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
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
We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic condu...We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.展开更多
In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE metho...In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.展开更多
Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimizati...Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimization design.The finite element method in ABAQUS is employed to solve the direct transient nonlinear heat conduction problem.Improved particle swarm optimization(PSO)method is developed and used to solve the transient nonlinear inverse problem.To investigate the inverse performances,some numerical tests are provided.Boundary conditions at inaccessible surfaces of a scramjet combustor with the regenerative cooling system are inversely identified.The results show that the new methodology can accurately and efficiently determine the boundary conditions in the scramjet combustor with the regenerative cooling system.By solving the transient nonlinear inverse problem,the improved particle swarm optimization for solving the transient nonlinear inverse heat conduction problem in a complex structure is verified.展开更多
A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry ...A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.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
The smoothing thin plate spline （STPS） interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the ...The smoothing thin plate spline （STPS） interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method （FEM） as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline （TPS） radial basis functions.展开更多
On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is ...On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.展开更多
We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β ...We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β = 1.33, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on the theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be α = 0.33, which is confirmed by a simple numerical calculation.展开更多
The phonon relaxation and heat conduction in one-dimensional Fermi Pasta-Ulam （FPU） β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence ...The phonon relaxation and heat conduction in one-dimensional Fermi Pasta-Ulam （FPU） β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autoeorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.展开更多
Studies on heat conduction are so far mainly focused on regular systems such as the one-dimensional（1D） and twodimensional（2D） lattices where atoms are regularly connected and temperatures of atoms are homogeneous...Studies on heat conduction are so far mainly focused on regular systems such as the one-dimensional（1D） and twodimensional（2D） lattices where atoms are regularly connected and temperatures of atoms are homogeneously distributed.However, realistic systems such as the nanotube/nanowire networks are not regular but heterogeneously structured, and their heat conduction remains largely unknown. We present a model of quasi-physical networks to study heat conduction in such physical networks and focus on how the network structure influences the heat conduction coefficient κ. In this model,we for the first time consider each link as a 1D chain of atoms instead of a spring in the previous studies. We find that κ is different from link to link in the network, in contrast to the same constant in a regular 1D or 2D lattice. Moreover, for each specific link, we present a formula to show how κ depends on both its link length and the temperatures on its two ends.These findings show that the heat conduction in physical networks is not a straightforward extension of 1D and 2D lattices but seriously influenced by the network structure.展开更多
In cryogenic wind tunnel tests,piezoelectric stacks are adopted to realize the vibration control of the cantilever sting.However,the free stroke and blocking force of the piezoelectric stack would decrease dramaticall...In cryogenic wind tunnel tests,piezoelectric stacks are adopted to realize the vibration control of the cantilever sting.However,the free stroke and blocking force of the piezoelectric stack would decrease dramatically as the temperature decreases.This paper proposes a convenient and effective warming structure for the piezoelectric stack,which could keep it working at operating temperatures when the ambient temperature drops.The piezoelectric stack actuator is wrapped with the heating film,and this resulting assembly is then wrapped with the aerogel material for thermal insulation.Both ends of the piezoelectric stack actuator make direct contact with the payload structure.Both one-dimensional and two-dimensional theoretical analyses of the heating conduction problem of the piezoelectric stack actuator are conducted.These analyses results are compared with those of the finite element simulation analysis.The finite element method results show a good consistency with the two-dimensional theoretical results,and a slight deviation of only 0.91 K is observed,indicating its potential for protecting piezoelectric stacks at low temperatures.展开更多
To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomal...To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.展开更多
Kernel gradient free-smoothed particle hydrodynamics （KGF-SPH） is a modified smoothed particle hydrodynamics （SPH） method which has higher precision than the conventional SPH. However, the Laplacian in KGF-SPH is ...Kernel gradient free-smoothed particle hydrodynamics （KGF-SPH） is a modified smoothed particle hydrodynamics （SPH） method which has higher precision than the conventional SPH. However, the Laplacian in KGF-SPH is approximated by the two-pass model which increases computational cost. A new kind of discretization scheme for the Laplacian is proposed in this paper, then a method with higher precision and better stability, called Improved KGF-SPH, is developed by modifying KGF-SPH with this new Laplacian model. One-dimensional （1D） and two-dimensional （2D） heat conduction problems are used to test the precision and stability of the Improved KGF-SPH. The numerical results demonstrate that the Improved KGF-SPH is more accurate than SPH, and stabler than KGF-SPH. Natural convection in a closed square cavity at different Rayleigh numbers are modeled by the Improved KGF-SPH with shifting particle position, and the Improved KGF-SPH results are presented in comparison with those of SPH and finite volume method （FVM）. The numerical results demonstrate that the Improved KGF-SPH is a more accurate method to study and model the heat transfer problems.展开更多
