Enthalpy Formulation Research Articles

A novel meshless radial basis reproducing kernel particle approach for 3D thermo-mechanical analysis of mushy zone phase-change problems

This paper presents a three-dimensional thermo-elastoplastic computational model for the analysis of phase change problems involving the mushy zone. The model utilizes a novel meshless radial basis reproducing kernel particle approach, incorporating a high-order kernel that integrates Gaussian and cosine functions. An energy balance equation for the entire domain is formulated using the effective heat capacity method, based on the enthalpy formulation. The governing equations are discretized using the Galerkin weak form to compute thermal residual stresses, with essential boundary conditions enforced through the penalty method. Plastic deformation is characterized using the von Mises criterion with isotropic hardening, and the strain term resulting from temperature-dependent material properties is incorporated into the incremental solution process. Determination of the plastic strain increment is based on the Prandtl–Reuss flow rule. The accuracy and efficiency of the proposed meshless approach were rigorously evaluated through numerical examples encompassing two- and three-dimensional problems. The computational results were compared against available analytical and validated numerical solutions. This comprehensive assessment substantiated the robustness and precision of the developed technique. The case studies presented elucidate the capacity of the novel meshless model to effectively predict temperature distributions and residual stress fields within mushy zone phase change phenomena, accommodating both regular and irregular geometries under various boundary conditions. Notably, the model demonstrated consistent stability and high accuracy across the spectrum of simulated scenarios, thus underscoring its potential as a valuable tool for investigating complex phase change processes.

Simultaneous close-contact melting on two asymmetric surfaces: Demonstration, modeling and application to thermal storage

The present study deals with melting in a geometry suitable for Latent-Heat Thermal Energy Storage (LHTES) systems, which are of importance for future industrial installations utilizing solar energy or waste heat. The intrinsically high thermal resistance of phase-change materials (PCM) can be remedied by taking advantage of close contact melting (CCM), where the solid phase is separated from a hot surface by only a thin liquid layer. The basic CCM takes place on a horizontal flat surface, but during the last decade its application in various finned LHTES units has been demonstrated experimentally and analyzed numerically.Specifically, the configuration studied in the present work is relevant to a horizontal double-pipe concentric storage unit with a longitudinally finned inner tube. While this rather simple geometry has been extensively studied in the past, the present work is completely novel in its demonstration and analysis of simultaneous close-contact melting on two generally asymmetric surfaces created by the longitudinal fins. A unique experimental apparatus is introduced, based on the so-called 'Mercedes' configuration of the fins. It is designed transparent, allowing for real-time observation of melting sequences. Close-contact melting is achieved by supplying heat to the outer shell of the unit: the solid phase is detached from the shell and moves, by translation and rotation, in the liquid phase. The results from these experiments demonstrate the feasibility of CCM on two asymmetric walls within this system, hinting at the potential for optimizing the melting rate by utilizing a larger portion of the extended surface for CCM.A key component of this study is the development of a reliable numerical approach, which goes beyond the limitations of widely-applied enthalpy-porosity method and combines the general enthalpy formulation, convective heat transfer and general rigid body motion that includes rotation. Therefore, a new numerical model has been devised, using an in-house code realized in MATLAB. A full set of the governing conservation equations is solved using a finite-difference framework, integrated with advanced numerical methods for the fluid-solid interaction and an enthalpy formulation for the phase change process. The model is validated carefully, and then numerical studies are conducted to elucidate the melting process.The present paper presents a further proof of the special role that close-contact melting (CCM) can play in properly designed thermal energy storage units and finned systems in general. It is demonstrated that the fins, when properly designed and oriented, can induce CCM in their vicinity, contributing to a very significant increase in the melting rate, which reflects charging of the unit.

New thermal solver for mitigating surface temperature instability in laser-induced heating

