Temperature Dependence Of Heat Research Articles

Characterization and Application of Cyrene as a Biomass-Based Solvent for Homogeneous Heck-Coupling Reaction.

Cyrene, a renewable, non-toxic substance having negligible vapor pressure, even at high temperatures, was proposed as a reaction medium for homogeneous Pd-catalyzed Heck-coupling reactions. It was first characterized by its temperature-dependent physicochemical properties, i.e., vapor pressure, density, surface tension, heat capacity, and viscosity, the key parameters of its reaction and process chemistry. Its refractive indices in the function of temperature were also determined. Hereafter, the effect of reaction parameters (Pd source, nature of the base, the water content of the reaction mixture, leaving group (-I, -Br, -Cl, and -OTf of aromatic substrates) on Pd-catalyzed Heck-coupling reaction was investigated using iodobenzene and styrene as model substrates. Subsequently, 4-substituted iodobenzene and styrene derivatives were applied to investigate the effect of electronic parameters on the reaction efficiency and functional group tolerance. To demonstrate the applicability of the system, thirteen stilbene derivatives were isolated with good to high yields and purity (> 95%) using 0.2 mol% of Pd, 1.5 eq. of Et3N as a base, in 1 mL of Cyrene for 2 h at 100 °C.

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

An analytical study of thermal environment’s effect on the free vibration of FGM double curved FG shells

The main objectif of this work is to examine the thermal environment’s effect of on the free vibration of double curvature shells made of functionally graded materials. A new mathematical model based on higher order shear deformation theory, is developed to incorporate the influence of dependent and independent thermal stresses, which can be uniform, linear, nonlinear, or sinusoidal on the mechanical properties of the double curvature shell. Two material couples, ( S i 3 N 4 / SUS 304 , ZrO 2 /Ti‐6Al‐4V ) , are considered as progressive materials, accounting for temperature-dependent and temperature-independent heat conduction and material properties in the thickness direction. The temperature field is assumed to be uniform across the shell surface but varies only in the thickness direction. The accuracy of the analytical results is validated by comparing them with existing literature results for functionally graded material (FGM) shells with infinite radii under dependent and independent temperature conditions. The study aims to demonstrate the thermal effects on material composition, as well as various specific geometric shapes such as plates, cylinders, spheres and ellipses and how different temperature laws influence the frequencies of vibrating double curvature FGM shells. Both existing theories accurately predict temperature-independent and temperature-dependent vibration responses of the shells. By verifying and comparing the results with the literature, a better agreement is achieved, thereby paving the way for further research in this field.

Analytical modeling of desublimation of a phase change material (PCM) in a porous medium with temperature-dependent volumetric heat sink and convection due to air-mixed vapor

The desublimation phase change heat and mass transfer process in a porous medium occurs during the conversion of vapor into solid form, which has several applications in chemical deposition and industrial coating. For economic feasibility, reducing the operating time of the conventional desublimation technique is of much interest. Toward this goal, current work presents a mathematical model for desublimation that accounts for a volumetric heat sink connected with temperature. A linear profile of the volumetric heat sink varying with temperature is modeled within the frozen region. Further, the rate of water vaporization (with mixed air) produces a convective term, which is also accounted for in the frozen region. Despite previous studies on desublimation phase change process, there is still insufficient mathematical modeling of this particular phenomena. The solution to the governing set of dimensionless partial differential equations is obtained analytically by employing the space-time transformation. Results indicate that the rate of desublimation process becomes faster with increasing the strength of the volumetric heat sink, which results in the reduction of the total operating time to desublimate of a phase change material. Higher values of the dimensionless temperature parameters also accelerate the desublimation process. On the other hand, a larger value of the convective term is found to slow down the desublimation process. The dimensionless moisture concentration profile in the vapor region increases with increasing the value of the Luikov number. Observations from this study are expected to aid in the fundamental design of processes including industrial coating, preservation of biological products, and evaporative deposition where desublimation plays a key role.

