Simulation Of Heat Conduction Research Articles

A closed-box kernel function for numerical simulation of transient heat conduction

A new kernel function, termed the closed-box kernel function, has been developed to address numerical simulation of transient heat conduction in the same medium. Firstly, this method is versatile and not limited to specific industrial scenarios or designated materials. Secondly, the method solves the spatial temperature at each time point only once, eliminating the need for multiple iterations. Thirdly, the method allows for controlled and adjustable simulation speed of heat conduction while maintaining high accuracy. After 24,700 iterations in the transient process, the relative error in temperature values is merely 0.000072. Fourthly, this numerical technique can break data dependency between spatial nodes, making it suitable for parallel computing with Graphics Processing Units (GPUs). The average speedup achieved is 94.0712 times faster compared to Central Processing Unit (CPU) computations. Finally, we provide mathematical examples to verify the correctness and accuracy of this numerical approach and present a computational framework for parallel computing in the Visual Studio (VS) programming environment to demonstrate its practicality in engineering applications.

A Localized Collocation Method Based on Nonsingular Fundamental Solutions for Steady-State Heat Conduction Analysis in Heterogeneous Materials

This paper further develops a localized nonsingular method of fundamental solutions (LNMFS) for effectively solving heat conduction problems in functionally graded materials (FGMs). In this numerical framework, the LNMFS approach is proposed as a solution for the inhomogeneous boundary value problems, where a pseudo-spectral Chebyshev collocation scheme (CCS) is employed for the approximation of the corresponding particular solutions. In the proposed LNMFS, the artificial boundary that is present in the existing method of fundamental solutions (MFS) is eliminated. Accordingly, the singularities are replaced by the normalized area integrals of the fundamental solution over small circular disks, which encompass the source nodes that intersect with the collocation nodes. The proposed method inherits the high accuracy of the nonsingular method of fundamental solutions (NMFS). Additionally, in contrast to the NMFS, the LNMFS not only possesses the capability to achieve solutions with a notable level of accuracy in nonharmonic boundary condition but also overcomes the constraint of exclusively simulating heat conduction issues in FGMs that exhibit specific spatial variations. The feasibility and accuracy of the recently developed method are demonstrated by means of comparing it with analytical solutions for several numerical examples.

Thermo‐Mechanical Study on Auxetic Shape Memory Periodic Open Cellular Structures—Part I: Characterization of Reentrant Geometry and Effective Heat Conductivity

Periodic open cellular structures (POCS) are additively manufactured supports for heterogeneous catalysts in the field of chemical reaction engineering. Constructed from a repeated unit cell, POCS offer excellent heat transport characteristics due to heat conduction in the continuous solid matrix. However, when inserted into tubular reactors, a loose fit between structure and tube wall results. This considerably hinders heat transfer across the wall. The novel POCS concept presented in this work aims at an intensified wall heat transfer by utilizing a reentrant structure design to ensure auxetic behavior. If the POCS is made of shape memory alloy, it can recover its original shape. Combining these two effects with an initial radial oversize, an interference fit with the tube is established. This contribution comprises the geometric description of reentrant POCS and heat conduction simulations for characterization of the effective heat conductivity, yielding scaling correlations dependent on geometric parameters. Moreover, the effective radial heat conductivity of POCS in cylindrical shape is explicitly investigated. The influencing factor identified is the ratio of tube diameter and cell size: while the ratio increases, the effective radial heat conductivity decreases, but remains well above the effective heat conductivity of the unit cell.

GPU Accelerating Algorithms for Three-Layered Heat Conduction Simulations

In this paper, we consider the finite difference approximation for a one-dimensional mathematical model of heat conduction in a three-layered solid with interfacial conditions for temperature and heat flux between the layers. The finite difference scheme is unconditionally stable, convergent, and equivalent to the solution of two linear algebraic systems. We evaluate various methods for solving the involved linear systems by analyzing direct and iterative solvers, including GPU-accelerated approaches using CuPy and PyCUDA. We evaluate performance and scalability and contribute to advancing computational techniques for modeling complex physical processes accurately and efficiently.