An accepted approach to computing laser-induced peak surface temperature is to employ the enthalpy formulation of the transient heat conduction equation [Grigoropoulos et al., Adv. Heat Transfer 28, 75–144 (1996); Sawyer et al., J. Laser Appl. 29, 022212 (2017)]. This approach is generally implemented using an explicit numerical scheme to solve the thermal transport equation. While it offers the advantage of modeling the solid-melt phase transition automatically, the approach results in instability-like behavior in the computed surface temperature. When laser-induced ablation becomes significant, the heating rate in the surface cell becomes unrealistically large. This results in spikes in the computed peak surface temperature due to large errors in calculating the heating rate. In this paper, we present a new approach, which we refer to as the Moving Frame Solver, that employs a moving-coordinate frame of reference, located at the receding evaporating surface. We also use an analytical representation for the phase transition region of the enthalpy-temperature relationship. The Moving Frame Solver combined with an implicit scheme leads to a stable solution without surface temperature, pressure, or velocity spikes. In other words, any instability in these computed parameters due to use of an explicit scheme (such as Dufort–Frankel) has been eliminated. Details of the new thermal solver and example calculations are presented. Numerical experiments suggest that the surface cell size needs to be small, ∼0.1 μm, to obtain a highly accurate solution with a typical metal such as aluminum. Using the Moving Frame Solver with a refined grid near the surface, but coarse elsewhere, enables accurate and stable surface temperature computation.

Simulation of Heat Transfer during Paraffin And Gallium Melting and Solidification Processes Utilizing Star CCm+

Energy storage systems are essential as the world works to minimize its dependency on fossil fuel energy for environmental and economic reasons. Because of their high capacity for latent heat storage. The numerical study of benchmark cases of solidification and melting was undertaken, and the results of these investigations are presented in this project. Numerical analysis is conducted to examine the brief solidification process of a pure liquid phase-change material within a rectangular enclosure when natural convection is present. The horizontal boundaries are both taken to be adiabatic, with one vertical barrier maintained at a temperature below the material's melting point and the other above. In this work, a numerical investigation of the melting of wax (namely N-octadecane) is presented. The numerical simulations of the experiments were carried out using STAR CCM+, and the results were compared with the results of other numerical simulations (FLOW 3D). The numerical simulations of gallium melting were carried out with a commercial code, STAR CCM+, which captures the solid-liquid interface with a fixed grid. This software captures the solid-liquid interface for phase change simulations in complex geometries with the enthalpy formulation technique. In addition, it demonstrates that computational fluid mechanics has reached a state of development where it permits reliable flow computations with solidification and melting. Casting with metal melts can be studied to provide information to engineers during the design process of new casting tools. The available simulation tools can also be used to predict existing casting processes and determine the origins of defects. The key findings are as follows: The interface shape during the solidification of gallium from above is always determined in large part by anisotropy in heat conductivity and interface growth morphology. Natural convection in the liquid slows down the rate of melting and adds more complexity to the morphology and transport mechanisms at the interface.

Numerical analysis of the influence of geometry parameters on charging and discharging performance of shell-and-tube latent thermal energy storage with longitudinal fins

In this paper, heat transfer during charging and discharging processes in longitudinally finned vertical shell-and-tube latent thermal energy storage (LTES) has been numerically analyzed. The influence of three different LTES geometry parameters; LTES aspect ratio (defined as the ratio between the LTES height and tube pitch), fin number and fin thickness on the LTES thermal performance during charging and discharging has been evaluated. Mathematical model, describing transient three-dimensional problem of fluid flow and heat transfer during phase change of the phase changed material (PCM) has been defined using the enthalpy formulation. The solution was obtained numerically, using the finite volume method and ANSYS Fluent as the numerical solver, where existing numerical procedure was expanded with a set of self-written user-defined functions to simulate heat transfer during the PCM phase change. The model and numerical procedure have been validated by comparing the numerical results to the results from experimental measurements, obtained on a constructed LTES tank which uses paraffin RT 25 as the PCM and water as the heat transfer fluid (HTF). Using the experimental LTES configuration as reference, LTES thermal performance has been evaluated according to two performance indicators; accumulated/released thermal energies in defined charging/discharging times and times at which the PCM is completely melted/solidified. In the analysis, LTES aspect ratio varied from 6.3 to 12.8, fin number varied from 4 to 12, while fin thickness varied from 0.5 mm to 4 mm. For selected ranges of investigated geometry parameters, the LTES configuration with the aspect ratio of 12.8 and the LTES configuration with 12 fins are the most favorable in terms of both performance indicators, while LTES configurations with fin thicknesses of 2 and 4 mm provide the most favorable option in terms of accumulated/released thermal energy and time at which the PCM is completely melted/solidified, respectively. Obtained results provide practical guidelines for designing longitudinally finned shell-and-tube LTES. Further investigations will be focused on obtaining optimal values of all three investigated parameters based on various objectives.