Large electrocaloric effect across the non-hysteretic electrostructural phase transition in lead-free (Ba0.88Ca0.12)(Ti0.94Sn0.06)O3 ceramics

Structural, dielectric, and electrocaloric properties were investigated in Pb-free ceramic (Ba0.88Ca0.12)(Ti0.94Sn0.06)O3 (BCST), synthesized using solid-state sintering method. Rietveld refinement of room temperature XRD data revealed the existence of pure perovskite tetragonal (P4mm) phase. Temperature-dependent XRD analyses confirmed a structural transition from tetragonal to cubic phase near 380 K. Temperature-dependent dielectric constant (εr) and specific heat capacity (Cp) confirmed the presence of thermal hysteresis in two phase transitions near 233 ± 10 K and 254 ± 10 K, and a non-hysteretic behavior at the Curie temperature (TC∼373 ± 10 K). A comprehensive Raman study corroborated the existence of phase transitions. Electrocaloric properties were determined using indirect method utilizing the non-hysteretic nature across TC. A large adiabatic temperature change of |∆T| = 0.52 K, isotropic entropy change |∆S| = 0.68 J/kg.K, electrocaloric coefficients, |∆T/∆E |= 0.311 K.mm/kV and |∆S/∆E| = 0.41 J.mm/K.kg.kV were obtained at 380 K for an electric field of 16.7 kV/cm. Obtained value of |∆T/∆E| is relatively good, reported among other BaTiO3-based ceramics.

Prandtl-eyring couple stressed flow within a porous region counting homogeneous and heterogeneous reactions across a stretched porous sheet

The movement of a non-Newtonian incompressible Prandtl-Eyring fluid layer over a stretching/shrinking permeable plate is shown in the current work. The flow is stressed by an additional couple stress, altered by a uniform normal magnetic field, and saturated in a permeable material. Heat transmission is demonstrated using a temperature-dependent heat source, an exponential space-dependent heat source, Joule heating, and viscous dissipations. Momentum, energy, and chemical type concentration equations, coupled with appropriate boundary conditions, support the mathematical structure. The novel aspect of the current work comes from considering species mass transfer using heterogeneous and homogeneous biochemical reactions along with the effects of thermal diffusion in the aforementioned flow. The reaction processes are isothermal with identical coefficients of chemical species. The leading nonlinear partial differential equations are transformed into ordinary differential equations utilizing appropriate similarity transformations. The homotopy perturbation method examines these equations. As a result, the primary objective distributions' analytical solutions are derived, and a graphical representation of them is produced to show the effects of the pertinent physical elements. The heterogeneity reaction serves as a dual role parameter in this diffusion, while the homogeneity reaction has been discovered to be a decreasing factor for particle diffusion. The ability of suction or injection via a permeable surface is observed to reduce the velocity and heat transmission, meanwhile, increasing chemical species condensation.

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Fractal Numerical Investigation of Mixed Convective Prandtl-Eyring Nanofluid Flow with Space and Temperature-Dependent Heat Source

Stickiness: A New Variable to Characterize the Temperature and Humidity Contributions toward Humid Heat

Abstract Extreme wet-bulb temperatures (Tw) are often used as indicators of heat stress. However, humid heat extremes are fundamentally compound events, and a given Tw can be generated by various combinations of temperature and humidity. Differentiating between extreme humid heat driven by temperature versus humidity is essential to identifying these extremes’ physical drivers and preparing for their distinct impacts. Here we explore the variety of combinations of temperature and humidity contributing to humid heat experienced across the globe. In addition to using traditional metrics, we derive a novel thermodynamic state variable named “stickiness.” Analogous to the oceanographic variable “spice” (which quantifies the relative contributions of temperature and salinity to a given water density), stickiness quantifies the relative contributions of temperature and specific humidity to a given Tw. Consistent across metrics, we find that high magnitudes of Tw tend to occur in the presence of anomalously high moisture, with temperature anomalies of secondary importance. This widespread humidity dependence is consistent with the nonlinear relationship between temperature and specific humidity as prescribed by the Clausius–Clapeyron relationship. Nonetheless, there is a range of stickiness observed at moderate-to-high Tw thresholds. Stickiness allows a more objective evaluation of spatial and temporal variability in the temperature versus humidity dependence of humid heat than traditional variables. In regions with high temporal variability in stickiness, predictive skill for humid heat-related impacts may improve by considering fluctuations in atmospheric humidity in addition to dry-bulb temperature. Significance Statement Extreme humid heat increases the risk of heat stress through its influence over humans’ ability to cool down by sweating. Understanding whether humid heat extremes are generated more due to elevated temperature or humidity is important for identifying factors that may increase local risk, preparing for associated impacts, and developing targeted adaptation measures. Here we explore combinations of temperature and humidity across the globe using traditional metrics and by deriving a new variable called “stickiness.” We find that extreme humid heat at dangerous thresholds occurs primarily due to elevated humidity, but that stickiness allows for thorough analysis of the drivers of humid heat at lower thresholds, including identification of regions prone to low- or high-stickiness extremes.

