Heat Capacity Method Research Articles

Numerical investigations of a latent thermal energy storage for data center cooling

The thermal performance of a 115 L latent heat storage prototype for cooling data centers was investigated. Experimentally, the heat transfer power and heat absorbed by the heat exchanger during the charging and discharging processes were measured at two flow rates (5 and 10 L/min). Numerically, two phase-change models were developed using the enthalpy and effective heat capacity methods, respectively. The results showed that the enthalpy method provides an overall better prediction of the absorbed heat, whereas the other method only agrees well with the measured results during the melting process. Thus, it is suggested that further modification of the effective heat capacity with temperature improves the agreement between the results. For a volume flow rate of 5 L/min, the average heat transfer power predicted by the enthalpy model was 2290 W during the melting process and > 920 W during the solidification process due to the smaller temperature difference for heat transfer caused by supercooling. The prototype achieved the highest average heat exchange capacity rate when melted to a 50% of its total capacity. This study provides a baseline for predicting and improving the thermal performance of latent heat storage.

Numerical simulation on jet impingement heat transfer with microcapsule phase change material suspension: Single jet and array jet

The heat transfers on the single and array jet impingement with microcapsule phase change material (MEPCM) suspension are numerically investigated. The equivalent heat capacity method and DPM model are employed to treat the latent heat absorption and motion of the MEPCM particles in suspension, respectively, as well as the VOF method for tracking the free surface from suspension to air. The results show that the latent heat absorption and disturbance effect of the MEPCM particles can significantly improve the heat transfer of the suspension compared to the water. There exists an optimal jet distance at ΔL/D = 4.2 and an optimal suspension concentration at ηp = 5% to achieve the optimal heat transfer. The jet inlet temperature has a favourable range for the heat transfer enhancement, −0.83 <θj < 0.39, which is lower than the phase change temperature range of MEPCM particles. Compared to single jet, the array jet may provide a better heat transfer although the cross-flow between neighboring jets weakens the heat transfer of central jet column. Both of hole number and hole spacing for array nozzle have a non-monotonic effect on the heat transfer, with the optimums at N = 19 and S/D = 7, respectively.

A novel method for simultaneous determination of thermophysical properties and boundary conditions of phase change problems based on element differential method

Thermophysical properties and boundary conditions for phase change thermal management systems are challenging to be accurately determined, due to the phase change heat transfer phenomenon and complex working conditions. In this work, the element differential method (EDM) and a gradient-based method are combined to simultaneously predict thermal conductivity, mass specific heat, and boundary heat flux in two-dimensional (2D) and three-dimensional (3D) inverse phase change problems, for the first time. The multi-parameter identification for the 3D physical model with phase change is more general than the previous attempts. Moreover, the effective heat capacity method is employed to deal with phase change problems, to improve efficiency. The sensitivity coefficient is accurately determined by the complex-variable-differentiation method (CVDM) in the multi-parameter prediction. Finally, the effect of measurement points, measurement errors, and initial guessed values on the multi-parameter identification are investigated. This study demonstrates that the present method has good accuracy, efficiency, stability, and robustness in dealing with transient nonlinear inverse problems during phase change process.

Research on indoor dynamic temperature based on circulating water heating

During the heating season, cities in northeast China primarily emphasize the implementation of large-scale CHP central heating systems. However, the heat-electricity constraints associated with these heating units hinder the integration of clean energy sources such as wind power, photovoltaic, and other renewable energies. Despite efforts to reduce carbon emissions and address concerns related to urban haze formation, energy conservation, and emission reduction, coal remains the predominant energy source for heating.In light of these challenges, this paper aims to investigate the heat transfer characteristics of buildings during the heating season. It also examines the feasibility of implementing heating regulations and provides a theoretical foundation for establishing a regional heat model that incorporates low-carbon energy islands. The proposed model combines wind power, photovoltaic power generation, and other renewable energy sources supplemented with coal power.By employing the concentrated heat capacity method, this study develops a mathematical model to simulate the dynamic thermal process involved in heating buildings. The model encompasses various components, including the dynamic heat transfer model of the building’s envelope structure, which considers its heat storage characteristics, as well as the radiator model and the indoor air heat balance equation. Furthermore, the model comprehensively accounts for the influence of different indoor and outdoor disturbances on the heat transfer process, including the effects of solar radiation.To validate the model, a simulation program is implemented using Matlab. This program is capable of hourly calculations to determine the indoor temperature. By comparing the simulated temperature values with the measured ones, the rationality and accuracy of the model are verified.

