Temperature Dependent Specific Heat Capacity Research Articles

CFD simulation of solid/liquid phase change in commercial PCMs using the slPCMlib library

Modelling the solidification and melting behavior of phase change materials (PCMs) can present several challenges, including non-isothermal phase change, multi-step transitions, complex enthalpy-temperature relations and convective heat transfer. To tackle these challenges, this study proposes a novel numerical method based on real experimental data for modelling complex phase change behavior of commercial PCMs in Ansys Fluent CFD software. The phase transition of PCMs is simulated with the apparent heat capacity (AHC) method, which is implemented as a User-Defined Function (UDF). Heat convection is simulated with the Boussinesq approximation. The method is validated by comparing to the Ansys Fluent built-in Solidification and Melting (S&M) model for the case of piecewise constant heat capacity. The results show that AHC method provides excellent agreement with S&M model for a piecewise constant heat capacity model. In addition, the AHC method solves convergence problems even for narrow phase change temperature ranges when a smooth heat capacity function is assumed. Finally, the AHC model is also tested on a set of commercial PCMs exhibiting complex phase change behavior. Temperature dependent specific heat capacities are determined from heat capacity data provided by PCM manufacturing companies and are imported as cubic Hermite spline functions from the solid-liquid phase change material library slPCMlib available at https://slpcmlib.ait.ac.at/. From the presented case study and tested PCMs it can be concluded that the AHC method is numerically robust when used with sufficiently smooth heat capacity functions, and it can be recommended for the analysis of heat transfer with PCMs showing a complex phase change behavior.

Detailed Approach to Calculate the Heat Generation of Lithium-Ion Cells during Heat-Wait-Seek Tests in Accelerating Rate Calorimetry

By means of the Heat-Wait-Seek test in Accelerating Rate Calorimeters (ARC) the safety performance of Lithium-ion cells can be estimated. The most interesting measured parameters that can be extracted from these tests are the critical temperatures, such as the onset of self-heating, the venting or thermal runaway temperature. Another essential safety factor is the generated heat during cell failure. In general, the generated heat is calculated by an average heat capacity of the cell and the temperature difference in the experiment, which is not accurate enough especially when facing the challenges in specific volumetric energy density and safety of battery packs.In this study a more accurate way to calculate the generated heat is proposed, which consists of using temperature dependent heat capacity of the cell, based on its individual components. This leads to a significant difference in the calculated generated heat, for instance the specific heat capacity of NMC as a cathode material increases in the temperature range from 298 K to 398 K from 0.83 to 0.96 J/g·K, which is an increase of about 16 %. This leads to a difference in the calculated generated heat in this small range of 7 J/g (or 8 %), if a static specific heat capacity of 0.83 J/g·K and on the other hand a temperature dependent specific heat capacity is used. Moreover, the influence of additional heating steps, venting of the cell, melting of the separator and the overall accuracy of the measurement will be discussed. The investigation of these effects is in the focus of the project AnaLiBa (Analytics of Lithium-ion-Batteries), funded by the German Federal Ministry of Education and Research (BMBF) in the framework of the competence cluster Analytics/quality assurance (AQua). In this project the approach is applied to commercial type 21700 cells. The 21700 type cells are extensively used in battery packs, for instance in electric cars, due to their 20 % higher energy density with respect to the former used type 18650 cells. The cells were measured in an ES-ARC from Thermal Hazard Technologies, UK, using the Heat-Wait-Seek test. The generated heat was compared for either fresh cells and cells after cyclic aging. The cyclic aging was performed at 0 °C and 20 °C with a charging rate of 0.3C for 0 °C and 0.7C for 20 °C and a discharging rate of 2C for 20 °C and 0.5C for 0 °C until the state of health was at 80 % ±2 %. The two different temperatures studied in the cyclic aging were chosen as 0 °C to cause lithium plating and as 20 °C to cause a higher internal resistance due to a thicker solid-electrolyte-interface, which has a high influence on the measured properties in the Heat-Wait-Seek test and therefore on the generated heat.With this approach the generated heat in abuse tests can be calculated more accurately to simulate the propagation of heat during a single cell failure in a pack or to calculate the necessary thickness of a heat barrier for safer battery packs. This helps manufacturers to improve their battery pack design with respect to the specific volumetric energy density and safety.

