Variational Approach to 2D and 3D Heat Conduction Modeling

The paper proposes an approximate solution to the classical (parabolic) multidimensional 2D and 3D heat conduction equation for a 5 × 5 cm aluminium plate and a 5 × 5 × 5 cm aluminum cube. An approximate solution of the generalized (hyperbolic) 2D and 3D equation for the considered plate and cube is also proposed. Approximate solutions were obtained by applying calculus of variations and Euler-Lagrange equations. In order to verify the correctness of the proposed approximate solutions, they were compared with the exact solutions of parabolic and hyperbolic equations. The paper also presents the research on the influence of time parameters τ as well as the relaxation times τ ∗ to the variation of the profile of the temperature field for the considered aluminum plate and cube.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Axonal Conduction Velocity: A Computer Study

This paper derives rigorous statements concerning the propagation velocity of action potentials in axons. The authors use the Green’s function approach to approximate the action potential and find a relation between conduction velocity and the impulse profile. Computer simulations are used to bolster the analysis.

Variational Approach to Heat Conduction Modeling

It is known that Fourier’s heat equation, which is parabolic, implies an infinite velocity propagation, or, in other words, that the mechanism of heat conduction is established instantaneously under all conditions. This is unacceptable on physical grounds in spite of the fact that Fourier’s law agrees well with experiment. However, discrepancies are likely to occur when extremely short distances or extremely short time intervals are considered, as they must in some modern problems of aero-thermodynamics. Cattaneo and independently Vernotte proved that such process can be described by Heaviside’s telegraph equation. This paper shows that this fact can be derived using calculus of variations, by application of the Euler-Lagrange equation. So, we proved that the equation of heat conduction with finite velocity propagation of the thermal disturbance can be obtained as a solution to one variational problem.

Guide and control of thermal conduction with isotropic thermodynamic parameters based on a rotary-concentrating device

A rotary-concentrating device for thermal conduction is constructed to control and guide thermal energy transmitting in elastic plates.The designed device has the ability of concentrating for thermal conduction and controlling the processes of thermal diffusion in a plate.The multilayered isotropic material properties of the rotary-concentrating device are derived based on the transformation and rotary medium method and a rotation parameter to control the thermal diffusion process is introduced.The efficiency of the rotary-concentrating device for thermal conduction is verified.Stability of temperature fields in a plate with the rotary-concentrating device is analyzed to study the performance of rotary-concentrating.Numerical examples show that the constructed rotary-concentrating device for thermal conduction can effectively rotate and focus on the thermal energy into the device for a wide range of diffusion temperatures,which can enhance the thermal conduction.Therefore,this study can provide a theoretical support for potential applications in fields of energy harvesting and thermal conduction control.

Lightweight diamond/Cu interface tuning for outstanding heat conduction

With rapid developments in the field of very large-scale integrated circuits,heat dissipation has emerged as a significant factor that restricts the high-density integration of chips.Due to their high thermal conductivity and low thermal expansion coefficient,diamond/Cu composites have attracted considerable attention as a promising thermal management material.In this study,a surface tungsten carbide gradient layer coating of diamond particles has been realized using comprehensive magnetron sputtering technology and a heat treatment process.Diamond/Cu composites were prepared using high-temperature and high-pressure technology.The results show that,by adjusting the heat treatment process,tungsten carbide and di-tungsten carbide are generated by an in situ reaction at the tungsten–diamond interface,and W–WC–W_(2)C gradient layer-coated diamond particles were obtained.The diamond/Cu composites were sintered by high-temperature and high-pressure technology,and the density of surface-modified diamond/Cu composites was less than 4 g cm^(-3).The W–WC–W_(2)C@diamond/Cu composites have a thermal diffusivity as high as 331 mm^(2)s^(-1),and their thermal expansion coefficient is as low as 1.76×10^(-6)K^(-1).The interface coherent structure of the gradient layer-coated diamond/copper composite can effectively improve the interface heat transport efficiency.

Optimized CeO_(2) Nanowires with Rich Surface Oxygen Vacancies Enable Fast Li-Ion Conduction in Composite Polymer Electrolytes

Low-cost and flexible solid polymer electrolytes are promising in all-solid-state Li-metal batteries with high energy density and safety.However,both the low room-temperature ionic conductivities and the small Li^(+)transference number of these electrolytes significantly increase the internal resistance and overpotential of the battery.Here,we introduce Gd-doped CeO_(2) nanowires with large surface area and rich surface oxygen vacancies to the polymer electrolyte to increase the interaction between Gd-doped CeO_(2) nanowires and polymer electrolytes,which promotes the Li-salt dissociation and increases the concentration of mobile Li ions in the composite polymer electrolytes.The optimized composite polymer electrolyte has a high Li-ion conductivity of 5×10^(-4)4 S cm^(-1) at 30℃ and a large Li+transference number of 0.47.Moreover,the composite polymer electrolytes have excellent compatibility with the metallic lithium anode and high-voltage LiNi_(0.8)Mn _(0.1)Co_(0.1)O_(2)(NMC)cathode,providing the stable cycling of all-solid-state batteries at high current densities.

