NONLINEAR STABILITY OF RAREFACTION WAVES TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS FOR A REACTING MIXTURE WITH ZERO HEAT CONDUCTIVITY

In this paper,we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension.If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only,it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves,while the initial perturbation and the strength of rarefaction waves are suitably small.

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.

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.

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.

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.

Model of Fractional Heat Conduction in a Thermoelastic Thin Slim Strip under Thermal Shock and Temperature-Dependent Thermal Conductivity

The present paper paper,we estimate the theory of thermoelasticity a thin slim strip under the variable thermal conductivity in the fractional-order form is solved.Thermal stress theory considering the equation of heat conduction based on the time-fractional derivative of Caputo of order
is applied to obtain a solution.We assumed that the strip surface is to be free from traction and impacted by a thermal shock.The transform of Laplace(LT)and numerical inversion techniques of Laplace were considered for solving the governing basic equations.The inverse of the LT was applied in a numerical manner considering the Fourier expansion technique.The numerical results for the physical variables were calculated numerically and displayed via graphs.The parameter of fractional order effect and variation of thermal conductivity on the displacement,stress,and temperature were investigated and compared with the results of previous studies.The results indicated the strong effect of the external parameters,especially the timefractional derivative parameter on a thermoelastic thin slim strip phenomenon.

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.

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.

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.

Dynamic response of a thermal transistor to time-varying signals

Thermal transistor,the thermal analog of an electronic transistor,is one of the most important thermal devices for microscopic-scale heat manipulating.It is a three-terminal device,and the heat current flowing through two terminals can be largely controlled by the temperature of the third one.Dynamic response plays an important role in the application of electric devices and also thermal devices,which represents the devices’ability to treat fast varying inputs.In this paper,we systematically study two typical dynamic responses of a thermal transistor,i.e.,the response to a step-function input(a switching process)and the response to a square-wave input.The role of the length L of the control segment is carefully studied.It is revealed that when L is increased,the performance of the thermal transistor worsens badly.Both the relaxation time for the former process and the cutoff frequency for the latter one follow the power-law dependence on L quite well,which agrees with our analytical expectation.However,the detailed power exponents deviate from the expected values noticeably.This implies the violation of the conventional assumptions that we adopt.

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

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.

Fast precise integration method for hyperbolic heat conduction problems

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.

Fuzzy finite difference method for heat conduction analysis with uncertain parameters

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.

MODEL OF LASER-TIG HYBRID WELDING HEAT SOURCE

The welding mechanism of laser-TIG hybrid welding process is analyzed. Withthe variation of arc current, the welding process is divided into two patterns: deep-penetrationwelding and heat conductive welding. The heat flow model of hybrid welding is presented. As todeep-penetration welding, the heat source includes a surface heat flux and a volume heat flux. Theheat source of heat conductive welding is composed of two Gaussian distribute surface heat sources.With this heat source model, a temperature field is calculated. The finite element code MARC isemployed for this purpose. The calculation results show a good agreement with the experimental data.

A new complex variable meshless method for transient heat conduction problems

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.

A phase-field study on the oxidation behavior of Ni considering heat conduction

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.

Meshless analysis of three-dimensional steady-state heat conduction problems

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.