Improving the thermal efficiency of a solar water heater by using PCM

The study consists in comparing the thermal behavior of two solar water heaters: a conventional solar water heater and an PCM solar water heater. The aim of this work is to numerically study the importance of phase change materials (PCMs), by analyzing their potential for storing solar energy by latent heat of a phase change material. in an installation to produce domestic hot water. The mathematical model used to simulate the phase change in the PCM is based on the enthalpy formulation of the energy conservation equation. The finite difference method is used for the numerical resolution of the selected model. To validate the mathematical model, a comparison of the numerical predictions made with an analytical solution. The results show that the energy stored by PCM solar water heater is almost 320% more than the energy stored by conventional solar water heater.

Existence and uniqueness for a convective phase change model with temperature–dependent viscosity

In this article, we consider a class of phase change model with temperature–dependent viscosity, convection and mixed boundary conditions on a bounded domain that reflect melting and solidification in a variety of real-world applications, such as metal casting and crystal growth. The mathematical model, which is based on the enthalpy formulation, takes into consideration the thermophysical differences between the liquid and solid states. The moving liquid-solid interface is explicitly fulfilled as the energy and momentum equations are solved over the full physical domain. Under particular assumptions, we derive various a priori estimates and prove well-posedness results. Numerical simulation of the model employed in the paper is presented as an illustration of an example of a melting problem.

A molecular dynamics study of thermal conductivity and viscosity in colloidal suspensions: From well-dispersed nanoparticles to nanoparticle aggregates

This study investigates the microscopic transport behavior of nanofluids addressing some debatable points including the anomalous thermal conductivity (κ), against the predictions of classical effective medium theories. International Nanofluid Property Benchmark Exercise (INPBE) [J. Buongiorno et al., J. Appl. Phys. 106 (2009) 094312] has shown that no such anomaly found in well-dispersed nanofluids after conducting experiments for range of different types of nanofluids. However, a number of molecular dynamics based studies reported otherwise making inconsistent conclusion with INPBE. In this work, it is argued that the over predicted κ values reported in previous computational studies can be attributed to the ill-defined partial enthalpy formulation of the Green-Kubo method for multicomponent systems. Present study begins by addressing this issue via non-equilibrium molecular dynamics and shows that the results are in agreement with the conclusions of INPBE. Further, it is shown that the contribution of potential micro-mechanisms such as micro-convection due to Brownian motion, and the solid-like liquid layering are either absent or suppressed by the interface thermal resistance. The observed decreasing trend of viscosity enhancement to thermal conductivity enhancement ratio (Cη/Cκ) with increasing particle size indicates the improved heat transfer performance in nanofluids with larger nanoparticles. The effect of nanoparticle aggregation, the proposed originative mechanism of anomalous κ, is evaluated arranging nanoparticles as chain-like structures. A 67% improvement in κ is achieved with negligible viscosity variation. This rapidly reduces Cη/Cκ indicating better heat transfer performance with the presence of conductive paths due to the aggregation or in general extended nanostructures.

Numerical modelling of hyperbolic phase change problems: Application to continuous casting

Heat diffusion processes are generally modeled based on Fourier’s law to estimate how the temperature propagates inside a body. This type of modeling leads to a parabolic partial differential equation, which predicts an infinite thermal wave speed of propagation. However, experimental evidence shows that diffusive processes occur with a finite velocity of thermal propagation in many applications. In this paper, we develop a mathematical formulation to predict the finite speed of heat propagation in multidimensional phase change problems. The model generalizes the enthalpy formulation by adding a hyperbolic term. The governing equations are simulated by the finite element method. The proposed model is first verified by comparing numerical and experimental results illustrating the difference between the infinite and finite propagation velocity for heat inside biological tissues. Then, the results of the two and three-dimensional numerical solution of the continuous steel casting process are presented. We will illustrate that the effects of the initial conditions vanish faster when using the parabolic equation, while they persist in the hyperbolic modeling approach. The results demonstrate significant differences in the initial thermal dynamics and at the solid-liquid interface position when adding the hyperbolic term. The changes are more noticeable in the regions of the steel beam where rapid heat loss and, consequently, faster phase change occur.