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.

Simulation-based process parameter optimization for wire arc additive manufacturing

AbstractDuring manufacturing of components using wire arc additive manufacturing, specific cooling times are required to prevent overheating of the structure and geometrical distortions. Currently, these cooling times are inserted based on experience at certain interlayer temperatures — which reduces the reproducibility, leads to unwanted component properties, and increases the process time. In this contribution, instationary thermal finite element simulations are applied to compute the temperature evolution of additively manufactured components using the inactive element method. This allows to optimize the process parameters, which are — in our considerations here — the welding velocity and the cooling time of each layer, to reduce the total process time while achieving sufficient component properties. The optimization is carried out with the gradient-free Nelder–Mead simplex algorithm, where certain constraints of the process parameters are considered via penalty functions. To obtain reasonable simulation results, the temperature-dependent heat transfer of the experimental setup is modeled and calibrated with experimental data beforehand. It becomes apparent that thermal finite element simulations combined with a gradient-free optimization procedure are a suitable numerical tool to perform the optimization of process parameters for wire arc additive manufacturing. The optimized process parameters fulfill certain requirements regarding the cooling of the manufactured component. Moreover, the optimized parameters can significantly reduce the process time compared to manually chosen parameters. In our example, this is around 48 %.

Local thermal non-equilibrium effects on phase transition of fiber reinforced thermoplastic composites with temperature-dependent heat generation

Under the excitation of external fields, fiber reinforced thermoplastic (FRTP) composites can be thermally processed due to the internal heat generation, in which the local thermal non-equilibrium (LTNE) can be significant during the phase transition. In this study, a representative elementary volume scale Lattice Boltzmann model was developed to simulate the phase transition process of FRTP composites with the temperature-dependent internal heat source. The results from LTNE model and local thermal equilibrium (LTE) model were compared in terms of the phase interface evolution and the local temperature difference between fibers and matrix, so that the LTNE effects on phase transition behaviors were examined with different material properties and internal heat sources. It is found that the LTNE effects cannot be ignored in FRTP composites, and the main mechanisms include the dynamic local heat generation, endothermic phase transition of matrix, and relatively high thermal conductivity of fiber. A small heat exchange between the fibers and matrix results in a large local temperature difference and a slow phase transition. A high internal heat generation enhances the phase transition and LTNE effects, but an increase in the temperature range for heat generation leads to a slow phase transition with slight change in LTNE effects. With the increase of matrix fraction, LTNE effects first increase and then decrease due to the combined results of the more internal heat generation and the increase of endothermic mass of matrix and the less heat loss through fibers. This study is significant for guiding the reliable thermal processing of FRTP composites in emerging industrial applications.

Strain-dependent ultrafast carrier dynamics and spin–lattice interaction in LaMnO3 films

We investigate the ultrafast carrier dynamics and spin–lattice interaction in strained and unstrained LaMnO3 films via temperature-dependent femtosecond transient optical spectroscopy. The transient reflectivity measurements show two characteristic relaxation processes in both types of films, which are attributed to electron–phonon coupling and phonon-assisted spin–lattice interaction, respectively. The carrier dynamics and coupling between lattice and spin system are well described with the three-temperature model; the spin–lattice relaxation time constant is dominated by the temperature-dependent spin specific heat. Both the electron–phonon coupling and the spin–lattice interaction are enhanced in the strained film, as a result of the modified band structure and orbital ordering under biaxial compressive strain. Our results reveal the critical role of strain in the photo-induced dynamical interactions in LaMnO3.