Investigation of thermal diffusivity measurement technique based on photoacoustic signal response under the influence of three-dimesional heat transfer

In this study, we investigated the feasibility of measuring the thermal diffusivity of thermally thick solid material using the photoacoustic (PA) signal response in a three-dimensional heat diffusion state. For this purpose, we developed a heat conduction simulation model based on cylindrical coordinates to replicate the PA effect on three-dimensional heat diffusion. By numerical analysis, it was found that the phase of PA signal deviates from one-dimensional theory prediction when the lateral heat diffusion of the solid sample reaches the chamber wall of PA cell. Specifically, it was found that the phase lag inflects at the frequency where the sample’s thermal diffusion length μs is 0.91 mm at a chamber radius of 3 mm. By utilizing this correlation, the infection frequency can potentially provide the thermal diffusivity of the thermally thick sample. The experimental validation qualitatively confirmed that the phenomena observed in the numerical analysis occur in practice. However, quantitatively, the experimental results showed discrepancies from the numerical analysis, which is likely due to the influence of the radial distribution of laser intensity. Nonetheless, this issue can be resolved in practical applications through calibration using a reference sample. Numerical analysis suggested that for materials with thermal diffusivity lower than that of air, measuring thermal diffusivity could be seemingly impossible. However, the experimental results demonstrated that calibration with a reference sample having sufficiently lower thermal diffusivity than that of air effectively compensates for the influence of air’s thermal diffusion. The significant factor affecting the accuracy of thermal diffusivity determination with the proposed method is identifying the inflection frequency. It will be necessary to explore an appropriate method for determining the frequency by integrating multiple sources of information, such as simultaneously observing the amplitude of the PA signal.

Heat conduction simulation of chondrocyte-embedded agarose gels suggests negligible impact of viscoelastic dissipation on temperature change

Agarose is commonly used for 3D cell culture and to mimic the stiffness of the pericellular matrix of articular chondrocytes. Although it is known that both temperature and mechanical stimulation affect the metabolism of chondrocytes, little is known about the thermal properties of agarose hydrogels. Thermal properties of agarose are needed to analyze potential heat production by chondrocytes induced by various experimental stimuli (carbon source, cyclical compression, etc). Utilizing ASTM C177, a custom-built thermal conductivity measuring device was constructed and used to calculate the thermal conductivity of 4.5 % low gelling temperature agarose hydrogels. Additionally, Differential Scanning Calorimetry was used to calculate the specific heat capacity of the agarose hydrogels. Testing of chondrocyte-embedded agarose hydrogels commonly occurs in Phosphate-Buffered Saline (PBS), and thermal analysis requires the free convection coefficient of PBS. This was calculated using a 2D heat conduction simulation within MATLAB in tandem with experimental data collected for known boundary and initial conditions. The specific heat capacity and thermal conductivity of 4.5 % agarose hydrogels was calculated to be 2.85 J/g°C and 0.121 W/mK, respectively. The free convection coefficient of PBS was calculated to be 1000.1 W/m2K. The values of specific heat capacity and thermal conductivity for agarose are similar to the reported values for articular cartilage, which are 3.20 J/g°C and 0.21 W/mK (Moghadam, et al. 2014). These data show that cyclical loading of hydrogel samples with these thermal properties will result in negligible temperature increases. This suggests that in addition to 4.5 % agarose hydrogels mimicking the physiological stiffness of the cartilage PCM, they can also mimic the thermal properties of articular cartilage for in vitro studies.

Accelerating Transient Aerothermal Simulations of the BOLT II Flight Experiment

Aircraft with short flight durations may not reach thermal steady state due to limited time for aeroheating to conduct throughout their internal structure. Consequently, predictions of the solid temperature field require time-accurate simulation of the transient heat conduction. In this work, the use of an explicit super-time-stepping scheme to accelerate the time-accurate solution of the heat equation has been explored. The experience with this technique is documented here because, to the authors’ knowledge, it is not widely used in the hypersonics simulation community. The performance of the super-time-stepping scheme was investigated by comparison to a standard explicit scheme and an implicit time-differencing scheme. Both the super-time-stepping scheme and the implicit time-differencing scheme demonstrate significant speedup over the standard explicit scheme, with comparable wall-clock performance. The solid solver has been coupled with an existing open-source fluid solver to perform conjugate heat transfer simulations. The efficacy of the developed solver in simulating hypersonic aerothermal problems is demonstrated through verification and validation studies. By applying the coupled solver to the aerothermal analysis of the BOLT II flight experiment, the effectiveness of the super-time-stepping scheme in mitigating the computational expense associated with transient conjugate heat transfer simulations is demonstrated.