Mixing and heat transfer processes of the granular materials within rotary cylinders play a key role in industrial processes. The numerical simulation is carried out by using the discrete element method （DEM） to inv...Mixing and heat transfer processes of the granular materials within rotary cylinders play a key role in industrial processes. The numerical simulation is carried out by using the discrete element method （DEM） to investigate the influences of material properties on the bed mixing and heat transfer process, including heat conductivity, heat capacity, and shear modulus. Moreover, a new Prclet number is derived to determine the dominant mechanism of the heating rate within the particle bed, which is directly related to thermal and mechanical properties. The system exhibits a faster heating rate with the increase of ratio of thermal conductivity and heat capacity, or the decrease of shear modulus when inter-particle conduction dominates the heating rate; conversely, it shows a fast-mixing bed when particle convection governs the heating rate. The simulation results show good agreement with the theoretical predictions.展开更多
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 dime...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.展开更多
Plant heat conductivity largely depends on tissue structure. Different structures lead to different heat conductivity. As well, water transfer also plays a very important role in heat transfer in plants. We have studi...Plant heat conductivity largely depends on tissue structure. Different structures lead to different heat conductivity. As well, water transfer also plays a very important role in heat transfer in plants. We have studied leaf heat conductivity and tissue structure of 3- and 30-year-old Populus tomentosa Carr. trees using infrared thermal imaging, steady state heat conductivity surveys and paraffin section and investigated the relationship between leaf heat conductivity, tissue structure and water content of leaves. The results show that the temperature on leaf surfaces among the various varieties of trees was almost the same. Leaf heat conductivity, temperature and water content of leaves are positively correlated. The thicker the leaf tissue structures, the larger the heat resistance. That is, the tighter the cells and the smaller the interspaces, the smaller the heat conductivity, which is not conducive for heat transfer.展开更多
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...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.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
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.
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supported by the National Natural Science Foundation of China(Grant Nos.11102102,11472161,and 91130017)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2014AQ015)the Independent Innovation Foundation of Shandong University,China(Grant No.2013ZRYQ002)
文摘We build a fractional dual-phase-lag model and the corresponding bioheat transfer equation, which we use to interpret the experiment results for processed meat that have been explained by applying the hyperbolic conduction. Analytical solutions expressed by H-functions are obtained by using the Laplace and Fourier transforms method. The inverse fractional dual-phase-lag heat conduction problem for the simultaneous estimation of two relaxation times and orders of fractionality is solved by applying the nonlinear least-square method. The estimated model parameters are given. Finally, the measured and the calculated temperatures versus time are compared and discussed. Some numerical examples are also given and discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11171208)the Special Fund for Basic Scientific Research of Central Colleges of Chang’an University, China (Grant No. CHD2011JC080)
文摘In this paper, the complex variable reproducing kernel particle （CVRKP） method and the finite element （FE） method are combined as the CVRKP-FE method to solve transient heat conduction problems. The CVRKP-FE method not only conveniently imposes the essential boundary conditions, but also exploits the advantages of the individual methods while avoiding their disadvantages, then the computational efficiency is higher. A hybrid approximation function is applied to combine the CVRKP method with the FE method, and the traditional difference method for two-point boundary value problems is selected as the time discretization scheme. The corresponding formulations of the CVRKP-FE method are presented in detail. Several selected numerical examples of the transient heat conduction problems are presented to illustrate the performance of the CVRKP-FE method.
基金supported by the National Natural Science Foundation of China(Nos.12172078,51576026)Fundamental Research Funds for the Central Universities in China(No.DUT21LK04)。
文摘Accurately solving transient nonlinear inverse heat conduction problems in complex structures is of great importance to provide key parameters for modeling coupled heat transfer process and the structure’s optimization design.The finite element method in ABAQUS is employed to solve the direct transient nonlinear heat conduction problem.Improved particle swarm optimization(PSO)method is developed and used to solve the transient nonlinear inverse problem.To investigate the inverse performances,some numerical tests are provided.Boundary conditions at inaccessible surfaces of a scramjet combustor with the regenerative cooling system are inversely identified.The results show that the new methodology can accurately and efficiently determine the boundary conditions in the scramjet combustor with the regenerative cooling system.By solving the transient nonlinear inverse problem,the improved particle swarm optimization for solving the transient nonlinear inverse heat conduction problem in a complex structure is verified.