Investigation of radial heat conduction with 1D self-consistent model in helicon plasmas

A 1D radially self-consistent model in helicon plasmas has been established to investigate the influence of radial heat conduction on plasma transport and wave propagation.Two kinds of 1D radial fluid models,with and without considering heat conduction,have been developed to couple the 1D plasma-wave interaction model,and self-consistent solutions have been obtained.It is concluded that in the low magnetic field range the radial heat conduction plays a moderate role in the transport of helicon plasmas and the importance depends on the application of the helicon source.It influences the local energy balance leading to enhancement of the electron temperature in the bulk region and a decrease in plasma density.The power deposition in the plasma is mainly balanced by collisional processes and axial diffusion,whereas it is compensated by heat conduction in the bulk region and consumed near the boundary.The role of radial heat conduction in the large magnetic field regime becomes negligible and the two fluid models show consistency.The local power balance,especially near the wall,is improved when conductive heat is taken into account.

High-performance vertical GaN field-effect transistor with an integrated self-adapted channel diode for reverse conduction

A vertical GaN field-effect transistor with an integrated self-adapted channel diode(CD-FET)is proposed to improve the reverse conduction performance.It features a channel diode(CD)formed between a trench source on the insulator and a P-type barrier layer(PBL),together with a P-shield layer under the trench gate.At forward conduction,the CD is pinched off due to depletion effects caused by both the PBL and the metal-insulator-semiconductor structure from the trench source,without influencing the on-state characteristic of the CD-FET.At reverse conduction,the depletion region narrows and thus the CD turns on to achieve a very low turn-on voltage(V_(F)),preventing the inherent body diode from turning on.Meanwhile,the PBL and P-shield layer can modulate the electric field distribution to improve the off-state breakdown voltage(BV).Moreover,the P-shield not only shields the gate from a high electric field but also transforms part of C_(GD)to CGS so as to significantly reduce the gate charge(Q_(GD)),leading to a low switching loss(E_(switch)).Consequently,the proposed CD-FET achieves a low V_(F)of 1.65 V and a high BV of 1446 V,and V_(F),Q_(GD)and E_(switch)of the CD-FET are decreased by 49%,55%and 80%,respectively,compared with those of a conventional metal-oxide-semiconductor field-effect transistor(MOSFET).

Efficient proton conduction in porous and crystalline covalent-organic frameworks(COFs)

To attain the objectives of carbon peaking and carbon neutrality,the development of stable and highperformance ion-conducting materials holds enormous relevance in various energy storage and conversion devices.Particularly,crystalline porous materials possessing built-in ordered nanochannels exhibit remarkable superiority in comprehending the ion transfer mechanisms with precision.In this regard,covalent organic frameworks(COFs)are highly regarded as a promising alternative due to their preeminent structural tunability,accessible well-defined pores,and excellent thermal/chemical stability under hydrous/anhydrous conditions.By the availability of organic units and the diversity of topologies and connections,advances in COFs have been increasing rapidly over the last decade and they have emerged as a new field of proton-conducting materials.Therefore,a comprehensive summary and discussion are urgently needed to provide an"at a glance"understanding of the prospects and challenges in the development of proton-conducting COFs.In this review,we target a comprehensive review of COFs in the field of proton conductivity from the aspects of design strategies,the proton conducting mechanism/features,the relationships of structure-function,and the application of research.The relevant content of theoretical simulation,advanced structural characterizations,prospects,and challenges are also presented elaborately and critically.More importantly,we sincerely hope that this progress report will form a consistent view of this field and provide inspiration for future research.