Numerical Investigation of Melting in Pressurized Water Reactor Fuel Rod Considering Operational Parameters of the Core

The meltdown of a fuel rod is a severe accident resulting from the overheating of the reactor core. In the present study, a numerical investigation of this process, focusing on the loss of coolant has been conducted. The objective of this study is to conduct a numerical simulation of transient heat conduction and melting at various points within a typical pressurized water reactor fuel rod. In this analysis, heat conduction in the radial direction of a fuel rod, including the UO2 fuel pellet, the gap, and the zircaloy cladding, is investigated. The FRAPCON steady-state code is employed to calculate the operational parameters of the fuel rod. The calculated parameters, such as coolant and fuel temperatures, fission gas fraction, gap heat transfer coefficient, and burnup, are utilized to evaluate and compare the melting phenomena at different time intervals. In the investigation of the phase change in various parts of the pellet and fuel rod, the explicit finite difference (FD) method is utilized with enthalpy instead of temperature-dependent equations. Finally, the temperature history, phase change, and melting map at different points along the radial and axial directions of the fuel rod during coolant loss and heat transfer coefficient reduction are evaluated based on various operating parameters of the core. To enhance the quality of the results, an uncertainty analysis of effective parameters is conducted. According to this analysis, the heat transfer coefficient of the coolant under accident conditions (0.2 ± 5% kWm−2K−1) and the thermal conductivity of the fuel have the most significant impact on the temperature history and melting process. Highlights include the following: 1. The meltdown of a nuclear fuel rod is analyzed under a loss-of-coolant accident. 2. The enthalpy formula is discretized by the explicit FD numerical method. 3. Effective parameters in melting, such as coolant temperature, burnup, and gap heat transfer coefficient, are obtained by FRAPCON. 4. The temperature history, phase changes, and melting map of various radial points within the fuel pellet and cladding along the axial direction of the fuel rod are determined.

A three-dimensional criticality safety analysis code for spent fuel solution system

The nuclear criticality safety analysis is crucial for the nuclear safety of spent fuel reprocessing plants. Thus, a set of numerical tools with high accuracy and efficiency to predict the criticality and simulate the hypothetical accidents in the reprocessing procedure is of great importance. Among them, this paper focus on the analysis of the storage tank which is used for dissolution and storage of the spent fuel. According to the characteristics of spent fuel solution system, a parallel 3D critical safety analysis tool for fissile solution system, Hydra-TD, is developed. Generally, it contains the cross-section generation model, the three-dimensional space-time neutron kinetics model, and the R-Z two-dimensional heat conduction and radiolysis gas simulation model. The verifications based on the experiments of the SILENE and TRACY facility are conducted. The results show good accuracy of the prediction of the first fission power peak, multiplication time and total fission energy, indicating the reliability of these numerical models.

Hyper-reduced-order model for estimating convection heat transfer coefficients of turbine rotors

