Transient Heat Conduction Model Research Articles

Understanding tool cutting-edge microstructure and deformation mechanism induced by adhesive wear in the turning of nickel-based superalloys

Nickel-based superalloy has great potential in the aerospace industry as key components. However, difficult-to-machine characteristics have further limited its application. Thermal-barrier coatings of the titanium-based family on carbide tools offer exceptional performance in cutting superalloys, combining high-temperature stability and remarkable toughness. This work primarily concentrates on understanding cutting-edge microstructure and deformation induced by tool adhesive wear in the turning of nickel-based superalloys with experiment and modelling. The dominant tool wear mechanisms are revealed to be adhesive wear and abrasive wear by SEM/EDS. The microstructure of the cutting-edge interface is qualitatively and quantitatively investigated by SEM/EDS and EBSD. The adhesive layer thickness at cutting edge is about 10–30 μm. The GND density of WC grains at cutting edge is 15-20 × 1014/m. The nanomechanics properties of the tool wear interface were quantitatively evaluated by nanoindentation. The average hardness of WC and Ni-superalloy at cutting-edge interface is evaluated to be 15–19 GPa and 6.2–6.5 GPa, respectively. Further, the underlying deformation mechanisms induced by tool wear behaviours are revealed through the transient heat conduction model and cutting-edge stress distribution model. This research offers a framework and mechanism for the cutting tool wear surface/interface characteristics targeted to the difficult-to-cut superalloy materials.

Optimization of tree-shaped fin structures towards enhanced discharging performance of metal hydride reactor for thermochemical heat storage based on entransy theory

Integrating fin structures into metal hydride (MH) bed can enhance heat discharging performance of the reactor for thermochemical heat storage. In this study, based on the entransy theory, the entransy dissipation rate (Eh,st) or the entransy dissipation (Eh,tr) of a simplified two-dimensional (2D) steady-state or transient heat conduction model for the MH bed was used to be an objective to optimize the tree-shaped fin (TSF) structures. Furthermore, response surface method (RSM) was adopted to explore the relationship between Eh,st or Eh,tr and structural parameters (i.e., branch number N, branch level M, length ratio α, width index β, and angle ratio γ). The results show that RSM can effectively predict influences of structural parameters of TSFs on heat discharging performance. Based on RSM with entransy theory, the obtained optimal combination parameters were N = 8, M = 3, α = 1, β = 0.5, and γ = 1, corresponding to the maximum gravimetric exergy-output rate (GEOR) of 20.98 W/kg. Furthermore, the GEOR with optimized fins was 11.5 % higher than that with unoptimized TSFs. The optimization method based on the entransy theory was effective to optimize the TSF structures by solving 2D model instead of three-dimensional model, and shorten the calculation time for optimization.

A continuum mixture model for transient heat conduction in multi-phase composites

The difference between transient thermal responses of each constituent in composites is one of the important factors to cause significant nonuniform deformation, high stress gradient and failure of composites. While direct numerical simulations for transient heat conduction in multi-phase composites are highly costly and even formidable, classical homogenization methods are focused on predicting the effective conductivities and the macroscopic thermal responses of a whole representative volume element, leaving the prediction of this difference at the macroscopic level to be a challenging issue during structural analysis of composite materials. In order to solve this issue, we propose a continuum mixture model for the transient heat conduction in multi-phase composites through dynamic homogenization methods. The derived governing equations retain the identity of each constituent behaviour and relate them to the overall response of each constituent. All the coefficients in the equations can be directly determined by the constituent phases and geometric parameters through explicit relations. The precision of the model is verified by comparison with direct numerical simulations. The results indicate that the model not only captures the disparate thermal responses of each constituent at the macroscopic level, but also accurately predicates the macro-average responses. The methodology can be generalized to other non-equilibrium thermodynamic phenomena such as diffusion and other kinds of conduction in multi-phase systems.

A Flexible Multifunctional Electronic Skin for Intelligent Tactile Perception

The electronic skin has accurate digital sensing capability and human-like skin structure to realize in-situ measurement and perception. It has broad application prospects such as artificial intelligence, health monitoring, and robotics. However, multifunction integration, structure design, and signal demodulation are still the key points that hinder the development of e-skin. To solve this problem and for the application of robotic fingers, we propose a new multifunctional electronic skin in this paper with five sensing functions including temperature, thermosensation, pressure, wind speed and wind direction. It also has the characteristics of softness and smallness, which is suitable for fingers. Considering the geometry and application scenario of the “finger-sensor-object” touch, a new transient heat conduction model is developed and validated, which can achieve quantitative sensing and calculating of the material’s thermal parameters. Six objects were quantitatively identified in the experiments. Moreover, an interactive control logic between sensors and smart robots is innovatively proposed to improve the utilization of sensor-sensitive units. The proposed flexible multifunctional electronic skin provides a new idea for the application of wearable smart devices and intelligent sensing of robots.