The volumetric thermal capacitor method for nonlinear heat transfer in phase-change materials

Recently, there was an increase in the study of phase change materials mainly due to thermal storage studies or modeling of manufacturing processes. Usually, these problems, which have a moving boundary, are solved with the enthalpy formulation. This paper presents a new methodology to address the unsteady enthalpy term in the heat diffusion equation. The Volumetric Thermal Capacitor method is developed to solve the non-linear heat diffusion equation with the enthalpy function. The alternative method applies the integration by parts rule to divide the enthalpy term into three components. This approach allows the use of non-linear thermal properties without simplifications or generalized considerations. The method is compared to the classical formulation. The routines were implemented and executed in parallel on a CUDA-C in-house code. Simulated and lab-controlled experiments validated the proposed methodology. The results highlighted the differences between the models for experiments with intense heat flux. The proposed model presented a better agreement with the experimental data than the classical model for high-temperature cases. The Volumetric Thermal Capacitor method proved to be more stable and accurate than the classical method.

Simple model for the laser powder interaction during direct metal deposition

In this paper, a simple model is presented for simulating laser and powder interaction during a coaxial laser cladding process, which is a very important part of direct metal deposition. The powder is delivered coaxially with the laser. The idea is to completely melt the powder before it hits the substrate. The laser is being attenuated as it propagates through the cloud of powders. The laser beam that penetrated through the cloud is used to melt the substrate. The track of 3D printing is formed by resolidification as the laser or the substrate scans. The laser attenuation is modeled by the Beer–Lambert law. The heat transfer within each powder is modeled by a lumped capacitance method. We use an enthalpy formulation to easily model and track the melting. The resulting 1D differential equation is solved numerically using Euler's method. The enthalpy and temperature plot is presented. We make use this model to determine the standoff distance. The effects of powder velocity, laser power, powder number density, and powder radius on the standoff distance are investigated and presented.

A modified electrolyte non‐random two‐liquid model with analytical expression for excess enthalpy: Application to theMEA‐H2O‐CO2system

AbstractAccurate thermodynamic properties of electrolyte systems are critical for the design and operation of many chemical processes. A comprehensive description of the thermodynamic framework for multielectrolyte mixed solvent systems is presented, where the parameter structure of the symmetric electrolyte‐non‐random two liquid (e‐NRTL) model is reformulated and a thermodynamically consistent and analytically derived formulation for the excess enthalpy is developed from the e‐NRTL model. The refined parameter structure of the e‐NRTL model avoids numerical singularities of the analytical formulation for the excess enthalpy in the absence of ionic species and extends the derived excess enthalpy formulation to non‐electrolyte systems. The thermodynamic framework is demonstrated for the MEA‐H2O‐CO2case study using experimental data on thermodynamic quantities for the binary MEA‐H2O system and the ternary MEA‐H2O‐CO2system. The model is implemented in Pyomo and will be available for release in the Institute for the Design of Advanced Energy Systems (IDAES) computational platform.

Efficient utilization of PCM in building envelope in a hot environment condition

The thermal performance of the building envelope must be adjusted to promote sustainability, reduce energy consumption, and reduce greenhouse gas emissions. In this case, the elements' thermal resistance and heat storage capacity are critical. Due to their high energy density and ability to absorb/release heat under nearly isothermal conditions, phase change materials are extremely competitive and have a wide range of applications. The effectiveness of using PCM in the building envelope is studied in this investigation under exceptionally hot climatic conditions. A thermal model is developed based on the nonlinear transient heat conduction equation to predict the time-dependent thermal response of a multilayer building envelope wall. The enthalpy formulation is used to account for the phase change process, and the mathematical model is solved numerically using the finite element method. A typical exterior multilayer wall's thermal performance is studied and utilized as a benchmark. Then, at various points throughout the wall, a PCM layer is incorporated. The effect of the PCM on wall temperature distribution, heat movement into the interior area, and the fraction of molten material in the PCM layer is investigated. Optimization analysis is used to establish the suitable PCM melting temperature interval, with the heat flow at the internal surface of the wall as the objective function to be minimized. The thermal energy flow into the internal space can be reduced by approximately 50% when the PCM settings are improved. The findings of this investigation demonstrate that the suggested computational model is effective in calculating the optimal PCM, resulting in a significant improvement in the external wall's thermal performance. Integrating PCM into the building envelope is a viable technique for the region, as it has the potential to reduce the amount of heat entering the building, hence lowering the air conditioning load and lowering energy consumption.