Forced convection heat transfer occurs inside the steam turbine, and it is crucial for thermal and strength analysis to accurately estimate the convection heat transfer coefficients of the turbine rotor. This paper presents a hyper-reduced-order model for efficiently estimating the forced convection heat transfer coefficients of a steam turbine rotor. Unlike the full-order finite element method, the hyper-reduced-order model uses the discrete empirical interpolation method to approximate the domain integration of transient heat conduction simulations. This approach greatly reduces the degrees of freedom of numerical integration, thus substantially improving the computational efficiency of forward heat conduction problems. The hyper-reduced-order model and Levenberg–Marquardt algorithm are combined to minimize temperature errors between the numerical simulation results and remote sensor measurements and iteratively estimate the heat transfer coefficients of forced convection in the rotor. The accuracy and efficiency of the proposed model are verified through a transient heat conduction simulation. Moreover, the effects of the initial guess values and measurement errors are investigated to demonstrate the universality and robustness of the proposed approach in determining the convection heat transfer coefficient. Compared with the full-order finite element model, the proposed hyper-reduced-order model can increase the efficiency of forward heat conduction simulations of the turbine rotor by more than 10 times, and it only takes 0.87 s computer runtime in single transient step simulation, and then rapidly estimate the forced convection heat transfer coefficients. Furthermore, the performance of the proposed approach is insensitive to the initial guess values, and it exhibits great robustness under measurement error. The mean errors are 4.78 %, 2.67 % and 10.51 % when the initial values are 0.015 mW·mm−3·°C−1, 0.05 mW·mm−3·°C−1 and 0.15 mW·mm−3·°C−1 respectively. When there is no measurement error, the estimated error of the convection heat transfer coefficients is 2.67 %, and even if the measurement error reaches 5 %, and the accuracy loss is only 5.57 %. Consequently, this approach is highly suitable for estimating convection heat transfer coefficients during the dynamic operation of steam turbines, and this research provides reliable guidance for the optimization design and safe operation of steam turbines.

Multiscale phonon thermal transport in nano-porous silicon

We performed a comprehensive multi-scale phonon-mediated thermal transport study of nano-porous silicon (np-Si) films with average porosities in the range of φ = 30%–70%. This depth-resolved thermal characterization involves a combination of optical methods, including femtosecond laser-based time-domain thermo-reflectance (TDTR) with MHz modulation rates, opto-thermal micro-Raman spectroscopy, and continuum laser wave-based frequency domain thermo-reflectance (FDTR) with kHz modulation rates probing depths of studied samples over 0.5–1.2, 2–3.2, and 23–34 μm, respectively. We revealed a systematic decrease in thermal conductivity (k) with the rise of φ, i.e., with the lowering of the Si crystalline phase volumetric fraction. These data were used to validate our semi-classical phonon Monte Carlo and finite element mesh simulations of heat conduction, taking into account disordered geometry configurations with various φ and pore size, as well as laser-induced temperature distributions, respectively. At high φ, the decrease in k is additionally influenced by the disordering of the crystal structure, as evidenced by the near-surface sensitive TDTR and Rutherford backscattering spectroscopy measurements. Importantly, the k values measured by FDTR over larger depths inside np-Si were found to be anisotropic and lower than those detected by the near-surface sensitive TDTR and Raman thermal probes. This finding is supported by the cross-sectional scanning electron microscopy image indicating enhanced φ distribution over these micrometer-scale probed depths. Our study opens an avenue for nano-to-micrometer scale thermal depth profiling of porous semiconducting media with inhomogeneous porosity distributions applicable for efficient thermoelectric and thermal management.

Multi-GPU parallel acceleration scheme for meshfree peridynamic simulations

Peridynamics (PD) using integral equations has unique advantages in modeling structural damage evolution, but the expensive computational and memory costs associated with the nonlocal nature of PD severely limit its engineering applications. This study presents a CUDA-based multi-GPU parallel scheme for meshfree PD simulation, which is compatible with dual-horizon PD supporting multiscale spatial discretization. Efficient utilization of computing resources across all available GPUs is achieved by rationalizing data structures across multiple GPUs and using the CUDA memory model. Using atomic operations to avoid computational dual-bond forces further improves code performance. The classical Kalthoff-Winkler experiment and compact-tensile fatigue test were first carried out using 3 NVIDIA Tesla T4 GPUs. Two examples showed that the proposed scheme significantly accelerates the PD model and that the acceleration enhances approximately linearly with the number of GPUs. The speedup of the PD interaction force computation reaches up to 560.7x. Compared to double-precision floating-point values, the GPU performs much better in handling single-precision values. Finally, a PD simulation of rail head heat conduction under moving heat sources with nearly 76 million particles was realized, demonstrating the potential of the proposed scheme to support large-scale PD simulations.