Time Lag Characteristics of Building Envelop Materials on Peak Energy Demand in Typical Hot and Humid Climate of India

Abstract Using a one-dimensional model for transient heat conduction through building enclosure walls, the present research examines the effects of thermophysical building envelop parameters on transient heat exchange, peak cooling, and heating load for northern part of India. For space cooling and heating applications, the thermal performance of four distinct walling systems commonly employed in the climatic conditions of India was examined. Results demonstrate that when the thermal conductivity of the wall increases, the time lag reduces. As wall thickness rises from 230 mm to 310 mm, there is an increase in the time lag during cooling and heating modes. Additionally, the results show that the time lag between conduction and solar load increases as wall thickness increases. As wall thermal mass increased by 20% in cooling mode, the time of peak load was shifted by 2 h. When operating in cooling mode in contrast to heating mode, high thermal mass is more effective in shifting the time of occurrence of peak energy consumption.

POD-based reduced-order modeling study for thermal analysis of gas-cooled microreactor core

Small modular reactors require multi-physics coupling calculations to balance economy and stability, due to their compact structures. Traditional tools used for light water reactors are not effective in addressing the several modeling challenges posed by these calculations. The lumped parameter method is commonly used in the thermal analysis for its high computational speed, but it lacks accuracy due to the thermal model is one-dimensional. While computational fluid dynamics software (CFD) can provide high-precision and high-resolution thermal analysis, its low calculation efficiency making it challenging to be coupled with other programs. Proper Orthogonal Decomposition (POD) is one of the Reduced Order Model (ROM) methods employed in this study to reduce the dimensionality of sample data and to improve the thermal modelling of gas-cooled microreactors. In this work, a non-inclusive POD with neural network method is proposed and verified using a transient heat conduction model for a two-dimensional plate. The method is then applied to build a reduced order model of the gas-cooled micro-reactor core for rapid thermal analysis. The results show that the root mean square error of the reactor core temperature is less than 1.02% and the absolute error is less than 8.2°C while the computational cost is reduced by several orders of magnitude, shortening the calculation time from 1.5-hour to real-time display. These findings proved the feasibility of using POD and neural network in the development of ROMs for gas-cooled microreactor, providing a novel approach for achieving precise thermal calculation with minimized computational costs.

Morphology formation during the nonisothermal thermally‐induced phase separation (TIPS) process

AbstractIn high‐viscosity polymer solutions and blends, temperature variations during the quench process of the thermally‐induced phase separation (TIPS) influence the dynamics and thermodynamics of phase separation. Hence, this study aims to investigate the impact of temperature variations on the morphology formation during the TIPS process. First, the influence of temporal temperature variations on phase separation is investigated by coupling a transient heat conduction model and the Cahn–Hilliard equation, and the results are compared with the isothermal phase separation process. Next, the morphology formation during phase separation is inspected by applying quench from two opposite sides of the sample to the same and different temperatures through coupling the Fourier heat transfer equation and the Cahn–Hilliard equation. The influence of the enthalpy of demixing on the morphology formation and the competition between the heat and mass transfer is also evaluated. It is confirmed that temporal variations of temperature alone have a significant impact on the morphology formation during the TIPS process. In addition, quenching the system to the same and different temperatures both leads to anisotropic morphology formation, which is affected by the quench rate, quench temperature, solution viscosity, and enthalpy of demixing. Upon applying different quench temperatures from opposite sides, two different types of morphologies and droplet sizes were formed as a result of the difference in the cooling rates between the two sides. Employing the enthalpy of demixing during phase separation induced a shallow quench effect on the deep quench side due to the fact that the heat moved toward the lowest temperature in the system, which led to the formation of a distinctive structure.

