Three-dimensional Heat Conduction Research Articles

Heat transport during drop impact onto a heated wall covered with an electrospun nanofiber mat: The influence of wall superheat, impact velocity, and mat thickness

Nanofiber surface coating is a promising method for the enhancement of heat transfer during spray cooling. In the present work, the drop dynamics as well as local and overall heat transfer during single drop impact onto a heated wall covered with a polyacrylonitrile (PAN) nanofiber mat are investigated to obtain insight into the mechanisms governing the heat transport enhancement. The influence of wall superheat, drop impact velocity, and mat thickness on the hydrodynamics and heat transfer from the heated wall to the fluid is studied. The experiments were conducted inside a temperature-controlled test cell with a pure vapor atmosphere maintained with refrigerant FC−72 (perfluorohexane). The temperature field at the solid-fluid interface was observed with a high-speed infrared camera, and the heat flux field was derived by solving a three-dimensional transient heat conduction equation within the substrate. The presence of the nanofiber mat on the heater surface suppresses the drop receding phase due to the pinning of the contact line at the end of the spreading phase. Two different heat transfer scenarios are observed depending on the wall superheat and drop impact velocity: scenario (I), in which the liquid drop completely penetrated through the porous nanofiber mat and made contact with the heater surface; and scenario (II) in which the vapor produced inside the pores of the nanofiber mat prevented the liquid drop from touching the heater surface. In scenario (I), an up 450% heat flow enhancement during the sessile drop evaporation stage has been observed. In scenario (II), a 80% heat flow enhancement at this stage has been registered.

An Implementation of LASER Beam Welding Simulation on Graphics Processing Unit Using CUDA

The maximum number of parallel threads in traditional CFD solutions is limited by the Central Processing Unit (CPU) capacity, which is lower than the capabilities of a modern Graphics Processing Unit (GPU). In this context, the GPU allows for simultaneous processing of several parallel threads with double-precision floating-point formatting. The present study was focused on evaluating the advantages and drawbacks of implementing LASER Beam Welding (LBW) simulations using the CUDA platform. The performance of the developed code was compared to that of three top-rated commercial codes executed on the CPU. The unsteady three-dimensional heat conduction Partial Differential Equation (PDE) was discretized in space and time using the Finite Volume Method (FVM). The Volumetric Thermal Capacitor (VTC) approach was employed to model the melting-solidification. The GPU solutions were computed using a CUDA-C language in-house code, running on a Gigabyte Nvidia GeForce RTX™ 3090 video card and an MSI 4090 video card (both made in Hsinchu, Taiwan), each with 24 GB of memory. The commercial solutions were executed on an Intel® Core™ i9-12900KF CPU (made in Hillsboro, Oregon, United States of America) with a 3.6 GHz base clock and 16 cores. The results demonstrated that GPU and CPU processing achieve similar precision, but the GPU solution exhibited significantly faster speeds and greater power efficiency, resulting in speed-ups ranging from 75.6 to 1351.2 times compared to the CPU solutions. The in-house code also demonstrated optimized memory usage, with an average of 3.86 times less RAM utilization. Therefore, adopting parallelized algorithms run on GPU can lead to reduced CFD computational costs compared to traditional codes while maintaining high accuracy.

A novel PCM/expanded graphite composite sphere with high thermal conductivity and excellent shape stability used for a packed-bed thermal energy system