Probing electron–phonon coupling in magnetic van der Waals material NiPS3: A non-magnetic site-dilution study

NiPS3 is a van der Waals antiferromagnet which has been shown to exhibit spin-phonon and spin-charge coupling in the antiferromagnetically ordered state below TN = 155 K. It is also a rare Ni-based negative charge-transfer-type insulator with Ni valence in a linear superposition state ψ= αd8+ βd9L−+ γ d10L−2 , where L− is the ligand hole. Here, we study high-quality single-crystals of Ni1−x Zn x PS3 (0 < x < 0.2) using temperature-dependent specific heat and Raman spectroscopy probes. We show that in pristine NiPS3, the phonon mode at 176 cm−1 (P2), associated with the vibrations of Ni ions, exhibits a distinct Fano asymmetry. The Fano resonance is particularly pronounced in the paramagnetic phase above TN, which was further confirmed by temperature dependent Raman data on the Zn-doped crystals. In the Zn-doped crystals, while the magnetism weakens following the mean-field prediction for site-dilution in a honeycomb lattice, the Fano coupling |1/q| strengthens, increasing monotonically with increasing Zn-doping. The x-ray photoemission spectra suggest an increase in the weight of the d9 and d10 components in the Zn-doped crystals. These observations indicate the presence of strong electron–phonon coupling in Ni1−x Zn x PS3, in addition to the spin-phonon, and spin-charge coupling previously reported.

Radiation-driven thermoacoustic energy conversion in absorbing media

Thermoacoustic engines rely on an instability that can convert heat into an intense acoustic wave — oscillating pressure and velocity. Being heat-driven, thermoacoustic engines are a promising technology for solar energy conversion, potentially cheap, reliable, and robust, with no moving parts and no exotic materials. Herein, we present an as-yet overlooked mode of triggering a thermoacoustic instability in such engines, driven by radiation. This mode of operation can potentially eliminate much of the viscous losses associated with high-amplitude thermoacoustic energy conversion by eliminating the need for a solid, porous medium with which to mediate heat transfer. A theoretical framework is developed for modeling such devices, with a simplified analysis illustrating that any non-uniform, temperature-dependent heat source has the potential to trigger the thermoacoustic instability. It is then further demonstrated that radiation can indeed drive such instability, with numerical results showing that energy conversion is more substantial when the oscillation period is matched with the characteristic radiative heating time of the gas. A limit-cycle analysis indicates that, for a traveling wave acoustic field, potential efficiencies of up to 90% of Carnot’s efficiency may be achieved, with power densities of up to 5 MW/m3. While several of the assumptions made in the model likely result in lower performance for a real system, the analysis demonstrates the great potential offered by this approach, for future development.

Analysis of heat and mass transfer of a non-linear convective heat generating fluid flow in a porous medium with variable viscosity

The present study addresses the significance of analyzing the heat and mass transfer characteristics of a non-linear convective fluid flow featuring variable viscosity within a porous medium. Our focus lies on understanding the impact of varying viscosity on the hydromagnetic coupling stress, particularly in the presence of internal heat generation. The fluid is confined within a porous medium, and convection cooling takes place at both wall of the fluid. A key assumption in our investigation is the nonlinearity nature of the buoyancy force, specifically when there is a substantial difference in temperature and concentration within the fluid and its surroundings, the buoyancy force becomes quadratic. The exploration of couple stress fluids, alongside considerations of temperature-dependent internal heat generation and mass transfer, contributes to advancing our understanding of thermal system performance. By accounting for nonlinearity in density, temperature, and concentration, the research aims to provide more accurate results than previous linear models, crucial for optimizing energy consumption in practical applications such as nuclear reactors and heat exchangers. Dealing with this type of problem often pose significant challenges, as they often lack analytical solutions, necessitating the use of more advanced numerical methods or approximation techniques. We employ Spectral Quasilinearisation Method (SQLM) to solve the coupled non-linear boundary value problems (PDE) arising from the model, momentum equation, energy equation, concentration equation, and entropy generation. The obtained results are then validated using the Runge–Kutta method and a good agreement is achieved. The findings for the dimensionless velocity, temperature, mass concentration and entropy generation are presented in graphics and in table manner, and effects of controlling parameters are extensively explained. The results highlight that an increase in variable viscosity leads to an enhancement in the velocity profile, while simultaneously reducing the temperature in the system. Furthermore, increments in the non-linear convection parameter and coupling stress parameter result in an appreciation of the velocity profile, temperature profile, and entropy generation rate.