A self-scaling sequential quasi-Newton method for estimating the heat transfer coefficient distribution in the air jet impingement

Accurate knowledge of the heat transfer coefficient (HTC) distribution is of great significance to the control and optimization of the heat transfer system in the air jet impingement. For this purpose, the estimation of the temporally-spatially varying HTC in the air jet impingement is studied based on the inverse heat conduction problem. The transient two-dimensional heat conduction model of the target disc under a single cooling air jet is established and utilized as the direct problem. A self-scaling sequential quasi-Newton method (SS-SQNM) is developed for accurately and efficiently solving the inverse problem. As a modification of the sequential quasi-Newton method (SQNM), the SS-SQNM adopts the self-scaling updating equation to accelerate the single-step convergence rate during iteration, and thus attains higher inversion efficiency than the SQNM. A series of numerical tests are carried out to investigate the performance of the SS-SQNM and the effects of the regularization parameters on inverse results. The results reveal that the SS-SQNM can give stable and accurate estimates of the HTC when regularization parameters are appropriately selected through the discrepancy principle. The mean absolute percentage error of the estimated HTC distribution is generally less than 10.2% in the presence of measurement noises. Additionally, the iteration number required by the SS-SQNM for inversion is only about 7.81%∼27.78% of that of the SQNM under the same conditions, which saves lots of computational time for the SS-SQNM. Therefore, the SS-SQNM developed in this study is a promising inverse algorithm, which can be employed to estimate the HTC distribution in the air jet impingement with reasonable accuracy and efficiency.

An Analytic Model of Transient Heat Conduction for Bi-Layered Flexible Electronic Heaters by Symplectic Superposition.

In a flexible electronic heater (FEH), periodic metal wires are often encapsulated into the soft elastic substrate as heat sources. It is of great significance to develop analytic models on transient heat conduction of such an FEH in order to provide a rapid analysis and preliminary designs based on a rapid parameter analysis. In this study, an analytic model of transient heat conduction for bi-layered FEHs is proposed, which is solved by a novel symplectic superposition method (SSM). In the Laplace transform domain, the Hamiltonian system-based governing equation for transient heat conduction is introduced, and the mathematical techniques incorporating the separation of variables and symplectic eigen expansion are manipulated to yield the temperature solutions of two subproblems, which is followed by superposition for the temperature solution of the general problem. The Laplace inversion gives the eventual temperature solution in the time domain. Comprehensive time-dependent temperatures by the SSM are presented in tables and figures for benchmark use, which agree well with their counterparts by the finite element method. A parameter analysis on the influence of the thermal conductivity ratio is also studied. The exceptional merit of the SSM is on a direct rigorous derivation without any assumption/predetermination of solution forms, and thus, the method may be extended to more heat conduction problems of FEHs with more complex structures.

Incorporating two-dimensional conduction modeling techniques into an energy simulation program: The EnergyPlus radiant system example

Due to the inherent complexity of multi-dimensional solutions for transient conduction in a multilayered building element, most heat balance-based algorithms assume that conduction occurs only in one dimension—through the building element between the inside and outside environments. Usually, since the length and width of the elements are much greater than the thickness of the element, this is a valid assumption. However, there are some cases such as hydronic radiant slabs where this assumption may not lead to an accurate estimate of the energy consumption of the system. In a hydronic radiant slab, water tubes are embedded in a slab, and hot or chilled water is circulated to meet any heating or cooling loads. The energy consumption of such a system will depend highly on the temperature of the water being sent to the slab (i.e., produced by the boiler or chiller). The temperature of the water that must be sent to the slab will depend on the spacing of the tubes, the multilayer construction of the building element, and the boundary conditions to which the construction is exposed. Thus, to accurately predict the energy consumption of such a system, a transient two-dimensional heat conduction model must be integrated with a heat balance-based simulation. This paper demonstrates the potential loss of accuracy associated with the one-dimensional radiant system models by providing a comparison of one- and two-dimensional solutions using EnergyPlus.

Transient Heat Conduction in the Orthotropic Model with Rectangular Heat Source.

Epidermal electronic systems (EESs) are a representative achievement for utilizing the full advantages of ultra-thin, stretchable and conformal attachment of flexible electronics, and are extremely suitable for integration with human physiological systems, especially in medical hyperthermia. The stretchable heater with stable electrical characteristics and a uniform temperature field is an irreplaceable core component. The inorganic stretchable heater has the advantage of maintaining stable electrical characteristics under tensile deformation. However, the space between the patterned electrodes that provides tensile properties causes uneven distribution of the temperature field. Aiming at improving the temperature distribution uniformity of stretchable thermotherapy electrodes, an orthotropic heat transfer substrate for stretchable heaters is proposed in this paper. An analytical model for transient heat conduction of stretchable rectangular heaters based on orthotropic transfer characteristics is established, which is validated by finite element analysis (FEA). The homogenization effect of orthotropic heat transfer characteristics on temperature distribution and its evolutionary relationship with time are investigated based on this model. This study will provide beneficial help for the temperature distribution homogenization design of stretchable heaters and the exploration of its transient heat transfer mechanism.