Peridynamic modeling of transient heat conduction in solids using a highly efficient algorithm

This article presents a novel peridynamic algorithm to model the transient heat conduction in two-dimensional (2-D) problems. The peridynamic method is used to solve the heat transfer equation, and a new algorithm is developed to simulate heat conduction efficiently. The new peridynamic algorithm can simulate the heat conduction for the whole geometry within only 2 s when using up to 5,000 particles and 5,000 simulation steps, where the mesh-free nature of peridynamics is well utilized. Moreover, the thermal results obtained from the new peridynamic algorithm demonstrate high accuracy by solving several heat conduction problems under different boundary conditions. The results are validated against exact and analytical solutions and compared with other numerical models. The developed algorithm can be easily implemented in software packages and industrial applications.

A comprehensive study for evaluation of cell cooling coefficient of the batteries of fixed sizes and batteries with defects in manufacturing

For the evaluation of cooling performance of Li-ion battery thermal management systems, the commonly used metrics are lumped thermal conductivity, thermal conductance, Biot number, etc. However, such metrics are limited to describing the thermal performance of Lithium-ion batteries (LIBs) and expressing the heat rejection from a body generating heat within its volume. In this perspective, a new metric, such as cell cooling coefficient (CCC), can be introduced to measure the heat rejection capability of cells, which can be used to formulate efficient thermal management strategies. However, limited works describe the system's thermal performance based on CCC, which needs thorough investigation. This work illustrates a comprehensive heat conduction simulation using heat flux through electrode tabs, average temperature of electrode tabs, max cell temperature, total CCC, and the electrode CCC as the thermal indexes to describe the thermal behavior of batteries with five manufacturing defects and study the correlation between heat rejection performance and the CCC of the system. The results of the analysis claim that batteries with different manufacturing defects have different CCC values and thermal performance. Increasing the width of electrode tabs can increase the total CCC of the system, reduce the difference in the electrode CCC values, and further decrease the max cell temperature. The total CCC and the difference in the CCC value of each tab of the battery can be applied to describe the heat rejection performance of the system. The findings of this work can guide further work on optimizing the structure to improve the thermal performance of the cell.

Coupling transport equations to mechanics in the material point method using an approximate full capacity matrix inverse

Coupling solutions of one or more transport equations to mechanics modeling in the material point method (MPM), extends MPM to a platform for solving multi-physics problems. Unfortunately, the standard MPM approach to transport equations using a lumped transport capacity matrix is prone to large oscillations in particle values especially near interfaces, cracks, or rapid changes in transport value. Switching from lumped capacity matrix methods to an approximate full capacity matrix approach can eliminate those oscillations. Although this switch can cause unwanted numerical diffusion, that problem can be suppressed using periodic or blending options. Several examples illustrate the new methods for heat conduction, solvent transport, poroelasticity, and phase field fracture simulations. In thermal calculations, the new methods improve accuracy for tracking thermodynamics state functions.

An implicit thermo-mechanical coupling model for heat conduction and thermal cracking in brittle materials

In this paper, an implicit thermo-mechanical coupling model is developed to simulate heat conduction and thermal cracking in brittle materials. In the thermal analysis, an implicit particle heat conduction model (PHCM) is proposed. A linear algebraic system of heat conduction equations is derived based on the temperatures of the particle system and the heat flux among adjacent particles. An analytical expression is introduced for the involved correction coefficient, with which the macroscopic thermal conductivity coefficient can be directly adopted without calibration. Furthermore, a thermal conductivity reduction coefficient is introduced to account for the thermal resistance of the cracks. In the mechanical analysis, particle discontinuous deformation analysis (PDDA), which is an implicit variant of the discrete element method, is employed. The PHCM is first verified against analytical and finite element solutions for transient heat conduction problems. The results show that the PHCM is an effective and accurate heat conduction model that readily reflects the thermal resistance of cracks. Then, the thermo-mechanical coupling model is verified by the expansion of heated specimens under different conditions. Finally, the successful application of the coupling model in the simulation of thermal shock tests demonstrates its effectiveness for thermal cracking problems.