His-Purkinje conduction system pacing combined with atrioventricular node ablation improves quality of life in older patients with persistent atrial fibrillation refractory to multiple ablation procedures

BACKGROUND Recurrence of atrial fibrillation(AF)is common in patients with persistent AF even after multiple ablation procedures.His-Purkinje conduction system pacing(HPCSP)combined with atrioventricular node ablation(AVNA)is effective in managing patients with AF and heart failure.This study aimed to determine whether HPCSP combined with AVNA can improve quality of life and alleviate symptoms in older patients with symptomatic persistent AF refractory to multiple ablation procedures,as well as evaluate the feasibility and safety of this therapy.METHODS Older patients(≥65 years)with symptomatic persistent AF refractory to at least two ablation procedures were treated with combined HPCSP and AVNA.The success rates and complications were recorded.Pacing parameters,European Heart Rhythm Association(EHRA)scores,and Atrial Fibrillation Effect on Quality-of-Life(AFEQT)scores obtained perioperatively were compared with those recorded at the 6-month follow-up examination.RESULTS Thirty-one patients were enrolled;of those,only thirty patients were eventually treated with AVNA because one patient developed a complete atrioventricular block following the withdrawal of the His bundle pacing lead.The success rates were 100%for HPCSP(22 cases with His bundle pacing,and 9 cases with left bundle branch pacing)and 93.3%(28/30)for AVNA,respectively.By the 6-month follow-up examination,EHRA scores improved significantly(3.00±0.73 vs.2.44±0.63,P=0.014)and AFEQT scores increased markedly(49.6±20.6 vs.70.9±14.0,P=0.001).No severe complications developed.CONCLUSIONS When used in older patients with symptomatic persistent AF refractory to multiple ablation procedures,HPCSP combined with AVNA significantly alleviated symptoms and improved quality of life during short-term follow-up.This therapy was proved to be safe and effective in this patient population.

A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method(LKM)with the dual reciprocity method(DRM).Firstly,the temporal derivative is discretized by a finite difference scheme,and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation.Secondly,the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution.And then,the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation,respectively.The LKM is a recently proposed local radial basis function collocationmethod with themerits of being simple,accurate,and free ofmesh and integration.Compared with the traditional domain-type and boundary-type schemes,the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains.Numerical experiments,including two-and three-dimensional heat transfer models,demonstrated the effectiveness and accuracy of the new methodology.

Assessment of Different Optimization Algorithms for a Thermal Conduction Problem

In this study,three computational approaches for the optimization of a thermal conduction problem are critically compared.These include a Direct Method(DM),a Genetic Algorithm(GA),and a Pattern Search(PS)technique.The optimization aims to minimize the maximum temperature of a hot medium(a medium with uniform heat generation)using a constant amount of high conductivity materials(playing the role of fixed factor constraining the considered problem).The principal goal of this paper is to determine the most efficient and fastest option among the considered ones.It is shown that the examined three methods approximately lead to the same result in terms of maximum tem-perature.However,when the number of optimization variables is low,the DM is the fastest one.An increment in the complexity of the design and the number of degrees of freedom(DOF)can make the DM impractical.Results also show that the PS algorithm becomes faster than the GA as the number of variables for the optimization rises.

Research on the heat conduction mechanism of induction brazecoating

Induction brazecoating technology is an important means to improve the surface properties of materials.In this paper,copper plate and corundum are selected as substrates for induction brazecoating respectively.The temperature variation of powder and paste coating is systematically studied,and the heat conduction mode and path in the brazecoating process are analyzed.The results show that rise of the coating temperature mainly depends on the heat absorption from the substrate.The liquid-solid interface conducts heat violently and advances step by step,which promotes the melting spread of metal filler metal.The powdery brazecoating material is in a free state,and there is a gas insulation film between the powder particles and the diamond,making it difficult for substrate to conduct heat to the coating.The binder not only assists forming,shell making and oxygen isolation,but also plays an important role during melting.

Conduction pathways of resource endowment affecting carbon intensity:Based on interprovincial data in China

By establishing a mathematical model and a basic analytical framework for the impact of resource endowments on carbon intensity,a traditional panel model without spatial panel effects was firstly constructed,a Durbin-Wu-Hausman test was conducted,and the model was set as a fixed-effects model based on the statistical values;secondly,the traditional panel model without spatial effects was estimated,and LM tests and robustness tests were conducted on the regression residuals.The LM test was then used to remove the fixed effect terms by the de-meaning method,and the Matlab 7.0 software was used to estimate the model.The stepwise introduction of variables was used to observe the effect of each variable on economic growth and to analyze the relationship between the magnitude and significance of the regression parameters of each variable.Finally,the path of conduction effect of resource endowment through mediating variable sinfluencing economic growth and carbon emissions,and thus carbon intensity,was constructed.The conclusion is that carbon intensity is inversely proportional to economic growth for a given level of carbon emissions.Therefore,if resource endowment promotes economic growth through mediating variables,it will lead to a decrease in carbon intensity,which is conducive to the achievement of emission reduction targets;conversely,if resource endowment hinders economic growth through mediating variables,it will lead to an increase in carbon intensity,which is not conducive to the achievement of emission reduction targets.