Structure and thermoelectric properties of half-Heusler-like TiFeCuxSb alloys

Previous research on the ternary Ti-Fe-Sb system has revealed that stoichiometric TiFeSb cannot exist as a stable compound, whereas a single-phase TiFe1.33Sb alloy with the half-Heusler-like structure has been synthesized by adding excessive Fe. In this work, we report that TiFeSb can also be stabilized by filling additional Cu to the vacant 4d site of the half-Heusler lattice. Our experiments indicate that the TiFeCuxSb (x = 0–0.25) samples exhibit a p-type conduction with extremely high carrier concentration ((0.5 –2.5) × 1022 cm−3)), while these samples attain very large Seebeck coefficients, over 100 μV/K in the whole measured temperature range for the samples with x = 0.15–0.25. In addition, a logarithmic divergence of the temperature-dependent specific heat capacity (CP/T) is observed at low temperatures, implying the strange-metal behavior of TiFeCuxSb samples. The partial filling of the vacant 4d site results in significantly reduced lattice thermal conductivity, leading to the low total thermal conductivity of 2.8 W·m−1·K−1 at 823 K for the TiFeCu0.20Sb sample. Consequently, a dimensionless figure of merit zT of 0.54 at 923 K is realized for TiFeCu0.20Sb, demonstrating that promising thermoelectric materials with intriguing physical properties can be discovered in the composition gap of half- and full-Heusler alloys.

Theoretical prediction method of Young's modulus and yield strength of micron particle reinforced metal matrix composites at different temperatures

To begin with, a theoretical characterization model of temperature and porosity dependent Young's modulus for micron particle reinforced metal matrix composites is established by considering the evolution of properties of reinforced particles and metal matrix with temperature. Additionally, combining the existing strengthening mechanism theory and incorporating the influence of grain boundary slip on the related strengthening mechanism and the yield strength of metal matrix, a temperature dependent yield strength analysis model of micron particle reinforced metal matrix composites is proposed. These models only require material parameters at room temperature and temperature dependent specific heat capacity at constant pressure for application. In addition, the predicted results from these models are reasonable and consistent with measured results. Moreover, based on the established models, the effects of key material parameters and main mechanisms on Young's modulus and yield strength of composites and their variation with temperature are explored. Furthermore, the variation of various control mechanisms with the particle size and temperature is clarified. It lays a theoretical foundation for the development of micron particle reinforced metal matrix composites that are suitable for high-temperature environments and for the optimization of their key parameters.

Heat capacity and index of refraction of polyzwitterions

Specific heat capacities and indices of refraction were measured for a series of six sulfobetaine zwitterionic polymers and compared to topological and group contribution models. Poly(sulfobetaine methacrylate) (PSBMA), poly(sulfobetaine acrylate) (PSBA), poly(ethyl sulfobetaine methacrylate) (PESBMA), poly(sulfobetaine methacrylamide) (PSBMAm), poly(sulfobetaine 2-vinylpyridine) (PSB2VP) and poly(sulfobetaine 4-vinylpyridine) (PSB4VP) were specially synthesized with changes of chemical structure in order to study effects of either the polymer backbone or the side group on their properties. Temperature modulated differential scanning calorimetry (TMDSC) as well as quasi-isothermal TMDSC were used to determine the temperature dependent specific heat capacity, cp(T) from 30 to 200 °C. The solid state specific heat capacities were measured for all the polyzwitterions, while liquid state heat capacity measurements were limited to PSBA and PESBMA. Ellipsometry at wavelengths from 300 nm to 3000 nm was used to measure the index of refraction for polyzwitterion thin films at room temperature. Theoretical room temperature values of cp and n were calculated for the polyzwitterions using topological and group contribution methods and compared to the measured values. The measured index of refraction values agree well with predictions for the polyzwitterions. However, for the solid state heat capacity, the model produces accurate prediction only for PSB2VP and PSB4VP. The discrepancy between the measured and predicted cp values is most likely due to the reduction of vibrational degrees of motion in the solid state for some of the polyzwitterions due to physical crosslinking.