基金Project supported by the National Natural Science Foundation of China(Grant No.11002054)the Foundation of Hunan Educational Committee(Grant No.12C0059).
文摘A meshless numerical model is developed for analyzing transient heat conductions in three-dimensional （3D） axisymmetric continuously nonhomogeneous functionally graded materials （FGMs）. Axial symmetry of geometry and boundary conditions reduces the original 3D initial-boundary value problem into a two-dimensional （2D） problem. Local weak forms are derived for small polygonal sub-domains which surround nodal points distributed over the cross section. In order to simplify the treatment of the essential boundary conditions, spatial variations of the temperature and heat flux at discrete time instants are interpolated by the natural neighbor interpolation. Moreover, the using of three-node triangular finite element method （FEM） shape functions as test functions reduces the orders of integrands involved in domain integrals. The semi-discrete heat conduction equation is solved numerically with the traditional two-point difference technique in the time domain. Two numerical examples are investigated and excellent results are obtained, demonstrating the potential application of the proposed approach.
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 Key Program of the National Natural Science Foundation of China (Grand No. 51138001)the China-German Cooperation Project (Grand No. GZ566)+1 种基金the Innovative Research Groups Funded by the National Natural Science Foundation of China (Grand No. 51121005)the Special Funds for the Basic Scientific Research Expenses for the Central University (Grant No. DUT13LK16)
文摘The smoothing thin plate spline （STPS） interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method （FEM） as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline （TPS） radial basis functions.
基金supported by the National Natural Science Foundation of China(Grant No.51078250)the Research Project by Shanxi Scholarship Council of Shanxi Province,China(Grant No.2013-096)the Scientific&Technological Innovation Program for Postgraduates of Taiyuan University of Science and Technology,China(Grant No.20125026)
文摘On the basis of the complex variable moving least-square （CVMLS） approximation, a complex variable meshless local Petrov-Galerkin （CVMLPG） method is presented for transient heat conduction problems. The method is developed based on the CVMLS approximation for constructing shape functions at scattered points, and the Heaviside step function is used as a test function in each sub-domain to avoid the need for a domain integral in symmetric weak form. In the construction of the well-performed shape function, the trial function of a two-dimensional （2D） problem is formed with a one-dimensional （1D） basis function, thus improving computational efficiency. The numerical results are compared with the exact solutions of the problems and the finite element method （FEM）. This comparison illustrates the accuracy as well as the capability of the CVMLPG method.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10605020)the Natural Science Foundation of Zhejiang Province of China (Grant No. Y605376.)
文摘We propose a new concept, the centre of energy, to study energy diffusion and heat conduction in a one-dimensional hard-point model. For the diatom model, we find an anomalous energy diffusion as （x2） - tβ with β = 1.33, which is independent of initial condition and mass rate. The present model can be viewed as the model composed by independent quasi-particles, the centre of energy. In this way, heat current can be calculated. Based on the theory of dynamic billiard, the divergent exponent of heat conductivity is estimated to be α = 0.33, which is confirmed by a simple numerical calculation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50976052,51136001,and 50730006)the Program for New Century Excellent Talents in University,China+1 种基金the Tsinghua University Initiative Scientific Research Program,Chinathe Tsinghua National Laboratory for Information Science and Technology TNList Cross-discipline Foundation,China
文摘The phonon relaxation and heat conduction in one-dimensional Fermi Pasta-Ulam （FPU） β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autoeorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11135001 and 11375066)the National Basic Research Program of China(Grant No.2013CB834100)
文摘Studies on heat conduction are so far mainly focused on regular systems such as the one-dimensional（1D） and twodimensional（2D） lattices where atoms are regularly connected and temperatures of atoms are homogeneously distributed.However, realistic systems such as the nanotube/nanowire networks are not regular but heterogeneously structured, and their heat conduction remains largely unknown. We present a model of quasi-physical networks to study heat conduction in such physical networks and focus on how the network structure influences the heat conduction coefficient κ. In this model,we for the first time consider each link as a 1D chain of atoms instead of a spring in the previous studies. We find that κ is different from link to link in the network, in contrast to the same constant in a regular 1D or 2D lattice. Moreover, for each specific link, we present a formula to show how κ depends on both its link length and the temperatures on its two ends.These findings show that the heat conduction in physical networks is not a straightforward extension of 1D and 2D lattices but seriously influenced by the network structure.
