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 ...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.展开更多
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 approximat...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.展开更多
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. T...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.展开更多
Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attr...Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.展开更多
This paper aims to apply a virtual boundary element method(VBEM)to solve the inverse problems of three-dimensional heat conduction in orthotropic media.This method avoids the singular integrations in the conventional ...This paper aims to apply a virtual boundary element method(VBEM)to solve the inverse problems of three-dimensional heat conduction in orthotropic media.This method avoids the singular integrations in the conventional boundary element method,and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm.When the VBEM is applied to the inverse problems,the numerical instability may occur if a virtual boundary is not properly chosen.The method encounters a highly illconditioned matrix for the larger distance between the physical boundary and the virtual boundary,and otherwise is hard to avoid the singularity of the source point.Thus,it must adopt an appropriate regularization method to deal with the ill-posed systems of inverse problems.In this study,the VBEM and different regularization techniques are combined to model the inverse problem of three-dimensional heat conduction in orthotropic media.The proper regularization techniques not only make the virtual boundary to be allocated freer,but also solve the ill-conditioned equation of the inverse problem.Numerical examples demonstrate that the proposed method is efficient,accurate and numerically stable for solving the inverse problems of three-dimensional heat conduction in orthotropic media.展开更多
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 conducti...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.展开更多
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 ...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.展开更多
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 tem...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.展开更多
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...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.展开更多
The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue...The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.展开更多
A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh rat...A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh ratio r = Deltat/(Deltax)(2) = Deltat/(Deltay)(2) = Deltat/(Deltaz)(2) less than or equal to 1/2, which is better than that of all the other explicit difference schemes. And when the order of truncation error is 0((Deltat)(2) + (Deltax)(4)), the stability condition is r less than or equal to 1/6, which contains the known results.展开更多
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...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.展开更多
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 problem...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.展开更多
A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to t...A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.展开更多
A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue...A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.展开更多
Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction areinvestigated analytically and numerically. The corresponding dispersion relation is a sixth-orderalgebraic equation, governed b...Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction areinvestigated analytically and numerically. The corresponding dispersion relation is a sixth-orderalgebraic equation, governed by six non-dimensional parameters: two thermoelastic couplingconstants, one chirality parameter, the ratio between extensional and torsional moduli, the Fouriernumber, and the dimensionless thermal relaxation. The behavior of the solutions is discussedfrom two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxationon the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wavecelerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered.However, with large wavenumbers, the solutions behave differently depending on the thermalrelaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from theclassical result of the speed of second sound.展开更多
An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness...An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.展开更多
Phase-field modeling approach has been used to study the oxidation behavior of pure Ni when considering heat conduction. In this calculation, the dependence of the coefficient of the Cahn–Hilliard equation Lc on the ...Phase-field modeling approach has been used to study the oxidation behavior of pure Ni when considering heat conduction. In this calculation, the dependence of the coefficient of the Cahn–Hilliard equation Lc on the temperature T was considered. To this end, high-temperature oxidation experiments and phase-field modeling for pure Ni were performed in air under atmospheric pressure at 600,700, and 800?C. The oxidation rate was measured by thermogravimetry and Lc at these temperatures was determined via interactive algorithm. With the Lc-T relationship constructed, oxidation behavior of Ni when considering heat conduction was investigated. The influence of temperature boundaries on the oxidation degree, oxide film thickness, and specific weight gain were discussed. The phase-field modeling approach proposed in this study will give some highlights of the oxidation resistance analysis and cooling measures design of thermal protection materials.展开更多
Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditi...Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.展开更多
In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is pres...In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 12102043, 12072375U2241240)the Natural Science Foundation of Hunan Province of China (Nos. 2023JJ40698 and 2021JJ40710)。
文摘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.
文摘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.
文摘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.
基金supported by the Natural Science Foundation of Ningbo,China (Grant Nos.2009A610014 and 2009A610154)the Natural Science Foundation of Zhejiang Province,China (Grant No.Y6090131)
文摘Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson's equation or the Laplace equation with Dirichlet, Neuman, or mixed conditions. When the problems are too complex, it is difficult to find an analytical solution, the only choice left is an approximate numerical solution. This paper deals with the numerical solution of three-dimensional steady-state heat conduction problems using the meshless reproducing kernel particle method (RKPM). A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced by the penalty method. The effectiveness of RKPM for three-dimensional steady-state heat conduction problems is investigated by two numerical examples.
基金This study was supported by“the Fundamental Research Funds for the Central Universities”(Grant No.2015B37814)the Postgraduate Research and Practice Innovation Program of Jiangsu Province(Grant No.KYLX15_0489)+1 种基金the National Natural Science Foundation of China(Grant No.51679081)“the Fundamental Research Funds for the Central Universities”(Grant No.2018B48514).