Thermal scrutinization of a triangular porous fin induced by linear and nonlinear temperature-dependent heat generation and magnetic field effect: the case of Darcy model

Thermal scrutinization of a triangular porous fin induced by linear and nonlinear temperature-dependent heat generation and magnetic field effect: the case of Darcy model

The implications of a temperature-dependent heat capacity DCp(t) on temperature-dependent gating in thermoTRPs

The implications of a temperature-dependent heat capacity DCp(t) on temperature-dependent gating in thermoTRPs

Early age cracking relevant to mass concrete dam structures during the construction schedule

Managing the early-age thermal behavior of mass concrete structures like dams, dykes, bridge piers, thick raft foundations, etc., is the major concern during their construction. The heat of hydration (HOH) of the fresh concrete pour does not get easily dissipated to ambiance since concrete is predominantly a poor conductor of heat. Eventually, in the presence of external boundary conditions (thermal or mechanical), the slower rate of heat dissipation may at times induce a substantial thermal gradient within the mass concrete which further may induce thermal stresses leading to the formation of cracks. The article attempts to develop a thermo-mechanical numerical model based on the finite element (FE) methodology to mimic the early age behavior of mass concrete that accounts for time and temperature-dependent heat generation during the hydration process with the evolution of thermal and mechanical properties over time. A two-stage sequential thermo-mechanical model is developed consisting of a thermal model to assess the thermal history of a particular concrete mix which is experimentally validated by performing thermal monitoring of a fresh concrete pour for 10 days, and a mechanical model to assess the stress and the cracking states, the model utilizes the concrete damage plasticity (CDP) model based on the principle of continuum damage mechanics which is characterized by experimental results. Later on, the methodology so developed is employed over a practical scenario of the dam construction process considering the relevant boundary conditions to arrive at a suitable optimum lift height and pouring frequencies.

Complete thermodynamic characterization of second-order phase transition magnetocaloric materials exclusively through magnetometry

To fully assess and improve the performance of near room-temperature magnetic refrigerants, it is crucial to measure and compare their three most relevant thermodynamic properties, and their dependence on temperature (T) and applied magnetic field (H): the isothermal entropy change, ∆Siso(T,H); the adiabatic temperature change, ∆Tad(T,H); and the heat capacity, Cp(T,H). Typically, each thermodynamic property requires its own specialized measurements, which are very time-demanding and can be challenging to setup. In this work, we report a complete thermomagnetic characterization of a benchmark magnetocaloric material, gadolinium, using a single and commercially available SQUID magnetometer. By improving a recently reported method with incremental field ramping steps for measuring temperature through magnetization, we obtained a ∆Tad(T) curve under a 1 T field change with its peak amplitude and maximizing temperature respectively within 2 % and 0.8 % of previously reported values for gadolinium. We were also able to estimate the temperature dependent heat capacity, Cp(T,μ0H=0.85T), using the ∆Tad(T) measurements from magnetometry combined with magnetization versus temperature curves at different field values. This estimate of Cp around the transition temperature of gadolinium is within a relative error of 11 % of the experimental and reported values. The reported methodology allows the complete characterization of a second-order magnetocaloric material (∆Siso(T,H), ∆Tad(T,H), Cp(T,H)) around its Curie temperature using a single and widely available device, which can accelerate studies of different magnetocaloric materials’ performance, and approximate their implementation in magnetic refrigeration and/or waste heat energy harvesting industries.

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.