Computational Modeling of an Earth-Air Heat Exchanger Integrated with Phase Change Materials: A Case Study Performed for the Viamão City, Rio Grande do Sul State, Brazil

The earth-air heat exchanger (EAHE) is a sustainable option that allows the electrical energy consumption reduction in buildings. The objective of this study is to evaluate the influence of the incorporation of the thermal energy storage principle based on phase change materials (PCM) into the EAHE on its thermal potential. For this, a three-dimensional numerical model of the PCM coupled to the EAHE (EAHE-PCM) was developed based on the effective heat capacity method and adapted to the climatic conditions and soil characteristics of the Viamão city, Rio Grande do Sul State, Brazil. It was found that for a duct diameter and length of 0.11 m and 25.77 m, the incorporation of PCM to EAHE improved by 8.90% and 3.97% in the average annual thermal potential of heating and cooling, respectively. In addition, the average monthly thermal potential increased 19.70% (heating) and 8.48%(cooling), for the months of May and December, respectively, when the PCM was integrated into the system.

Thermo-fluid performance enhancement in a long double-tube latent heat thermal energy storage system

Thermodynamic analysis and flow rate optimization for the long double-tube latent heat thermal energy storage systems (LHTESS) are performed. Computer modeling is carried out using created software and is based on a developed 3D non-steady non-linear coupled thermo-fluid mathematical model that combines the apparent heat capacity method and finite volume method for the sodium nitrate (NaNO3) phase change materials (PCM) and for the Syltherm800 heat transfer fluid (HTF). The mathematical model and numerical algorithm are verified through comparison with experimental data. It is found that the laminar flow of HTF ensures the uniform temperature in PCM and in HTF and this temperature is equal to the PCM melting temperature. It is proved that the PCM and HTF average temperatures along the LHTESS can be equalized using spatial and temporal velocity variations of the HTF. Mutual impact of the heat transfer and fluid mechanics parameters in the long double-tube LHTESS was studied by correlation between Nusselt numbers and Reynolds numbers. The optimal HTF flow rate parameters were analyzed based on the non-equilibrium thermodynamics method. It is discovered that the laminar regime 0 < Re < 2000 and the turbulent regime 12000<Re<15000 are the most optimal for long double-tube LHTESS of the described geometry.

Numerical Simulation of Effect of Inclination Angle on Heat Storage Properties of Phase Change Paraffin

In order to explore the heat storage properties of phase change paraffin, a calculation model for melting heat storage of phase change paraffin was established based on the equivalent heat capacity method. A finite element software (COMSOL) was used to study the influence of different inclination angles on heat storage properties of phase change paraffin. The results show that the melting process of phase change paraffin is determined by heat conduction and natural convection heat transfer, natural convection heat transfer plays a significant role in the process of heat storage in phase change paraffin. Phase change paraffin exhibits distinct melting heat storage efficiency under different inclination angles. When changes from -90° to 90°, the melting time of paraffin decreases gradually. When , the melting time of paraffin is the slowest, when , the melting time of paraffin is the fastest, and the melting speed of paraffin is increased by about 8.6 times.