文摘This paper aims to apply a virtual boundary element method(VBEM)to solve the inverse problems of three-dimensional heat conduction in orthotropic media.This method avoids the singular integrations in the conventional boundary element method,and can be treated as a potential approach for solving the inverse problems of the heat conduction owing to the boundary-only discretization and semi-analytical algorithm.When the VBEM is applied to the inverse problems,the numerical instability may occur if a virtual boundary is not properly chosen.The method encounters a highly illconditioned matrix for the larger distance between the physical boundary and the virtual boundary,and otherwise is hard to avoid the singularity of the source point.Thus,it must adopt an appropriate regularization method to deal with the ill-posed systems of inverse problems.In this study,the VBEM and different regularization techniques are combined to model the inverse problem of three-dimensional heat conduction in orthotropic media.The proper regularization techniques not only make the virtual boundary to be allocated freer,but also solve the ill-conditioned equation of the inverse problem.Numerical examples demonstrate that the proposed method is efficient,accurate and numerically stable for solving the inverse problems of three-dimensional heat conduction in orthotropic media.
基金National Natural Science Foundation of China(Grant No.52072327)the China National Key R&D Program(2021YFB3701802)+6 种基金Scientific and Technological Projects of Henan Province(No.232102231050)the Higher Education and Teaching Reformation Project(2014SJGLX064)the Project for Work-station of Zhongyuan scholars of Henan Province(Nos.214400510002,224400510023)the Science and Technology Major Project of Henan Province(No.221100230300)the Postgraduate Education Reform and QualityAcademic Degrees&Graduate Education Reform Project of Henan Province(No.2021SJGLX060Y)the Postgraduate Education Reform and Quality Improvement Project of Henan Province(No.YJS2022JD34)the Science and Technology on Plasma Physics Laboratory(Grant No.JCKYS2021212010).
文摘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.
基金National Natural Science Foundation of China(No.51907039)Shenzhen Technology Project(Nos.JCYJ20190806142603534 and ZDSYS201707280904031)+1 种基金ESPEOS project(No.PID2019108034RB-I00/AEI/10.13039/501100011033)funded by the Agencia Estatal de Investigacion(Spanish National Research Agency)。
文摘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.
基金supported by the 2020 Ningbo “3315 Talent Introduction Plan” Innovative Team (C-Class)the major project of Ningbo “Scientific and Technological Innovation 2025”(Grant No.2020Z111)Science and Technology Major Project of Zhejiang Province (No.203ZP20220161)
文摘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.
基金supported by the NationalNatural Science Foundation of China (No.11802151)the Natural Science Foundation of Shandong Province of China (No.ZR2019BA008)the China Postdoctoral Science Foundation (No.2019M652315).
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.42277165,41920104007,and 41731284)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant Nos.CUGCJ1821 and CUGDCJJ202234)the National Overseas Study Fund(Grant No.202106410040)。
文摘The three-dimensional numerical manifold method(3D-NMM),which is based on the derivation of Galerkin's variation,is a powerful calculation tool that uses two cover systems.The 3D-NMM can be used to handle continue-discontinue problems and extend to THM coupling.In this study,we extended the 3D-NMM to simulate both steady-state and transient heat conduction problems.The modelling was carried out using the raster methods(RSM).For the system equation,a variational method was employed to drive the discrete equations,and the crucial boundary conditions were solved using the penalty method.To solve the boundary integral problem,the face integral of scalar fields and two-dimensional simplex integration were used to accurately describe the integral on polygonal boundaries.Several numerical examples were used to verify the results of 3D steady-state and transient heat-conduction problems.The numerical results indicated that the 3D-NMM is effective for handling 3D both steadystate and transient heat conduction problems with high solution accuracy.
文摘A class of two-level explicit difference schemes are presented for solving three-dimensional heat conduction equation. When the order of truncation error is 0(Deltat + (Deltax)(2)), the stability condition is mesh ratio r = Deltat/(Deltax)(2) = Deltat/(Deltay)(2) = Deltat/(Deltaz)(2) less than or equal to 1/2, which is better than that of all the other explicit difference schemes. And when the order of truncation error is 0((Deltat)(2) + (Deltax)(4)), the stability condition is r less than or equal to 1/6, which contains the known results.
基金This work has been supported by the National Natural Science Foundation of China (10162002) and Foundation for University Key Teacher by the Ministry of Education and The Yunnan Foundation of Natural Science (1999A0023M).
