_ivp function modeled transient heat transfer. The model accounted for conduction, natural convection within the liquid phase, and latent heat of fusion. The effective heat capacity method was used to simulate the phase change interval (-5°C to -2°C). The governing equations included transient heat diffusion and convective boundary conditions.
Validation: Model accuracy was assessed by comparing simulated center-point temperatures against experimental data at 10-minute intervals over a 50-minute duration. Statistical metrics included the Coefficient of Determination ( $R^2$ ), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Bias.

Key Results
The study revealed significant variations in melting kinetics driven by geometric constraints:

Rectangular Geometry (Optimal for Rapid Discharge): This configuration demonstrated the fastest thermal response, raising the PCM temperature from -15.0°C to 12.0°C within 50 minutes. The high surface-area-to-volume ratio and planar walls facilitated intense buoyancy-driven natural convection loops once the PCM passed the initial phase-change band. It reached 0°C within 40 minutes.
Triangular Geometry (Optimal for Thermal Buffering): This shape exhibited the slowest melting kinetics, terminating at -0.63°C after 50 minutes. The acute vertices acted as fluid stagnant zones, choking convective movement and creating localized thermal resistance. This delay in phase change suggests suitability for applications requiring sustained thermal buffering.
Cylindrical Geometry (Highest Predictive Fidelity): The cylindrical cell showed moderate thermal response (reaching 3.97°C at 50 minutes) but achieved the highest correlation between simulation and experiment ( $R^2 = 0.9826$ , RMSE = 0.7896°C). Its cornerless, symmetric boundaries allowed for smooth, concentric temperature gradients, minimizing modeling errors.
Square Geometry: Performed intermediately, with an $R^2$ of 0.951. Its symmetry allowed for balanced thermal propagation but inhibited the formation of the strongest natural convection currents compared to the rectangular shape.

Model Performance and Limitations
The numerical model maintained robustness across all configurations, with $R^2$ values exceeding 0.85. However, the study noted specific challenges in modeling sharp corners. The triangular and square geometries exhibited positive biases (simulation underestimating actual temperatures), attributed to the difficulty of capturing anisotropic heat flows and restricted fluid loops at acute vertices. Conversely, the cylindrical model showed a slight negative bias, indicating a minor systematic overestimation of temperatures.

Significance and Claims
The paper claims that container geometry is a primary determinant of PCM performance, acting as either a bottleneck or a catalyst for heat transfer. The findings provide practical design guidelines for industrial applications:

Rectangular geometries are identified as optimal for high-flux energy discharge scenarios requiring rapid temperature changes, such as quick-chilling facilities.
Triangular and square geometries are positioned as effective solutions for systems requiring slow, controlled, and sustained release of latent heat.
Cylindrical geometries offer superior predictive stability for modeling uniform thermal environments.

The study concludes that even subtle design decisions regarding cell geometry significantly influence the efficiency of PCM-based thermal energy storage systems, offering a foundational model for optimizing portable cooling units without relying solely on complex additives or fin structures.

More like this