Consistent description of phase-change processes in substances with density contrast: A finite volume based approach

Phase-change is an important phenomenon and usually it causes a concomitant change in the density of the underlying materials. As applications of phase-change grow, it is important to develop numerical tools that can model this phase-change behaviour accurately; many efforts have improved the ability of numerical algorithms to do so; however, with materials in which phase-change causes significant change in density, these approaches are inadequate in predicting the phase-change interface or the temperature profiles during this process. To address these limitations, we present a “moving mesh” method that explicitly accounts for volumetric expansion during the melting (or, evaporation) process by introducing liquidus or vapour cells at appropriate locations adjacent to the interface. This moving mesh approach is used in conjunction with the apparent heat capacity method implemented through a finite volume scheme to represent the one-dimensional propagation of the melting (or, vapour) front during heating. This new algorithm has been validated for the Stefan's analytical solution, in addition to verifying the conservation of energy principle. We subsequently use our approach to investigate phase-change phenomena for a host of materials with a large gamut of density contrasts between the various phases, and compare the results to those obtained using a fixed-grid approach. The moving mesh method forecasts an early commencement of melting (or, evaporation) at a given position, a comparatively rapid movement of the front, and a larger volume fraction of the molten (or, vapour) phase, for substances that expand upon phase change, while the opposite is observed for the melting of ice, considered as a special case in this study. We hope that the proposed scheme will be adopted in addressing phase-change problems involving significant density contrasts.

Numerical Simulation of bio-heat transfer for cryoablation of regularly shaped tumours in liver tissue using multiprobes

The present study focuses upon pre-operative planning strategy for cryosurgical treatment of multiple regularly shaped tumours inside a three dimensional liver tissue. Numerical simulations provide an optimal framework to predict the number of cryo-probes, their placement, operation time and thermal necrosis to the tumour and surrounding healthy tissues. An efficient cryosurgery process requires keeping the tumour cell under lethal temperature which is between −40 °C to −50 °C. The freezing process of undesired tumour tissues involves phase transition from liquid phase to solid phase, the accurate capturing of transition front and size or location of ice balls generated in the process are the important factors of cryosurgery. In this study, fixed domain heat capacity method has been utilized to take into account the latent heat of phase change in bio-heat transfer equation. The ice balls generated with different number of probes haven been analysed. Numerical simulations have been carried out using standard Finite Element Method with COMSOL 5.5 and results obtained are validated with previous studies.

A multidimensional numeric study on smoldering-driven pyrolysis of waste polypropylene

The ex-situ smoldering driven pyrolysis reactor can simultaneously remediate the organically contaminated soil/sand and valorize the plastic waste to value-added fuels. This study establishes a multidimensional model to investigate the pyrolysis of polypropylene driven by self-sustained smoldering. The melting and decomposing processes during the pyrolysis of polypropylene have been simulated using the modified apparent heat capacity method and lumped kinetic model. Using a porous structure with high thermal conductivity in the pyrolysis domain proved to be a practical approach to address the non-uniform temperature distribution and low heating rate of plastics during pyrolysis. The research focus of this study is to obtain high-quality plastic pyrolysis liquid (oil, C6–C24) within a reasonable operating time (duration of the plastic pyrolysis process). Also, the operating conditions (Darcy air velocity, initial char concentration, and PP content) determine the yield of pyrolysis products by regulating the temperature and vapor residence time. Therefore, the sensitivity analyses of pyrolysis duration and oil yield to operating conditions have been performed. It is also found that the interface wall (between smoldering and pyrolysis chambers) heat transfer coefficient determines the smoldering chamber's thermal performance. This study provides new insights into the valorization of waste plastics and the remediation of contaminated soil/sand.

Geodesic Convolutional Neural Network Characterization of Macro-Porous Latent Thermal Energy Storage