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China (Nos. 10902020 and 10721062)
文摘A fast precise integration method is developed for the time integral of the hyperbolic heat conduction problem. The wave nature of heat transfer is used to analyze the structure of the matrix exponential, leading to the fact that the matrix exponential is sparse. The presented method employs the sparsity of the matrix exponential to improve the original precise integration method. The merits are that the proposed method is suitable for large hyperbolic heat equations and inherits the accuracy of the original version and the good computational efficiency, which are verified by two numerical examples.
基金supported by the National Special Fund for Major Research Instrument Development(2011YQ140145)111 Project(B07009)+1 种基金the National Natural Science Foundation of China(11002013)Defense Industrial Technology Development Program(A2120110001 and B2120110011)
文摘A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.
基金supported by the National Science Foundation of United States (Grants IIP-1362146 and CMMI-1462749)
文摘Harmonic thermoelastic waves in helical strands with Maxwell–Cattaneo heat conduction areinvestigated analytically and numerically. The corresponding dispersion relation is a sixth-orderalgebraic equation, governed by six non-dimensional parameters: two thermoelastic couplingconstants, one chirality parameter, the ratio between extensional and torsional moduli, the Fouriernumber, and the dimensionless thermal relaxation. The behavior of the solutions is discussedfrom two perspectives with an asymptotic-numerical approach: (1) the effect of thermal relaxationon the elastic wave celerities, and (2) the effect of thermoelastic coupling on the thermal wavecelerities. With small wavenumbers, the adiabatic solution for Fourier helical strands is recovered.However, with large wavenumbers, the solutions behave differently depending on the thermalrelaxation and chirality. Due to thermoelastic coupling, the thermal wave celerity deviates from theclassical result of the speed of second sound.
基金supported by the Innovation Training Project for Students in NUAA(No.2016C-X0010-129)the Key Laboratory of Aircraft Environment Control and Life Support(NUAA),Ministry of Industry and Information Technology
文摘An increment-dimensional scaled boundary finite element method (ID-SBFEM) is developed to solve the transient temperature field.To improve the accuracy of SBFEM,the effect of high frequency factor on dynamic stiffness is considered,and the first-order continued fraction technique is used.After the derivation,the SBFE equations are obtained,and the dimensions of thermal conduction,the thermal capacity matrix and the vector of the right side term in the equations are doubled.An example is presented to illustrate the feasibility and good accuracy of the proposed method.
基金supported by the Beijing Jiaotong University (Grant C15JB00080)
文摘Phase-field modeling approach has been used to study the oxidation behavior of pure Ni when considering heat conduction. In this calculation, the dependence of the coefficient of the Cahn–Hilliard equation Lc on the temperature T was considered. To this end, high-temperature oxidation experiments and phase-field modeling for pure Ni were performed in air under atmospheric pressure at 600,700, and 800?C. The oxidation rate was measured by thermogravimetry and Lc at these temperatures was determined via interactive algorithm. With the Lc-T relationship constructed, oxidation behavior of Ni when considering heat conduction was investigated. The influence of temperature boundaries on the oxidation degree, oxide film thickness, and specific weight gain were discussed. The phase-field modeling approach proposed in this study will give some highlights of the oxidation resistance analysis and cooling measures design of thermal protection materials.
基金supported by National Natural Science Foundation of China(11101244,11271231)National Tackling Key Problems Program(20050200069)Doctorate Foundation of the Ministry of Education of China(20030422047)
文摘Transient behavior of three-dimensional semiconductor device with heat conduc- tion is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions. The electric potential is defined by an ellip- tic equation and it appears in the following three equations via the electric field intensity. The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation. A mixed finite volume element approximation, keeping physical conservation law, is used to get numerical values of the electric potential and the accuracy is improved one order. Two con- centrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences. This method can overcome numerical oscillation, dispersion and decreases computational complexity. Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened. An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations. This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.
基金Project supported by the National Natural Science Foundation of China(Grant No.11171208)the Shanghai Leading Academic Discipline Project,China(Grant No.S30106)the Innovation Fund for Graduate Student of Shanghai University of China (Grant No.SHUCX120125)
文摘In this paper, based on the improved complex variable moving least-square (ICVMLS) approximation, a new complex variable meshless method (CVMM) for two-dimensional (2D) transient heat conduction problems is presented. The variational method is employed to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. As the transient heat conduction problems are related to time, the Crank-Nicolson difference scheme for two-point boundary value problems is selected for the time discretization. Then the corresponding formulae of the CVMM for 2D heat conduction problems are obtained. In order to demonstrate the applicability of the proposed method, numerical examples are given to show the high convergence rate, good accuracy, and high efficiency of the CVMM presented in this paper.