Dynamic constitutive models of Ti-6Al-4V based on isothermal ture stress–strain curves

Ti-6Al-4V titanium alloy is a typical difficult-to-cut material used in many fields. The selection of cutting parameters exerts tremendous influences on the material removal process. Finite element numerical simulation is a low-cost method to obtain optimized cutting parameters. Finite element simulation requires the study of machining properties of machined materials. The material removal and related physical phenomena during machining are characterized by the dynamic mechanical properties of the machined material. In this paper, the dynamic mechanical properties of Ti-6Al-4V have been tested by the high temperature split Hopkinson pressure bar system to obtain true stress–strain curves under different conditions. The sensitivity of strain and temperature of Ti-6Al-4V has been analyzed. The influence of temperature-dependent specific heat capacity, which has been tested by a laser thermal conductivity tester, on adiabatic temperature rise has been considered. Adiabatic temperature rise has been calculated separately with constant specific heat capacity and temperature-dependent specific heat capacity. True stress–strain curves have been switched to true stress–strain isothermal curves to analyze separately the influence of strain rate and temperature on true stress. Based on true stress–strain isothermal curves, the constitutive models of power-law and Johnson–Cook have been introduced to fit the experimental results. The fitting results of the two constitutive models have been compared with the experiment results, which have an average error less than 6%.

New insights into temperature-dependent ice properties and their effect on ice shell convection for icy ocean worlds

Ice shell dynamics are a critical control on the habitability of icy ocean worlds. Here, we present a systematic study evaluating the effect of temperature-dependent material properties on these dynamics. We review the published thermal conductivity data for ice, which demonstrates that the most commonly used conductivity model in planetary science represents a lower bound. We propose a new model for thermal conductivity that spans the temperature range relevant to the ice shells of ocean worlds. This increases the thermal conductivity at low temperatures near the surface by about a fifth. We show that such an increase in thermal conductivity near the cold surface favors conduction over convection in the ice shell of Europa. Furthermore, we find that including temperature dependent specific heat capacity decreases the energy stored in the conductive lid. Thus, the timescale for ice shell response to thermal perturbations is reduced by approximately one third. An ice shell that is more sensitive to thermal perturbations may help to explain surface features such as chaotic terrains which require large additions of energy to the near-surface ice.

Bismuth Doping Alters Structural Phase Transitions in Methylammonium Lead Tribromide Single Crystals.

We study the effects of bismuth doping on the crystal structure and phase transitions in single crystals of the perovskite semiconductor methylammonium lead tribromide, MAPbBr3. By measuring the temperature-dependent specific heat capacity (Cp), we find that as the Bi doping increases, the phase transition assigned to the cubic to tetragonal phase boundary decreases in temperature. Furthermore, after doping we observe one phase transition between 135 and 155 K, in contrast to two transitions observed in the undoped single crystal. These results appear strikingly similar to previously reported effects of mechanical pressure on perovskite crystal structure. Using X-ray diffraction, we show that the lattice constant decreases as Bi is incorporated into the crystal, as predicted by density functional theory. We propose that bismuth substitutional doping on the lead site is dominant, resulting in BiPb+ centers that induce compressive chemical strain that alters the crystalline phase transitions.

Theoretical Evaluation of the Melting Efficiency for the Single-Screw Micro-Extrusion Process: The Case of 3D Printing of ABS

One of the challenges for single-screw micro-extrusion or additive manufacturing (AM), thus 3D printing, of polymers is controlling the melting efficiency so that energy and equipment costs can be minimized. Here, a numerical model is presented for AM process design, selecting acrylonitrile–butadiene–styrene (ABS) as viscoelastic reference polymer. It is demonstrated that AM melting is different compared to conventional melting due to variation in extrusion dimensions, leading to a different balance in heating by conduction and viscous heat dissipation as caused by the shearing between the melt layers in the associated film layer near the barrel. The thickness of this melt film layer is variable along the screw length, and it is shown that simplified models assuming an overall average value are too approximate. It is highlighted that the screw frequency, pitch angle and compression ratio are important process parameters to control the point of melt finalization. In addition, the power-law index reflecting the shear thinning nature of the polymer melt is showcased as a key parameter. Moreover, AM process results assuming constant and temperature dependent specific heat capacities and thermal conductivities are compared. The current work opens the door for on-line AM process control, addressing all relevant operating and material parameters.