Abstract High-temperature latent heat thermal energy storage with metallic alloy phase change materials (PCMs) utilize the high latent heat and high thermal conductivity to gain a competitive edge over existing sensible and latent storage technologies. Novel macroporous latent heat storage units can be used to enhance the limiting convective heat transfer between the heat transfer fluid and the PCM to attain higher power density while maintaining high energy density. 3D monolithic percolating macroporous latent heat storage unit cells with random and ordered substructure topology were created using synthetic tomography data. Full 3D thermal computational fluid dynamics (CFD) simulations with phase change modeling was performed on 1000+ such structures using effective heat capacity method and temperature- and phase-dependent thermophysical properties. Design parameters, including transient thermal and flow characteristics, phase change time and pressure drop, were extracted as output scalars from the simulated charging process. As such structures cannot be parametrized meaningfully, a mesh-based Geodesic Convolutional Neural Network (GCNN) designed to perform direct convolutions on the surface and volume meshes of the macroporous structures was trained to predict the output scalars along with pressure, temperature, velocity distributions in the volume, and surface distributions of heat flux and shear stress. An Artificial Neural Network (ANN) using macroscopic properties—porosity, surface area, and two-point surface-void correlation functions—of the structures as inputs was used as a standard regressor for comparison. The GCNN exhibited high prediction accuracy of the scalars, outperforming the ANN and linear/exponential fits, owing to the disentangling property of GCNNs where predictions were improved by the introduction of correlated surface and volume fields. The trained GCNN behaves as a coupled CFD-heat transfer emulator predicting the volumetric distribution of temperature, pressure, velocity fields, and heat flux and shear stress distributions at the PCM–HTF interface. This deep learning based methodology offers a unique, generalized, and computationally competitive way to quickly predict phase change behavior of high power density macroporous structures in a few seconds and has the potential to optimize the percolating macroporous unit cells to application specific requirements.

Thermal-seepage coupled numerical simulation methodology for the artificial ground freezing process

This paper proposes a thermal-seepage coupled numerical simulation methodology for the artificial ground freezing (AGF) process using measured soil freezing characteristic curve (SFCC). Firstly, the relation equation between pore ice content and temperature is established based on the measured SFCC, and a thermal-seepage coupled simulation method of AGF is proposed. After that, the performance of the proposed method was investigated based on soil column and large-scale model tests. Finally, the proposed method is compared with the traditional apparent heat capacity method. The results show that: (1) By introducing SFCC, the relation equation between pore ice content and temperature can be established with a clear physical meaning and a direct parameter determination process; (2) The proposed method can reasonably simulate the thermal and hydraulic field of AGF with or without seepage; (3) Compared with the traditional apparent heat capacity method, the proposed method has a conform to physical essence of phase transition and potential heat release and shows comprehensive improvement in theoretical basis, calculation accuracy, robustness and efficiency. Overall, the research results can provide a further understanding and improvement for numerical simulation in AGF.

Study on flow and heat transfer characteristics of 3D molten aluminum droplet printing process

The molten metal droplet printing technology can effectively realize a precise preparation of complex electronic devices at the micro scale by relying on the metallurgical bonding among the tiny molten metal droplets, which can improve the metallographic structure and mechanical properties of the fabricated parts. In this paper, the interaction process between metal droplets and movable substrates during the preparation of electronic devices is studied based on the coupled level set volume of fluid method (CLSVOF) and equivalent heat capacity method. The influence of the micro-bubbles and wall infiltration characteristics on the impingement spreading flow of metal droplets and their heat transfer cooling process is also investigated. The evolution mechanisms of droplet geometry and the distribution characteristics of droplet internal temperature and heat flow density during the impingement spreading process are discussed. The mechanism of high-temperature region formation under superhydrophobic wall conditions is analyzed. Results show that the microbubbles inhibit the spread of molten metal droplet. Under the same conditions, the spreading radius of hollow metal droplet is smaller than that of solid droplet, and their spreading height is higher than that of solid droplet. Different wall infiltration characteristics have similar degrees of influence on the spread of solid and hollow droplets. A larger wall contact angle for the same impingement mode at the same moment corresponds to a smaller droplet spreading radius and the higher the spreading height. With the participation of microbubbles, the heat transfer cooling process inside metal droplet becomes slow and demonstrates a less uniform temperature and heat flow density distribution. A high-temperature region is easily formed inside droplet under superlyophobic wall conditions, which triggers an uneven heat transfer cooling process at the bottom of the droplet. The results benefit to reveal the law of metal microdroplet impingement molding on different working surfaces and provide a theoretical reference for the preparation of electronics-related devices.