In this research, a novel phase change material (NPCM) sphere was developed and its application in a packed-bed thermal energy storage (PBTES) system during thermal energy storage was studied. Paraffin wax (PW) with a melting point of 40 °C was selected as phase change material (PCM), expanded graphite (EG) as thermal conductivity enhancement material, and epoxy resin (ER) as a surface coating. The results show that the three-dimensional heat conduction network constructed by EG foam improves the thermal conductivity of PW/EG. The thermal conductivity of NPCM is anisotropic. The thermal conductivities perpendicular and parallel to the EG compression direction are 9.03 (W/m·K) and 5.58 W/(m·K). NPCM has excellent shape stability with a leakage rate of only 2.95 %. Then, a PBTE system was built to record the temperature evolution of NPCM spheres at various inlet temperatures and volume flow rates during thermal energy storage, and thermodynamic analysis was performed. The results are as follows. (1) The temperature of the NPCM sphere near the inlet rises more rapidly and the melting time of PCM is shorter. (2) Increasing the inlet temperature improves the heat transfer and shortens the melting time of PCM while increasing the temperature inhomogeneity of the NPCM spheres. Increasing the inlet temperature increases the energy storage capacity. However, higher inlet temperature leads to lower energy efficiency and exergy efficiency. The energy efficiency and exergy efficiency are 49.66 % and 67.64 % for the inlet temperature of 60 °C, respectively. When the inlet temperature increases from 60 °C to 80 °C, the energy efficiency and exergy efficiency decrease by 16.13 % and 16.22 %, respectively. (3) Higher inlet volume flow rate also promotes heat transfer and reduces the melting time of the PCM, but has little effect on the temperature inhomogeneity of the NPCM spheres. Increasing the inlet volume flow rate does not increase the energy storage capacity. Similarly, increasing the inlet volume flow rate also results in a decrease in energy efficiency and exergy efficiency. At the inlet volume flow rate of 19.28 m3/h, the energy efficiency and exergy efficiency are 41.65 % and 56.67 %, respectively. When the inlet volume flow rate increases from 19.28 m3/h to 25.16 m3/h, the energy efficiency reduces by 7.80 % while the exergy efficiency reduces by 7.41 %. This research provides a foundation for the application of the NPCM sphere.

Effects of Flow Pulsation and Surface Geometry On Heat Transfer Performance in a Channel with Teardrop-Shaped Dimples Measured by Transient Technique

Abstract This study focuses on the heat transfer performance of a pulsating flow over a channel surface with teardrop-shaped dimples. Heat transfer measurements were performed by a transient technique with compensation of three-dimensional heat conduction under a bulk Reynolds number of 25,000. Seven types of surfaces with the teardrop-shaped dimples were examined, where dimple arrangement (in-line/staggered) and inclination angle (0-60 deg) were varied. A pulsating flow with the Strouhal number of 0.15 was generated by vibrating a rubber film section on the channel wall using a vibration generator. The pulsation amplitude was evaluated by calculating the root-mean-square value of the phase averaged velocity. Two conditions of the pulsation amplitudes were examined (0.09 and 0.12 of mean velocity). The results showed that the surface-averaged Nusselt number and friction factor for the pulsating flow increased from those for the steady flow. The highest increases of the surface-averaged Nusselt number and heat transfer efficiency index appeared in the 30deg in-line arrangement, and those were 16.1% and 9.8%, respectively, at most as compared with the steady case. Due to the flow pulsation, the local Nusselt number was enhanced at the leading-edge region of the dimples, and supplementary RANS/URANS results showed that the flow separation size was shrunk by the flow pulsation there.

Implementation of the preCICE coupling interface for AC2/ATHLET

Abstract The design of new nuclear reactor types as well as the analysis of certain phenomena in existing reactors require to consider different physical models and three-dimensional phenomena like the effect of turbulence in fluids and three-dimensional (3D) heat conduction in complex structures. One-dimensional (1D) lumped parameter system codes used to simulate transients in nuclear reactors lack high-resolution models. Special codes like computational fluid dynamics (CFD) or computational structural mechanics codes (CSM) can simulate those, but they require significantly more computational resources. Therefore, different coupling methods have been developed to limit the use of computationally expensive codes to those parts of a plant where they are really needed and couple them with systems codes, which simulate the rest. The library preCICE enables simultaneous coupling of multiple simulation programs, e.g., the 3D CFD code OpenFOAM and the 3D CSM code CalculiX. preCICE coupling interfaces were developed for the system code ATHLET. We focused on fluid-fluid couplings and conjugate heat-transfer couplings. Coupled simulations were performed for an experiment at the test facility TALL for the transition from forced to natural circulation coupling ATHLET with OpenFOAM, and a generic building condenser geometry coupling the three codes ATHLET, CalculiX, and OpenFOAM. The correct integral transfer of the quantities at the coupling interfaces was verified. However, it was found that coupled quantities at the interfaces need to be converted from 0D to 2D and backwards considering the underlying physics, which goes beyond the pure numerical considerations of the preCICE library.