Computational Model of Shell and Finned Tube Latent Thermal Energy Storage Developed as a New TRNSYS Type

This paper presents the development of a computational model of latent thermal energy storage (LTES) in a shell and tube configuration with longitudinal fins. The model describes the physical process of transient heat transfer between the heat transfer fluid (HTF) and the phase change material (PCM) in LTES. For modeling the phase change of the PCM, the enthalpy formulation was used. Based on a one-dimensional computational model, a new Trnsys type was developed and written in Fortran. Validation of the LTES model was performed by comparing numerically and experimentally obtained data for the melting and solidification of paraffin RT 25 as the PCM and water as the HTF. Numerical investigations of the effect of HTF inlet temperature and HTF flow rate on heat transfer in LTES confirmed that significant improvement in heat transfer between the HTF and PCM could be achieved by increasing the HTF inlet temperature during charging or decreasing the HTF inlet temperature during discharging. Increasing the HTF flow rate did not significantly improve the heat transfer between the HTF and PCM, both during charging and discharging. The presented, experimentally validated LTES model could be used to analyze the feasibility of integrating LTES into various thermal systems and ultimately help define the specific benefits of implementing LTES systems.

Simulating Thermal Interaction of Gas Production Wells with Relict Gas Hydrate-Bearing Permafrost

The thermal interaction of a gas production well with ice-rich permafrost that bears relict gas hydrates is simulated in Ansys Fluent using the enthalpy formulation of the Stefan problem. The model admits phase changes of pore ice and hydrate (ice melting and gas hydrate dissociation) upon permafrost thawing. The solution is derived from the energy conservation within the modeling domain by solving a quasilinear thermal conductivity equation. The calculations are determined for a well completion with three casing strings and the heat insulation of a gas lifting pipe down to a depth of 55 m. The thermal parameters of permafrost are selected according to laboratory and field measurements from the Bovanenkovo gas-condensate field in the Yamal Peninsula. The modeling results refer to the Bovanenkovo field area and include the size of the thawing zone around wells, with regard to free methane release as a result of gas hydrate dissociation in degrading permafrost. The radius of thawing around a gas well with noninsulated lifting pipes operating for 30 years may reach 10 m or more, while in the case of insulated lifting pipes, no thawing is expected. As predicted by the modeling for the Bovanenkovo field, methane emission upon the dissociation of gas hydrates caused by permafrost thawing around producing gas wells may reach 400,000–500,000 m3 over 30 years.

A precise time-domain expanding boundary element method based on enthalpy formulation for non-isothermal phase change problems

A precise time-domain expanding boundary element method (PTEBEM) based on the enthalpy formulation is developed for solving non-isothermal phase change problems in this paper. Assume that temperature and enthalpy are independent field variables, and expand all variables over a time period. This allows the variation of variables to be described more accurately and the nonlinear governing equation to transform into a linear recursive form. Subsequently the boundary element method (BEM) is employed to solve recursive problems based on a fixed grid, and the radial integration method (RIM) is used to convert the resulting domain integrals into equivalent boundary integrals. In the recursive solution process, temperature and enthalpy are connected through the relationship between the two. Finally, a self-adaptive computation criterion is proposed to ensure sufficient computational accuracy. The phase change interfaces can be given by interpolation of the temperature field. No additional nonlinear iterations are required throughout the simulation. The calculation results are satisfactory and prove the accuracy and robustness of the proposed method.

Model of a non-transferred arc cascaded-anode plasma torch: the two-temperature formulation

This study presents an analysis of a three-dimensional unsteady two-temperature simulation of atmospheric pressure direct current electric arc inside a commercial cascaded-anode plasma spray torch; it coupled the arc model with the torch electrodes and used an open-source computational fluid dynamics software (code_saturne). The previously published models of plasma spray torch either deal with conventional plasma torches or assume local thermodynamic equilibrium in cascaded-anode plasma torches. The paper presents the computation of the two-temperature argon plasma properties, compares two enthalpy formulations that differ in association of the ionization part of enthalpy and finally demonstrates the influence of the radiation heat loss data by comparingthe results for two different literature sources. It is the first to compare different enthalpy formulations in the context of plasma torch and discuss the differences in terms of the enthalpy gains and losses. It also explains why an unphysical simulation artifact of electron temperature lower than the heavy species temperature can occur in simulated plasma flow. The solution, then, consists in associating the ionization part of enthalpy to electrons and selecting the appropriate source of the data of radiation heat loss. However, negligible thermal non-equilibrium persists even in the hot core of electric arc, which ensures that the heavy species are heated up by collisions with electrons. The flexibility of the open-source software allows all the necessary modifications and adjustments to achieve satisfactory simulation results. Thus, the paper could be considered as a manual for development of a plasma spray torch model.