Finite Element Study on Temperature Field of Underwater Dredging Devices via the Artificial Ground Freezing Method

Increased urbanization has led to undesirable increases in the discharge of refuse waste and pollutants in urban and rural rivers. Blockages and river pollution adversely affect navigation and aquatic ecosystems and cause flooding during the flood season. Regular riverbed dredging is essential to protect local ecosystems and maintain waterways’ health. However, the current dredging methods cause secondary pollution during dredging. This study examined a new river dredging method with a parametric analysis of its reliability for different construction environments. ADINA software solved the temperature field model using the finite element method to build a three-dimensional transient heat conduction model. The analysis determined the distribution and development of the temperature field during the freezing process and the effective dredging range of the frozen device. We compared thermal conductivities, specific heat capacities, freezing device sizes, initial ground temperatures, and brine cooling plans to examine the effect of the soil’s thermophysical properties and construction environment on the dredging area of the freezing device.

Thermally sprayed metal matrix composite coatings as heating systems

• Thermally sprayed metal matrix composite heating elements were developed and tested. • Effect of ceramic reinforcement on heating performance of the coatings was studied. • Electrical properties of the coatings noticeably affected their heating rate. • A heat transfer model was developed to predict the coating temperature distribution. Wind turbine blades and aircraft wings operating in extreme cold environments are prone to severe ice accretion. The accumulated ice may cause aerodynamic deficiency, lower durability, power losses, and significant safety issues. This study introduces a novel coating-based heating system that takes advantage of a certain group of materials, namely, metal matrix composite (MMC) coatings. With nickel chromium-aluminum-yttrium (NiCrAlY) as the metal matrix, coatings with different ceramic and cermet reinforcing phases were fabricated to produce electrical heating elements. The effects of coating microstructure and ceramic phases on the electrical properties and electrical resistance of the heating elements were examined. In order to assess the heating performance, a number of Joule heating experiments were conducted on the fabricated coatings. It was observed that MMC coatings with dielectric or semi-conductive reinforcing phases had considerably higher electrical resistance, heating ramp-up rate, and steady state temperature. A 2-dimensional transient heat conduction model with energy generation at the upper layer was developed to predict the temperature distribution in the multi-layered coating system. A similar heat conduction problem was simulated using ANSYS Mechanical software. The simulated results and that of the analytical model were in good agreement with the experimental data. The results of this study suggest that implementing ceramic reinforcements into MMC coatings will result in significant improvements in heating efficacy, and reduce consumption of energy in coatings-based de-icing systems.

An analytic model for transient heat conduction in bi-layered structures with flexible serpentine heaters

An analytic model for transient heat conduction in bi-layered structures with flexible serpentine heaters

FE2 multi-scale framework for the two-equation model of transient heat conduction in two-phase media

In the study of transient heat conduction in heterogeneous two-phase media, the local thermal non-equilibrium condition calls for the use of a two-equation model to appropriately describe different temperatures in the two phases. We propose for the two-equation model an FE2 multi-scale framework that is capable of addressing nonlinear conduction problems. The FE2 framework consists of volume-averaged macroscale equations, well-defined microscale problems, and the information exchange between the two scales. Compared to a traditional FE2 method for the one-equation model, the proposed FE2 framework introduces an additional source term at the macroscale that is upscaled from the microscale interfacial heat transfer. At variance with the tangent matrices (i.e., effective conductivity) of the heat flux, the tangent matrices of the interfacial heat transfer depend on the microscopic length scale. The proposed FE2 framework is validated against single-scale direct numerical simulations, and some numerical examples are employed to demonstrate its potential.

Code development and analysis on the operation of liquid metal high temperature heat pipes under full condition

Heat pipe cooled reactor (HPR) is an innovative solid-core reactor which utilizes heat pipes to extract heat from the core to the energy conversion system. In this paper, a mathematical model for high-temperature heat pipes from a frozen state to a steady state is developed based on experimental data. The model is simplified and solved numerically. The two-dimensional transient heat conduction model of the wall and wick and the one-dimensional quasi-steady compressible vapor flow model are coupled to simulate the operation of a heat pipe when vaporization and condensation occur at the liquid–vapor interface. And the equivalent heat capacity model and the rarefied vapor model are introduced to simulate the process of heat pipe startup from a frozen state. Numerical results indicate that the model of heat pipe can predict the operation of high-temperature heat pipe with an error of less than 1.04% at steady state and 23.4% during the startup. Based on the simulation results, the velocity of vapor decreases with the heat transfer power in the steady state and the velocity of potassium vapor is 58.4% of sodium vapor velocity under the same operation condition. During the startup, when the rarefied-continuum interface located in the end of the evaporator section, the maximum vapor velocity occurs which is 1.3 times of steady velocity. This work makes it possible to predict the operation of a high-temperature heat pipe and provides a reference for the design and application of HPR.