A LOCALIZED MESHLESS METHOD FOR TRANSIENT HEAT CONDUCTION WITH APPLICATIONS

The localized radial basis function (RBF) meshless approach is well suited for modeling transient heat conduction. The advantages of meshless methods, such as ease of discretization, are well known. However, there are still few examples of the method extended to three-dimensional (3D) transient heat conduction for geometries of practical engineering importance; in particular, with respect to graphics processing units (GPUs). In this study, we investigated the localized RBF meshless method in 3D transient heat conduction and explored its application for GPUs. Numerical examples are provided with an application to modeling chip cooling and friction welding.

Scale-Dependent Generalized Thermoelastic Damping in Vibrations of Small-Sized Rectangular Plate Resonators by Considering Three-Dimensional Heat Conduction

Given that thermoelastic damping (TED) is one of the main causes of energy dissipation in miniaturized structures, calculation of its exact amount is of particular importance in the design of such elements. Considering three-dimensional (3D) heat transfer along with the scale effect on both mechanical and thermal areas is one of the decisive factors in the more rigorous modeling of TED in small-sized resonators. This paper exploits the modified couple stress theory (MCST) and dual-phase-lag (DPL) heat conduction model to establish an analytical TED relation for rectangular micro/nanoplate resonators with 3D heat conduction. At the start, the non-Fourier heat equation corresponding to 3D DPL model is derived. Then, the solution of temperature distribution is determined by employing infinite trigonometric series. Moreover, the scale-dependent frequency of the system is presented in the context of MCST. Eventually, with the help of entropy generation (EG) method, an analytical TED expression considering 3D heat conduction is established. The precision of the presented solution is examined by comparing it with a simpler model available in the literature. By choosing two common types of boundary conditions, i.e. fully-clamped (CCCC) and fully-simply (SSSS) supported plates, the influence of various factors on TED changes is comprehensively investigated in simulation section. According to the outcomes, in plates with a lower ratio of length and width to thickness, the dimension considered for heat conduction model has a noticeable impact on the variations of TED.

Detection of surface moving heat source using experimental temperature measurements on the opposite surface and inverse techniques

The identification of mobile sources is a widely researched area in multiple scientific and technical domains. Detecting mobile heat sources is an essential task in different fields, including fire safety, environmental monitoring, material science, and energy systems. In this investigation, we present an innovative solution to solve the inverse problem of detecting mobile heat sources, utilizing a three-dimensional transient inverse heat conduction problem (IHCP) formulation. The goal is to identify a moving heat source from thermographic infrared measurements of the rear face. The proposed method includes a finite volume approach with model reduction techniques to improve computational efficiency. Additionally, we use the conjugate gradient method to solve the inverse problem. We verified the proposed approach by conducting experiments on a metal plate with a moving heat source from a laser and comparing recalculated temperature of the front face with thermocouple measurements. Our results indicate that our method can detect the location and trajectory of the mobile heat source with high accuracy and efficiency. This study also highlighted the limits of source speed that can be detected by this method. This technique could be considered as an excellent option for real-time monitoring of mobile heat sources in practical applications.

Enhancement Effect of a Diamond Network on the Flow Boiling Heat Transfer Characteristics of a Diamond/Cu Heat Sink

The use of a micro heat sink is an effective means of solving the problem of high-power chip heat dissipation. Diamond/Cu composites exhibit high thermal conductivity and a linear thermal expansion coefficient that is compatible with semiconductor materials, rendering them ideal micro heat sink materials. The aim of this study was to fabricate diamond/Cu and Cu separately as heat sinks and subject them to flow boiling heat transfer experiments. The results indicate that the diamond/Cu heat sink displayed a decrease in wall superheat of 10.2–14.5 °C and an improvement in heat transfer coefficient of 38–51% compared with the Cu heat sink under identical heat fluxes. The heat sink also exhibits enhanced thermal uniformity. Secondary diamond particles are incorporated into the gaps of the main diamonds, thereby constructing a three-dimensional heat conduction network within the composite material. The diamond network enhances the internal heat flux of the material while also creating more nucleation sites on the surface. These increase the boiling intensity of the diamond/Cu heat sink, leading to better heat transfer performance. By combining the transient thermal model with computational fluid dynamics, a heat transfer model based on the diamond/Cu heat sink is proposed. The efficient heat dissipation capability of diamond/Cu heat sinks can lower the working temperature of microelectronic devices, thereby improving device performance and reliability during operation.