Highly thermally conductive electrically insulating composites composed of core–shell structure fiber boron nitride@titanium dioxide filler

AbstractWith the increasing integration and power density of electronic and electrical equipment, highly thermally conductive insulating materials have a wide range of application scenarios. In this paper, a novel core–shell structure fiber thermal conductive filler hexagonal boron nitride@anatase titanium dioxide (h‐BN@AT) has been prepared by electrospinning technology first. The h‐BN@AT/epoxy resin (EP) thermally conductive and insulating composite was prepared by hot pressing. When the filler content was 30 wt%, the optimal thermal conductivity (λ) of h‐BN@AT/EP composite was 7.62 W/(m·K) (in‐plane) and 0.76 W/(m·K) (out‐of‐plane), which were 3088% and 324% higher than EP. The incorporation of high aspect ratio core–shell structural fibers significantly improves the efficiency of thermal conduction (TC) pathways formation within the composite. Moreover, the utilization of one‐dimensional (1‐D) anatase titanium dioxide fiber (ATO) and two‐dimensional (2‐D) boron nitride (h‐BN) establishes a multi‐level TC channel in EP, significantly increasing the λ of the composite. Notably, the composite retains outstanding insulation properties. The innovative core–shell structural fibers filler developed in this study provides a feasible method for producing thermal conductivity insulating materials.Highlights A new type of core–shell structure h‐BN@AT fiber filler is designed. High thermal conductivity insulating composite h‐BN@AT/EP are prepared by hot pressing. h‐BN@AT can effectively improve the thermal conductivity of composite to ensure good electrical properties. The effect of h‐BN content in h‐BN@AT filler on the properties of the composite was obtained. The superiority of h‐BN@AT in heat conduction is verified by the classical heat conduction model and simulation.

Numerical Simulation of Heat Conduction in Laser Ablation Based on Optimal Weight Factor

Numerical Simulation of Heat Conduction in Laser Ablation Based on Optimal Weight Factor

Efficient BEM Modeling of the Heat Transfer in the Turbine Blades of Aero-Parts

The modeling of the turbine blades in aero-parts presents difficulties in conventional domain solution techniques, especially when internal cooling air passages and a thermal barrier coating (TBC) are applied. This paper presents a very efficient 3D modeling of the anisotropic heat conduction in turbine blades with the boundary element method (BEM), where both the TBC and cooling air passages are considered. The BEM is very ideal for this modeling, since only boundary meshes are required for it; however, a serious problem of nearly singular integration will arise in modeling with coarse meshes. In this article, an efficient modeling and computational algorithm using the BEM is applied for the simulation of heat conduction in the turbine blades of aero-parts. The present work proposes a simplified BEM model to replace multiple thin coating layers on the top of the blade. In the end, the veracity of the implemented BEM code as well as its computational efficiency are illustrated with a few examples, showing that the settled temperature on the substrate can be reduced by 20% by employing a TBC. As compared to the analyses with ANSYS, the percentages of difference were within 2%, while the CPU time spent by the BEM algorithm was about 1/8 of that of ANSYS, not to mention the meshing efforts saved by adopting by a treatment of equivalent convection.

Quantum bath augmented stochastic nonequilibrium atomistic simulations for molecular heat conduction.

Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking in the quantum Landauer-type transport model, such as many-body full force-field interactions, anharmonicity effects and nonlinear responses for large temperature biases. However, the classical MD reaches its limit in the environments where the quantum effects are significant (e.g. with low-temperatures substrates, presence of extremely high frequency molecular modes). Here, we present an atomistic simulation methodology for molecular heat conduction that incorporates the quantum Bose-Einstein statistics into an "effective temperature" in the form of a modified Langevin equation. We show that the results from such a quasi-classical effective temperature MD method deviates drastically when the baths temperature approaches zero from classical MD simulations and the results converge to the classical ones when the bath approaches the high-temperature limit, which makes the method suitable for full temperature range. In addition, we show that our quasi-classical thermal transport method can be used to model the conducting substrate layout and molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic models are explicitly simulated via the Morse potential and compared to pure harmonic interactions to show the effects of anharmonicities under quantum colored bath setups. Finally, the chain length dependence of heat conduction is examined for one-dimensional polymer chains placed in between quantum augmented baths.