Mathematical modelling of transient heat conduction by Step-Enriched Extended Finite Element Method

Mathematical modelling of transient heat conduction by Step-Enriched Extended Finite Element Method

Observation of heat transfer mechanisms in saturated pool boiling of water by high-speed infrared thermometry

We investigated experimentally the heat transfer mechanisms in saturated pool boiling of water. In the experiment, the temperature of a sapphire heated wall with a titanium thin-film heater was visualized using a high-speed infrared camera with a spatial resolution of 82 μm/pixel and a framing rate of 3,000 fps. Local heat transfer characteristics of the fundamental heat transfer processes, including microlayer evaporation, dry-out, transient heat conduction immediately after rewetting, and convective heat transfer, were investigated based on the surface heat flux distribution obtained by three-dimensional transient heat conduction analysis of the heated wall. The contribution of microlayer evaporation, which shows a high heat flux far exceeding the applied heat flux, to the bubble growth was found to be about 50%, and the heat transfer within the microlayer was dominated by one-dimensional heat conduction in the thickness direction. It was confirmed that the local heat removal immediately after rewetting of the dry patch can be reproduced by the transient heat conduction model. The enhancement of convection by the isolated bubble motion was small, while the interaction between bubbles agitated the liquid strongly and enhanced the convective heat transfer. Via partitioning the heat flux distribution by image analysis, the convective heat transfer was found to be the dominant wall heat transfer mode, and the contribution of the microlayer with an area coverage ratio with respect to the total heat transfer area of less than 10% was small, around 25%.

Quantitative thermosensation in a single touch

Thermosensation is the skin perception of thermal stimuli, including temperature and temperature changing rate. Measurements of the thermal transport properties of materials in the environment by robotic hand can help robots analyze environment conditions and make decisions. Existing methods for bulk materials demand ideal measurement conditions or complex measuring systems for material heating and temperature measurement. This paper introduces a flexible thermal sensor that can be used on robotic fingers to achieve rapid measurement of thermal conductivity and thermal diffusivity for different materials. A theoretical transient heat conduction model is proposed based on a touch-and-heat scenario in which the combination of robot finger, sensor and test material is regarded as semi-infinite object. According to this feature, an ultra-thin flexible thermal sensor composed of a central thermoresistor and a surrounding heater is designed and fabricated. The sensor is heated after contacting with different materials, and the temperature change on the sensor surface is recorded. Thermal conductivity and thermal diffusivity of the contacting materials are fitted using the proposed heat transfer model with fitting errors less than 4.5 % and 8.5 %, respectively. In this way, the thermal conductivity and thermal diffusivity of an object can be measured with a single touch by the robot finger in less than 2 s. The device and method presented in this work show the potential of the application in tactile sensing for robotic dexterous hand and manipulation.

Laser-Induced Selective Electroless Plating on PC/ABS Polymer: Minimisation of Thermal Effects for Supreme Processing Speed.

The selective surface activation induced by laser (SSAIL) for electroless copper deposition on Polycarbonate/Acrylonitrile Butadiene Styrene (PC/ABS) blend is one of the promising techniques of electric circuit formation on free-shape dielectric surfaces, which broadens capabilities of 3D microscopic integrated devices (3D-MIDs). The process consists of laser excitation, chemical activation of laser-excited areas by dipping in a liquid and electroless copper deposition of the laser-treated areas. The limiting factor in increasing throughput of the technology is a laser activation step. Laser writing is performed by modern galvanometric scanners which reach the scanning speed of several meters per second. However, adverse thermal effects on PC/ABS polymer surface abridge the high-speed laser writing. In this work, an investigation was conducted on how these thermal effects limit surface activation for selective metal deposition from the view of physics and chemistry. An advanced laser beam scanning technique of interlacing with precise accuracy and the pulse-on-demand technique was applied to overcome mentioned problems for fast laser writing. Initially, the modelling of transient heat conduction was performed. The results revealed a significant reduction in heat accumulation. Applied methods of laser writing allowed the overall processing rate to increase by up to 2.4 times. Surface morphology was investigated by a scanning electron microscope. Energy-dispersive X-ray spectroscopy was used to investigate the modification of atomic concentration on the surface after laser treatment. Experiments did not show a correlation between surface morphology and electroless plating on laser-treated areas. However, significant variation in the composition of the material was revealed depending on the surface activity for electroless plating.