MLS-based numerical manifold method based on IPIM for 3D transient heat conduction of FGMs

In this study, the moving least squares based numerical manifold method (MLS-NMM) is presented to solve three-dimensional (3D) transient heat conduction problems of functionally graded materials (FGMs), where the increment dimensional precise integration method (IPIM) is applied to integrate the ordinary differential equations derived from the semi-discrete form. In the 3D MLS-NMM, the influence domains of the MLS-nodes are taken as the mathematical patches which are used to construct the mathematical cover (MC), and the shape functions of the MLS-nodes are employed as the weight functions subordinate to the MC. MLS-NMM is utilized for spatial discretization of the weak form of the problem. The IPIM overcomes the shortcomings of traditional backward difference scheme dependent on the time step and greatly improves the computing efficiency. Meanwhile, a mass lumping technique is proposed for the 3D MLS-NMM. Furthermore, a number of numerical experiments on transient thermal conduction are conducted, suggesting that the 3D MLS-NMM based on IPIM and the proposed mass lumping has excellent accuracy, absolutely stable and high computing efficiency.

Numerical Simulation of Temperature Field during Electron Beam Cladding for NiCrBSi on the Surface of Inconel 718

This study investigates the Inconel 718 alloy coated with NiCrBSi powder using the ABAQUS software. An accurate conical heat source model is constructed based on the three-dimensional Fourier heat conduction law. The heat source subroutine Dflux.for is successfully integrated to achieve a highly realistic simulation of the welding heat source. Using this model, the analysis focuses on the temperature distribution in electron beam melting. Furthermore, the accuracy and reliability of the simulation are validated through actual coating experiments. By examining the impact of various procedural factors on the temperature distribution, it is found that optimal coating results and a tightly formed elliptical molten zone are attained at an electron beam current of 18 mA, and the scanning speed is 300 mm/min. The peak temperature in the melt pool in the coating area is 5087 K, while the lowest temperature on the isothermal in the heat-affected zone is 1409 K. Over time, there is a swift rise in temperature for the data points taken along both the X and Z trajectories, followed by rapid cooling after rapid heating. Coating experiments conducted under the optimal parameters demonstrate a dense coating layer and good bonding with the substrate, thereby validating the accuracy of the simulation.

Hyperbolic lattice Boltzmann method for three-dimensional non-Fourier heat conduction with phase change

The study described the simulation of 3D non-Fourier heat conduction with phase change using a hyperbolic lattice Boltzmann method (HLBM). The equilibrium distribution function was modified for the temperature to develop a new approach for handling the latent-heat source term. Unlike the commonly used lattice Boltzmann method (LBM), the hyperbolic collision operator was used in the HLBM process. The approach enabled the recovery of the enthalpy conservation equation and avoided the need for iteration stages or solving groups of linear equations. This suggests that the approach is more efficient and accurate than previous methods. Overall, the study demonstrates the potential of using HLBM for simulating complex thermal processes, particularly those involving phase change. The method could be useful in various applications, such as in the design of efficient heat exchangers or in understanding the behavior of materials during phase transitions.

Coupled Monte Carlo and Thermal-Hydraulics Modeling for the Three-Dimensional Steady-State Analysis of the Xi’an Pulsed Reactor

The Xi’an Pulsed Reactor (XAPR) is characterized by its small core size and integrated fuel moderator structure, which results in a non-uniform core power and temperature distribution. Consequently, a complex coupling relationship exists between its core neutronics and thermal hydraulics, necessitating the assurance for the operational safety of the XAPR. To optimize the experimental scheme in the reactor, a refined three-dimensional steady-state nuclear-thermal coupling analysis is imperative. This study focuses on investigating the coupling calculation of a three-dimensional steady-state neutronics and thermal-hydraulics model for the XAPR by utilizing an open-source multi-physical coupling framework known as Cardinal. The neutron transport equation is effectively solved using OpenMC, while a three-dimensional heat conduction model is employed to compute the heat conduction of the fuel elements. Furthermore, a parallel multi-channel model is utilized to determine the fluid heat transfer. The research is centered on the XAPR, whereby Monte Carlo and thermal-hydraulics coupling calculations of the core under steady-state full-power conditions are conducted, specifically at an operational capacity of 2 MW. The results demonstrate a strong agreement between the simulation and experimental outcomes. The maximum temperature recorded for the thermometric fuel element in the XAPR is 795.1 K, with a deviation of approximately −5.7% from the measured value. Moreover, the outlet fluid temperature of the thermal channel is observed to be 360 K, exhibiting a deviation of around −2.7% from the measured value.