基金the National Natural Science Foundation of China(No.11872207)Aeronautical Science Foundation of China(No.20180952007)+2 种基金Foundation of National Key Laboratory on Ship Vibration and Noise(No.614220400307)Natural Science Foundation of Jiangsu Province(No.BK20200413)the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD)。
文摘In cryogenic wind tunnel tests,piezoelectric stacks are adopted to realize the vibration control of the cantilever sting.However,the free stroke and blocking force of the piezoelectric stack would decrease dramatically as the temperature decreases.This paper proposes a convenient and effective warming structure for the piezoelectric stack,which could keep it working at operating temperatures when the ambient temperature drops.The piezoelectric stack actuator is wrapped with the heating film,and this resulting assembly is then wrapped with the aerogel material for thermal insulation.Both ends of the piezoelectric stack actuator make direct contact with the payload structure.Both one-dimensional and two-dimensional theoretical analyses of the heating conduction problem of the piezoelectric stack actuator are conducted.These analyses results are compared with those of the finite element simulation analysis.The finite element method results show a good consistency with the two-dimensional theoretical results,and a slight deviation of only 0.91 K is observed,indicating its potential for protecting piezoelectric stacks at low temperatures.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11102102, 11072134, and 91130017)the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AQ014)the Independent Innovation Foundation of Shandong University, China (Grant No. 2010ZRJQ002)
文摘To better describe the phenomenon of non-Fourier heat conduction, the fractional Cattaneo heat equation is introduced from the generalized Cattaneo model with two fractional derivatives of different orders. The anomalous heat conduction under the Neumann boundary condition in a semi-infinity medium is investigated. Exact solutions are obtained in series form of the H-function by using the Laplace transform method. Finally, numerical examples are presented graphically when different kinds of surface temperature gradient are given. The effects of fractional parameters are also discussed.
文摘Kernel gradient free-smoothed particle hydrodynamics （KGF-SPH） is a modified smoothed particle hydrodynamics （SPH） method which has higher precision than the conventional SPH. However, the Laplacian in KGF-SPH is approximated by the two-pass model which increases computational cost. A new kind of discretization scheme for the Laplacian is proposed in this paper, then a method with higher precision and better stability, called Improved KGF-SPH, is developed by modifying KGF-SPH with this new Laplacian model. One-dimensional （1D） and two-dimensional （2D） heat conduction problems are used to test the precision and stability of the Improved KGF-SPH. The numerical results demonstrate that the Improved KGF-SPH is more accurate than SPH, and stabler than KGF-SPH. Natural convection in a closed square cavity at different Rayleigh numbers are modeled by the Improved KGF-SPH with shifting particle position, and the Improved KGF-SPH results are presented in comparison with those of SPH and finite volume method （FVM）. The numerical results demonstrate that the Improved KGF-SPH is a more accurate method to study and model the heat transfer problems.
基金supported by the National High Technology Research and Development Program of China(Grant No.2007AA05Z215)the Fundamental Research Funds for the Central Universities(Grant No.FRF-AS-10-005B)
文摘Mixing and heat transfer processes of the granular materials within rotary cylinders play a key role in industrial processes. The numerical simulation is carried out by using the discrete element method （DEM） to investigate the influences of material properties on the bed mixing and heat transfer process, including heat conductivity, heat capacity, and shear modulus. Moreover, a new Prclet number is derived to determine the dominant mechanism of the heating rate within the particle bed, which is directly related to thermal and mechanical properties. The system exhibits a faster heating rate with the increase of ratio of thermal conductivity and heat capacity, or the decrease of shear modulus when inter-particle conduction dominates the heating rate; conversely, it shows a fast-mixing bed when particle convection governs the heating rate. The simulation results show good agreement with the theoretical predictions.
基金supported by the Beijing Natural Science Foundation(1182004,Z180007,1192001).
文摘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.
基金the National Project of ScienceTechnology for the 11th Five-Year Plan in China (Grant No.2006BAD24B04)
文摘Plant heat conductivity largely depends on tissue structure. Different structures lead to different heat conductivity. As well, water transfer also plays a very important role in heat transfer in plants. We have studied leaf heat conductivity and tissue structure of 3- and 30-year-old Populus tomentosa Carr. trees using infrared thermal imaging, steady state heat conductivity surveys and paraffin section and investigated the relationship between leaf heat conductivity, tissue structure and water content of leaves. The results show that the temperature on leaf surfaces among the various varieties of trees was almost the same. Leaf heat conductivity, temperature and water content of leaves are positively correlated. The thicker the leaf tissue structures, the larger the heat resistance. That is, the tighter the cells and the smaller the interspaces, the smaller the heat conductivity, which is not conducive for heat transfer.
基金Project supported by the National Natural Science Foundation of China(Grant No.12075316)the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.21XNH091)(Q.R.)。
文摘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.
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.