Cerium Methacrylate Assisted Preparation of Highly Thermally Conductive and Anticorrosive Multifunctional Coatings for Heat Conduction Metals Protection

Preparing polymeric coatings with well corrosion resistance and high thermal conductivity(TC)to prolong operational life and ensure service reliability of heat conductive metallic materials has long been a substantive and urgent need while a difficult task.Here we report a multifunctional epoxy composite coating(F-CB/CEP)by synthesizing cerium methacrylate and ingeniously using it as a novel curing agent with corrosion inhibit for epoxy resin and modifier for boron nitride through"cation-π"interaction.The prepared F-CB/CEP coating presents a high TC of 4.29 W m^(−1)K^(−1),which is much higher than other reported anti-corrosion polymer coatings and thereby endowing metal materials coated by this coating with outstanding thermal management performance compared with those coated by pure epoxy coating.Meanwhile,the low-frequency impedance remains at 5.1×10^(11)Ωcm^(2)even after 181 days of immersion in 3.5 wt%NaCl solution.Besides,the coating also exhibits well hydrophobicity,self-cleaning properties,temperature resistance and adhesion.This work provides valuable insights for the preparation of high-performance composite coatings with potential to be used as advanced multifunctional thermal management materials,especially for heat conduction metals protection.

Morphological evolution and flow conduction characteristics of fracture channels in fractured sandstone under cyclic loading and unloading

In coal mining,rock strata are fractured under cyclic loading and unloading to form fracture channels.Fracture channels are the main flow narrows for gas.Therefore,expounding the flow conductivity of fracture channels in rocks on fluids is significant for gas flow in rock strata.In this regard,graded incremental cyclic loading and unloading experiments were conducted on sandstones with different initial stress levels.Then,the three-dimensional models for fracture channels in sandstones were established.Finally,the fracture channel percentages were used to reflect the flow conductivity of fracture channels.The study revealed how the particle size distribution of fractured sandstone affects the formation and expansion of fracture channels.It was found that a smaller proportion of large blocks and a higher proportion of small blocks after sandstone fails contribute more to the formation of fracture channels.The proportion of fracture channels in fractured rock can indicate the flow conductivity of those channels.When the proportion of fracture channels varies gently,fluids flow evenly through those channels.However,if the proportion of fracture channels varies significantly,it can greatly affect the flow rate of fluids.The research results contribute to revealing the morphological evolution and flow conductivity of fracture channels in sandstone and then provide a theoretical basis for clarifying the gas flow pattern in the rock strata of coal mines.

Nerve conduction models in myelinated and unmyelinated nerves based on three-dimensional electrostatic interaction

Until now, nerve conduction has been described on the basis of equivalent circuit model and cable theory, both of which supposed closed electric circuits spreading inside and outside the axoplasm. With these conventional models, we can simulate the propagating pattern of action potential along the axonal membrane based on Ohm＇s law and Kirchhoff＇s law. However, we could not fully explain the different conductive patterns in unmyelinated and myelinated nerves with these theories. Also, whether we can really suppose closed electrical circuits in the actual site of the nerves or not has not been fully discussed yet. In this report, a recently introduced new theoretical model of nerve conduction based on electrostatic molecular interactions within the axoplasm will be reviewed. With this new approach, we can explain the different conductive patterns in unmyelinated and myelinated nerves. This new mathematical conductive model based on electrostatic compressional wave in the intracellular fluid may also be able to explain the signal integration in the neuronal cell body and the back-propagation mechanism from the axons to the dendrites. With this new mathematical nerve conduction model based on electrostatic molecular interactions within the intracellular fluid, we may be able to achieve an integrated explanation for the physiological phenomena taking place in the nervous system.

HYBRID FEM WITH FUNDAMENTAL SOLUTIONS AS TRIAL FUNCTIONS FOR HEAT CONDUCTION SIMULATION

A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.

Solution of an Inverse Problem of Heat Conduction of 45 Steel with Martensite Phase Transformation in High Pressure during Gas Quenching

In order to simulate thermal strains, thermal stresses, residual stresses and microstructure of the steel during gas quenching by means of the numerical method, it is necessary to obtain an accurate boundary condition of temperature field. The surface heat transfer coefficient is a key parameter. The explicit finite difference method, nonlinear estimation method and the experimental relation between temperature and time during gas quenching have been used to solve the inverse problem of heat conduction. The relationship between surface temperature and surface heat transfer coefficient of a cylinder has been given. The nonlinear surface heat transfer coefficients include the coupled effects between martensitic phase transformation and temperature.