Phase Transitions in Mesogenic Third Generation Poly(Propyleneimine) Dendrimer and Its Iron(II) Complex

Two third generation liquid-crystalline dendrimers, poly(propyleneimine) derivatives with 3,4-bis(decyloxy)benzoic moieties at the periphery, were prepared, and their thermodynamic properties were studied. The formation of a columnar mesophase was verified by differential scanning calorimetry (DSC) and polarizing optical microscopy. It was for the first time that the specific heat capacity and magnetocaloric effect (MCE) of the iron complex G3-K2.10 ∙ (FeCl2)15 in the temperature 288–350 K in magnetic fields varying from 0 to 1.0 T were determined. The temperature-dependent specific heat capacity of the complexes in the range 210–460 K was measured on a differential scanning calorimeter and an original design microcalorimeter. The temperature-dependent heat capacity and magnetocaloric effect are extreme functions.

Gaseous Vapor Emission (GVE) Technique for Detection of Petrol Adulteration at Point of Sale (POS) Terminals

A one-dimensional mathematical modelling and simulation of the riser reactor in a fluid catalytic cracking unit was presented in this work. The seemingly increasing demand for lighter fractions of petroleum as source of energy has necessitated that the fluid catalytic cracking (FCC) unit be modelled with greater precision and accuracy. A more accurate model of the riser reactor that is one of the primary functional elements of the FCC unit is important in improving the performance of the entire unit. Salient issues in the presented model were the four-lump kinetic model for the cracking mechanism, slip factor consideration between the phases, exponential catalyst activity deactivation model and the instantaneous estimation of the temperature dependent specific heat capacities of reacting species during the reaction. The model exhibited the behaviour expected of a riser reactor based on comparison with some industrial plant data and previous simulations. Simulation results showed that increase in the catalyst to oil ratio (COR) led to increase in gasoline yield only to a particular limit beyond which the yield began to decline. Presented results showed reasonable set of parameters for operating the riser which could lead to better yield. Keywords: One-dimensional (1-D), FCC, riser, hydrodynamic, lump kinetic, modelling, simulation.

Mathematical Programming for Heat Exchanger Network Design with Temperature-Dependent Specific Heat Capacity

Heat Exchanger Network (HEN) optimization by mathematical programming has been developed for half of century. Stage-wise superstructure by Yee and Grossmann (1990) is one of the most popular HEN design models dividing process temperature into stages under assumption of constant specific heat capacity (Cp). To make model more realistic, the model is developed under temperature-dependent Cp which is a cubic equation of temperature. To simplify this circumstance, non-linearity of Cp is linearized by applying partitions of linear equations of Cp at different temperature intervals. HEN from the modified stage-wise superstructure model with variable Cp by GAMS software version 24.2 is validated with crude preheat train case from commercial simulation program (Pro/II software version 9.1). The Cp from Pro/II software as a function of temperature is divided into three linear equations of Cp at three temperature intervals. A case study of crude preheat train without HEN consists of five hot product streams and one cold crude oil stream, consuming hot and cold utilities of 175,353.53 kW and 107,945.89 kW, respectively. The new model synthesizes HEN for the crude preheat train, consuming less hot and cold utilities of 82,100.93 kW and 14,654.38 kW. The synthesized HEN is validated by Pro/II software, giving duties of hot and cold utilities of 81,835.30 kW and 14,417.20 kW. Percent error of hot and cold utilities of HEN from GAMS model are only 0.31 % and 1.65 %, compared to ones from Pro/II software. Compared to Pro/II results, percent error of process HEN area and utility HEN area from new model are 1.22 % and 2.91 %, respectively. New model with variable Cp assumption gives a good agreement with validated HEN by Pro/II. Compared to examples from other publications, the model shows that it generates HEN design with less TAC and less computational time.

Measurement of Specific Heat and Crystallization in VS55, DP6, and M22 Cryoprotectant Systems With and Without Sucrose.