MLS-based numerical manifold method for steady-state three-dimensional heat conduction problems of functionally graded materials

In this study, the moving least squares based numerical manifold method (MLS-NMM) is firstly applied to discretize three-dimensional (3D) steady heat conduction problems of functionally graded materials (FGMs). In the 3D MLS-NMM, the influence domains of nodes in the moving least squares (MLS) are used as the mathematical patches to construct the mathematical cover (MC); while the shape functions of MLS-nodes as the weight functions subordinate to the MC. Compared with the traditional NMM using finite elements to form the MC, the cutting operations in generating the physical cover are unnecessary and the computation complexity is decreased significantly. Based on the Galerkin method, the discrete form of 3D heat conduction is derived. Finally, a series of numerical experiments concerning steady heat conduction problems are performed, suggesting that the proposed MLS-NMM enjoys advantages of both MLS and NMM in solving steady heat conduction.

Thermally-Induced Stresses in a Pre-Buckling State of a Circular Plate within the Fractional-Order Framework

This paper considers a transient thermoelastic problem in an isotropic homogeneous elastic thin circular plate with clamped edges subjected to thermal load within the fractional-order theory framework. The prescribed ramp-type surface temperature is on the plate's top face, while the bottom face is kept at zero. The three-dimensional heat conduction equation is solved using a Laplace transformation and the classical solution method. The Gaver–Stehfest approach was used to invert Laplace domain outcomes. The thermal moment is derived based on temperature change, and its bending stresses are obtained using the resultant moment and resultant forces per unit length. The results are illustrated by numerical calculations considering the material to be an Aluminum-like medium, and corresponding graphs are plotted.

A new general analytical PBEM for solving three-dimensional transient nonlinear heat conduction problems with spatially-varying heat generation

In this paper, a polygonal boundary element method (PBEM) is presented, to solve the transient nonlinear heat conduction problems with spatially variable heat generation and temperature-dependent thermal physical properties. A new general method is developed to analytically compute the domain integrals regarding arbitrary nonlinearly-varying thermal conductivity, specific heat, and density, by which the computations of numerous Gaussian points in the numerical method can be circumvented and the efficiency of the PBEM can be significantly improved. The finite difference scheme is employed to evaluate the transient term, and the Newton iterative method is used to search the exact solution of the nonlinear system equation. Four numerical examples are designed to examine the property of the proposed method. The results indicate that the proposed analytical PBEM can accurately solve the three-dimensional transient nonlinear heat conduction problems with heat generation.

Inverse Estimation of Effective Thermal Conductivity of Multilayer Materials Considering Thermal Contact Resistance

Abstract Multilayer materials have been widely used in engineering applications, attributed to excellent thermo-mechanical performances. However, the thermal or mechanical properties of multilayer materials remain elusive, owing to contact behaviors etc. factors. In order to address this issue, an innovative method is employed to estimate the effective thermal conductivity (ETC) of multilayer materials considering thermal contact resistance (TCR) between layers, and the equivalence performance is investigated by solving three-dimensional inverse heat conduction problems. First, the equivalence method is validated by available experimental data of a multilayered insulation composite material. Then, the precision of different equivalence methods is compared, and the results indicate that the anisotropic equivalence method has higher accuracy than the isotropic and orthotropic equivalences for the five-layer material in the present work. Finally, the robustness and stability of the anisotropic equivalence method are evaluated in detail. The present work provides a new alternative method for predicting the effective thermal conductivity of multilayer materials.