Numerical modeling of phase prediction and geometry evolution of micro-drilling using single pulse laser

Due to high production capability, long laser pulses are preferred over ultrashort pulses during Laser-based machining. To reduce metallurgical defects, viz. heat-affected zone, recast layer, and micro-cracks, it is essential to analyze the causes of these defects and to derive the remedies. Generally, an extensive experimental investigation is carried out for the same. The experimental analysis is time-consuming, tedious, and requires high capital investment. Therefore, in this work, a two-dimensional axisymmetric transient finite element method (FEM) based numerical model of Laser-material interaction was developed to explore the temperature evolution, phase change, and geometry evolution with the help of coupled heat transfer and deformed mesh. The heat transfer module was implemented by considering the phase change using the apparent heat capacity method. The model was duly validated for the evolution and geometry of the Laser-drilled hole. The model was found in agreement with the experimental results, with a percentage deviation of 12% in the prediction of the responses. The numerical model will help to predict the temperate evolution and hydrodynamic behavior of the material during the laser-material interaction. This, in turn, will help to mitigate the metallurgical defects.

Entropy generation analysis on thermo-hydraulic characteristics of microencapsulated phase change slurry in wavy microchannel with porous fins

• Combined design enables smaller temperature gradient and more uniform temperature. • Larger h m and lower ΔP can be concurrently gained in wavy MCHS with porous fins. • Thermal entropy is three orders of magnitude larger than the frictional entropy. • Thermal entropy increases with heat flux but the frictional entropy is opposite. • Lower irreversible losses can be achieved at the cost of higher power consumption. Recent advancement in micro/nano-scale electronic systems, the need for efficient heat dissipation has become more rigorous, and traditional thermal management solutions are facing enormous challenges. In this study, a novel combined design of wavy microchannel heat sink (MCHS) with porous fins and microencapsulated phase change material (MPCM) suspension is developed and numerically studied to achieve a balance between flow and heat transfer behaviors. The equivalent heat capacity method is adopted to deal with the phase change process of microcapsule particles in steady and laminar states, and the Brinkman–Darcy–Forchheimer model based on the volume-averaged method is employed to characterize the fluid flow in porous fins. A three-dimensional solid-fluid conjugate model is established based on the finite-volume method to investigate the effects of different coolant types (water and MPCM suspension), geometric parameters (wavy amplitude, wavelength, and channel width ratio), and working conditions (inlet flow velocity, heat flux, and slurry concentration) on the thermo-hydraulic properties and entropy generation of wavy MCHS. The results reveal that the combination of porous fins and MPCM suspension presents smaller temperature gradient and more uniform temperature distribution than conventional design. Larger heat transfer coefficient and lower pressure drop can be simultaneously obtained in wavy MCHS with porous fins than in solid fin configuration. The thermal entropy generation is three orders of magnitude larger than the frictional entropy generation, and the Bejan number is close to 1 for different microchannel configurations. Thermal entropy generation increases with increasing heat flux but the frictional entropy generation decreases. Lower irreversible losses can be achieved at the expense of greater pumping power consumption caused by increasing inlet velocity and suspension concentration. The superior effect of wavy MCHS with porous fins using MPCM suspension as coolant has been observed in all cases.

A review of methods for calculating of the interfacial heat transfer coefficient

As an important parameter for quenching and simulation, the interfacial heat transfer coefficient (IHTC) is hard to be directly measured through experiments. Researchers have come up with different methods to solve the problem. Currently, the numerical method, the heat balance method (HBM), the Beck’s non-linear estimation method (BEM), and the lumped heat capacity method (LCM) are the main methods of calculating the IHTC. In this paper, the direct heat conduction problem and the solution are firstly analysed, then the solutions and applications of different methods for calculating IHTC are summarized and reviewed. The different methods are compared at the end of the paper.

Latent heat storage system integrating phase change material in spherical capsules: A comparative study between three dynamic physical models

The main objective of this investigation is to carry out a detailed comparative study between three different thermal dynamic models for simulating a latent heat storage system using spherical capsules. These developed dynamic models are based on the apparent heat capacity method (model 1), on the heat source approach (model 2) and on the radial diffusion method (model 3). The main difference between the three models lies in the treatment of heat transfer inside the capsules. Obtained results from these models are first validated with experimental measurements from the literature and then used to investigate the thermal performance of the storage system under realistic exploitation conditions. Results show that all models are able to simulate the dynamic behavior of the storage system. The parametric study indicated that increasing the mass flow rate of the heat transfer fluid or reducing the capsule diameter can improve the energy performance of the thermal storage system and significantly reduce the discharge time.