A mini-review on numerical approach of microstructure prediction in eutectoid steel

Steels can exhibit various properties depending on their compositions, phases, and microstructures developed during heat treatment. The alloy of Fe-C limited to 0.8% of carbon has been classified as eutectoid steel, which has a crucial position in the Industrial world. Different Numerical methods tried to predict the generation and amount of volume of microstructures during the heat treatment process. The heat treatment process is an inherent and antediluvian metallurgical activity in which materials are constrain to thermal treatment to alleviate internal stresses, curtail brittleness and upgrade machinability. During heating and cooling, change in microstructures evolves, resulting in the variation in physical and mechanical properties of metals, influencing further processing and operation. It is essential to know about microstructural development during the heat treatment process to predict mechanical properties and stress–strain generation during operation. The heat transfer rate during the process (Heat Treatment) plays a vital role during phase transformation, which depends upon local cooling conditions and phase transformation heat (enthalpy) evolution, which changes the thermo-physical properties of the metal. Many different methods formulate heat transfer numerically. Some strategies to predict microstructure development are the finite element method (FEM), finite difference method (FDM), enthalpy formulation, & inverse heat conduction process (IHCP). This article has tried to overview various numerical approaches made for microstructure prediction for eutectoid steel and the effect of heat treatment on it.

Numerical evaluation of the latent heat thermal energy storage performance enhancement by installing longitudinal fins

Charging and discharging processes inside the shell-and-tube type latent heat thermal energy storage, which uses technical grade RT 25 paraffin as the phase change material and water as the heat transfer fluid, have been numerically investigated in order to evaluate the enhancement of the latent storage thermal performance when longitudinal fins are installed onto the tubes in comparison to the plain tube configuration. The study of latent storage tank performance enhancement using low thermal conductivity material, such as paraffin, is necessary to increase the efficiency of solar energy systems and reduce the operating cost of the system. Transient problem of three-dimensional fluid flow and heat transfer has been described with the defined mathematical model, in which simulation of phase change heat transfer is incorporated through the enthalpy formulation. Governing equations, with appropriate initial and boundary conditions, have been solved iteratively using the finite volume method in the ANSYS Fluent numerical solver using an upgraded numerical procedure. In order to validate the numerical procedure, numerical results have been compared with experimental measurements, obtained from experimental investigations carried out on the constructed shell-and-tube latent storage with longitudinal fins, and good agreement between numerical and experimental results is observed. The comparison of the two studied configurations shows a significant improvement in the overall heat transfer with the installation of fins in both the charging and discharging cycles, with a 52% reduction in the total melting time and a 43% reduction in the total solidification time compared to the plain tube configuration. Relative accumulated/released energy, defined as the ratio of accumulated/discharged energy and maximum storage capacity for the plain tube configuration, represents comprehensive latent storage efficiency and has been introduced as a performance enhancement metric. Finned tube latent storage is fully charged at relative accumulated energy value of 0.949, since maximum value of 1 can never be reached because of the decreased phase change material's mass due to fins. The same value is achieved 3 h later in the plain tube configuration. Similarly, finned tube latent storage is fully discharged at relative released energy value of 0.948, and the same value in plain tube configuration is reached 12 h later. Clearly, reduction in phase change material mass and obstruction of natural convection in the liquid phase due to installation of fins are negligible on the overall latent storage thermal performance during both charging and discharging. Results obtained by this investigation will be used as guidelines for further analyses focused on defining the optimal fin configuration and geometry parameters of shell-and-tube latent storage tanks.

The effects of fins number and bypassed energy fraction on the solidification process of a phase change material

Nowadays, utilizing latent heat thermal energy storage systems containing phase change materials (PCMs) has been considered one of the best ways for integrating and optimizing thermal energy systems. Although using fins has been suggested by many researchers for the heat transfer enhancement in these systems, this technique is not sufficient in some cases. So, finding its reasons is the main purpose of this paper. For this aim, four different cylindrical containers, one without fins and the others with radial fins, were intended. Then, solidification of the PCM inside the containers under the constant and time-dependent first, second, and third type boundary conditions was modeled by the finite volume method based on the enthalpy formulation. To analyze fins performance, bypassed energy fraction (β) criterion was proposed. The results show that under the first type boundary condition, the value of β is zero, and the fins have a major effect on the heat transfer enhancement, but under the second and third type boundary conditions, the value of this parameter is significant, and the fins have a lower effect. Furthermore, it is found that by increasing the fins number, the value of β and complete freezing time decreased. The results of this study were compared and validated with the results of the analytical approach.