Cryopreservation represents one if not the only long-term option for tissue and perhaps future organ banking. In one particular approach, cryopreservation is achieved by completely avoiding ice formation (or crystallization) through a process called vitrification. This "ice-free" approach to tissue banking requires a combination of high-concentration cryoprotective additives such as M22 (9.4 M), VS55 (8.4 M), or DP6 (6 M) and sufficiently fast rates of cooling and warming to avoid crystallization. In this article, we report the temperature-dependent specific heat capacity of the above-mentioned cryoprotective additives in small volumes (10 mg sample pans) at rates of 5°C/min and 10°C/min using a commercially available differential scanning calorimetry (TA Instruments Q1000), in the temperature range of -150°C to 30°C. This data can be utilized in heat-transfer models to predict thermal histories in a cryopreservation protocol. More specifically, the effects of temperature dependence of specific heat due to the presence of three different phases (liquid, ice, and vitreous phase) can dramatically impact the thermal history and therefore the outcome of the cryopreservation procedure. The crystallization potential of these cryoprotectants was also investigated by studying cases of maximal and minimal crystallization in VS55 and DP6, where M22 did not crystallize under any rates tested. To further reduce crystallization in VS55 and DP6, a stabilizing sugar (sucrose) was added in varying concentrations (0.15 M and 0.6 M) and was shown to further reduce crystallization, particularly in VS55, at modest rates of cooling (1°C/min, 5°C/min, and 10°C/min).

Thermodynamic geometry, condensation and Debye model of two-parameter deformed statistics

We consider the statistical distribution function of a two parameter deformed system, namely qp-deformed bosons and fermions. Using a thermodynamic geometry approach, we derive the thermodynamic curvature of an ideal gas with particles obeying qp-bosons and qp-fermions. We show that the intrinsic statistic interaction of qp-bosons is attractive in all physical ranges, while it is repulsive for qp-fermions. Also, the thermodynamic curvature of qp-boson gas is singular at a specified value of fugacity and therefore, a phase transition such as Bose–Einstein condensation can take place. In the following, we compare the experimental and theoretical results of temperature-dependent specific heat capacity of some metallic materials in the framework of q and qp-deformed algebras.

Anisotropic and temperature-dependent thermal conductivity of PbI2

The temperature-dependent components of the anisotropic thermal diffusivity of lead iodide (PbI2) have been measured by Laser Flash Analysis (LFA). The temperature range used was −100°C to +350°C. The temperature-dependent specific heat capacity cp was determined independently by Differential Scanning Calorimetry (DSC) to calculate the thermal conductivities for PbI2 from the thermal diffusivity data. At 27°C, the thermal conductivity in the c-axis-direction, k33, is 0.315Wm−1K−1, whereas the component perpendicular to the c-axis, k11, is 0.681Wm−1K−1. The anisotropy ratio k33/k11 changes from 1:2 at −100°C to 1:2.4 at +350°C. The temperature dependencies of both k33 and k11 in this range can be very well fitted with 3rd order polynomials.

Structure and thermal properties of as-fabricated U-7Mo/Mg and U-10Mo/Mg low-enriched uranium research reactor fuels

Aluminum-clad U-7Mo/Mg and U-10Mo/Mg pin-type mini-elements (with a core uranium loading of 4.5 gU/cm3) have been fabricated at the Canadian Nuclear Laboratories for experimental tests and ultimately for use in research and test reactors. In this study, the microstructure and phase composition of unirradiated U-7Mo/Mg and U-10Mo/Mg fuel cores were analyzed using optical and scanning electron microscopy, and neutron powder diffraction. Thermal properties were characterized using a combination of experimental measurements and thermodynamic calculations. The thermal diffusivity was measured using the laser flash method. The temperature-dependent specific heat capacities were calculated based on the linear rule of mixture using the weight fraction of different crystalline phases and their specific heat capacity values taken from the literature. The thermal conductivity was then calculated using the measured thermal diffusivity, the measured density and the calculated specific heat capacity. The resulting thermal conductivity is practically identical for both types of fuel. The in-reactor temperatures were predicted using conjugate heat transfer simulations.