Resolved simulations of single iron particle combustion and the release of nano-particles

We present a numerical study of the combustion of single iron particles in an O2–N2 atmosphere. By resolving the full boundary layer, mass and heat transfer are accurately modeled, including Stefan flow. Only the conversion of Fe to FeO is taken into account and evaporation is implemented to investigate the formation of nano-sized iron-oxides products. Temperature- and composition-dependent heat capacity and density are used and phase transitions from solid to liquid (and vice-versa) are accounted for by the apparent heat capacity method. The model is validated by comparing the time to maximum temperature (tmax) and the maximum temperature (Tmax) of a 40 and 50 µm particle in an O2–N2 atmosphere with experiments. The current model, which assumes infinitely fast internal transport, can well estimate the maximum particle temperature and the time to reach this maximum temperature, but it does not capture the particle size effect on the maximum temperature. Even though the particle temperature stays below its boiling temperature, a small but non-negligible amount of mass is lost due to evaporation of the particle. Evaporation of the particle and oxidization of the gaseous Fe-containing species in the boundary layer limit the maximum temperature of the particle when increasing the oxygen concentration. By means of a sectional model, the formation and growth of the iron oxide nano-particles is numerically investigated. It is shown that somewhat further downstream of the particle, the volume fraction of nano-particles attains a maximum. An average nano-particle diameter of 40 nm is found at t/tmax=1 in the wake of a 50 µm iron particle burning at 21% oxygen concentration.

A modified heat capacity method for unconstrained melting inside the spherical capsule for thermal energy storage

The spherical capsule is one of the most common geometrical configurations for latent heat thermal energy storage. This study develops a modified heat capacity method coupling with the volume of fluid model to calculate the unconstrained melting inside the spherical capsule. Based on the force balance of the sinking solid body PCM, the solid velocity is implicitly introduced and incorporated in the extended Darcy term. The forces exerted on the solid PCM are calculated through the volume integral. Then, the proposed model is used to simulate the reported unconstrained melting experiments inside a spherical capsule filled with n-octadecane. The influence of the mushy zone constant on the melting processes is discussed, and the natural convection, solid moving, heat transfer, and melting behaviors are analyzed. It is found that the melting rate decreases with the increase of the mushy zone constant. The present model with a suitable mushy zone constant can reasonably predict the unconstrained melting. Besides, the appropriate mushy zone constant tends to increase with a higher Ste number. The total charging heat transfer rate linearly decreases during the melting process after the melt layer shapes. The heat transfer rate of the contact melting below the solid PCM is about 60 %–80 % of the total heat transfer rate and is much higher than that of the natural convection above the solid PCM. The thickness of the melt layer between the bottom solid PCM and the capsule shell increases after the lifting phenomenon, and it is less than 1 % of the capsule diameter.

Parametric Study of Panel PCM–Air Heat Exchanger Designs

Heat exchangers, devices for the transfer of heat between two or more working fluids, are extensively used in cooling applications and heating applications. Heat exchangers in buildings are typically components of space-conditioning systems, as well as of water-heating applications. Heat exchangers are also sometimes used in applications that require storage and release of energy at specific times. Phase change materials (PCMs) enhance these heat-exchange processes, given their ability to melt and solidify at a fixed range of temperatures, absorbing or releasing significant amounts of latent heat. Five different configurations of PCM–air heat exchangers for thermal control in buildings are analyzed in this work. The heat exchangers were fitted with PCM encapsulated in plastic and composite pouches of various shapes, and packaged in stackable panel layers. Three-dimensional computational fluid dynamics (CFD) modeling of coupled incompressible fluid and conjugate heat transfer were performed on the designs. The phase change process was numerically modelled using the apparent heat capacity method. Steady-state CFD simulations provided quantification of pressure drop as a function of air flow velocity. Transient simulation results describe the thermal evolution of PCM in the pouches, helping to determine the best performing configuration with respect to total thermal charging time.