Experimental investigation and modeling of falling film heat transfer on partial dry-out condition

Falling film heat transfer has been applied for decay heat removal in more and more nuclear reactors, in which the coolant feed rate is set small to prolong the effective cooling time during accident conditions. Previous works have shown that the cooling surface is under partial dry-out condition for most of the time during the accident, while the existing falling film experiments are mainly focused on fully-wetted condition. In this paper, falling film experiments were conducted on a horizontal plain copper tube within 0.019–0.099 kg/m·s coolant flow rate, 0–164.1 kW/m2 heat flux, and dry-out condition is emphasized. In the experiments, it is found that the overall liquid coverage rate measured by infrared equipment was between 45.2 % and 100 %, and the dry-out process is recorded and analyzed as well. Moreover, HTC (Heat Transfer Coefficient) at wetting area is defined to characterize the heat transfer on the surface covered by liquid and is obtained based on a three-dimensional heat conduction model of test tube. Boiling HTCs on falling film are found 10 % approximately higher than that in pool boiling condition. The difference is attribute to the different mechanism of bubble departure and bubble growth environment, with which the falling film condition is found to result in a 1–3 times bubble departure diameter and a 0.85 times bubble growth rate compared with pool boiling condition. Finally, a general falling film heat transfer model is developed based on the conservation equations with consideration of liquid coverage, gas–liquid interface evaporation and liquid sub-cooling. The model shows effective for falling film heat transfer prediction on both fully-wetted and dry-out, convection and boiling conditions with different working fluids through the validation with a number of experimental data. The findings in this work could be helpful for the design and analysis of nuclear cooling system, as well as the falling film evaporation system.

Enhancing mechanical property and thermal conductivity of fluororubber by the synergistic effect of CNT and BN

Fluororubber (FKM) shows great potential in the sealing field of high-end equipment components due to its excellent mechanical properties and sealing performance. However its low thermal conductivity limits its application in a wider range of fields. Here, we compounded hexagonal boron nitride (BN) nanosheets and single-walled carbon nanotubes (CNT), and then introduced them into FKM matrix to enhance its thermal conductivity and mechanical properties, thus x-BN/CNT/FKM composites (x represents filler addition amount) were prepared. The results show that the synergy between BN and CNT contributes to the formation of three-dimensional filler network, which improves its mechanical properties and promotes the formation of efficient three-dimensional heat conduction network. Compared with original FKM and x-BN/FKM composites, x-BN/CNT/FKM composites shows better vulcanization performance, enhanced mechanical properties, thermal conductivity and thermal stability. Especially, the thermal conductivity of 2BN/CNT/FKM composites reached 0.395 W/(m·k), which was 28.2 % higher than that of original FKM composites. In addition, the thermal management performance analysis also shows that 2BN/CNT/FKM composites possess excellent heat transfer ability during heating and cooling processes. 2BN/CNT/FKM composites have great application potential in the fields of high-end sealing materials, due to their remarkably improved mechanical performance and thermal conductivity at low filling level.

Mathematical model of slab heating in a furnace with walking beams

Slab heating before hot rolling is necessary for obtaining required metal ductility. The most effective for this purpose are furnaces with walking beams that provide heat supply to all sides of the slab. However, the areas of slabs lower surfaces, contacting with water-cooled beams, are shielded from the radiation of the furnace lower heating zones and take the heat from the beams.To study the inhomogeneity of the slab temperature field and its dependence on the peculiarities of their transport system design, a mathematical model of slab heating in a furnace with walking beams was developed and programmatically implemented, based on numerical solution of a three-dimensional heat conduction problem with piecewise defined boundary conditions on the lower surface. For the open areas of the slab bottom surface, the same boundary conditions were set as on the top surface; and for the areas of contact with the beams, modified boundary conditions were set, taking into account the duration of this contact. For the numerical solution of the system of difference equations, the line-by-line method was applied, which allows us to obtain a system with a three-diagonal matrix of coefficients. The calculations carried out in the approximation of adiabaticity of the contact areas of the slab with the beams during the contact period allowed us to obtain temperature fields for different slab sections. As a result, a significant irregularity of temperature field of the slab lower surface was revealed, affecting the irregularity of temperature field of the entire slab. The developed program for calculating and visualizing the results can be used to study the temperature field of the slab under various heating modes if there is experimental information that allows one to clarify the tuning parameters of the model.