Thermal characterization of Li-ion cell electrodes by photothermal deflection spectroscopy

Contactless and temperature-dependent evaluation of thermal diffusivities of Li-ion cell electrodes based on photothermal deflection spectroscopy (PDS) measurements is introduced and applied to electrodes from three prismatic hardcase Li-ion cells. The accuracy of the method is validated using reference materials, which cover a wide range of thermal diffusivity. The effective thermal diffusivities of the three anode and cathode coatings and of the current collectors are determined in the temperature range of 5–45 °C.Furthermore, the temperature-dependent specific heat capacity of the electrodes is evaluated by differential scanning calorimetry (DSC) measurements in the same temperature range. Based on the experimental results the through-plane and in-plane thermal conductivity of the electrodes is calculated and compared to previously reported values. The results indicate significant influence of the porosity and manufacturing process on the effective thermal conductivity of the electrodes. The three mayor impact factors on thermal conductivity of electrodes are (i) composition, (ii) morphology of the coating and (iii) the thickness ratio of coating to current collector.

Particle–particle heat transfer coefficient in a binary packed bed of alumina and zirconia-ceria particles

Solar thermochemical processes for fuel production require the incorporation of heat recovery systems for substantial efficiency gains.A heat recovery concept for processes using a particulate redox material proposed by the authors utilizes a second particulate material as a solid heat transfer medium. This work is about the experimental investigation of the heat transfer between these two particle species in a binary packed bed. Experiments were performed at temperatures up to 250 °C regarding the influencing factors of contact time, mass ratio, average temperature, temperature difference and particle diameters. Design of experiments helped as a method to plan and analyze these experiments. In addition, the temperature dependent specific heat capacity, the density and the size of the investigated particles were experimentally analyzed.In order to consider heat losses to the experimental setup, a correction measurement campaign was undertaken.The results are in the form of a polynomial which predicts the heat transfer coefficient depending on its influencing factors. This polynomial was obtained by a stepwise linear regression method. Values between 90 and 260 W/m2 K are predicted for the given temperature range.In an alternative approach we characterized the heat transfer in terms of the temperature difference of one particle species.

Determination of temperature dependent thermophysical properties using an inverse method and an infrared line camera

Temperature dependent thermal diffusivities of two alloys (Al-4wt.% Cu and 70:30 α-brass) are determined using a one-dimensional inverse method that is based on a least-square scheme. Transient temperature histories required as input for the proposed inverse method are recorded using an infrared line camera during one-sided heating or cooling. An aerogel that is transparent for infrared radiation is used as insulation material, ensuring that heat conduction is essentially one-dimensional. Temperature profiles along the samples are obtained using up to 512 photo diodes as temperature sensors. Temperature dependent specific heat capacities of the Al–Cu alloy and brass, calculated using a thermochemical library based on the CALPHAD method, are employed to calculated thermal conductivities. The calculated thermal conductivities are in good agreement with literature values. It is shown that the combination of the numerical calculations and the heating experiments provides an efficient way to determine temperature dependent thermophysical properties of alloys.

Comparative Analysis of Different Configuration Domestic Refrigerators: A Computational Fluid Dynamics Approach

To reduce the tremendous increase in the energy consumption in the residential sector, there is a continuous need to improve the cooling efficiency and reduce running cost in domestic refrigerators. In this regard, three domestic refrigerator configurations have been considered. These configurations, namely, top mounted freezer (TMF), bottom mounted freezer (BMF), and side mounted freezer (SMF), were numerically simulated using ansys fluent 14 code. The refrigerators considered in this paper are air cooled by natural convection mechanism. For improved accuracy, piecewise polynomial function was used to obtain the temperature dependent specific heat capacity, while the discrete ordinate (DO) model was used to account for the radiation energy exchange between the refrigerator walls and cooling air. The effect of refrigerator opening and refrigerator load on the performance of the model refrigerators was also studied. Results show that cabinets that have the same relative position from the base (ground level) in TMF, BMF, and SMF configuration was observed to have similar cooling effectiveness irrespective of the compartment (i.e., freezer or fresh food). Load in the lowest parts of the model refrigerator consistently maintains the highest cooling effectiveness with about 15% more than their respective topmost cabinet. Thus, consumer preference of highly efficient compartment (either freezer or refrigerator) should be considered. After 300 min cooling time, the TMF and BMF cooling load are more than that of SMF by about 8%. This suggests that SMF with better cooling effectiveness will consume less energy and would have a lower running cost.