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
Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrod...Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections.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
Freeze-drying of structurally heterogeneous biomaterials such as porcine aorta presents considerable modeling challenges due to their inherent multilayer composition and moving sublimation interfaces.Conventional mode...Freeze-drying of structurally heterogeneous biomaterials such as porcine aorta presents considerable modeling challenges due to their inherent multilayer composition and moving sublimation interfaces.Conventional models often overlook structural anisotropy and dynamic boundary progression,while experimental determination of key parameters under cryogenic conditions remains difficult.To address these,this study develops a heat and mass transfer model incorporating a dynamic node strategy for the sublimation interface,which effectively handles continuous computational domain deformation.Additionally,specialized fixed nodes were incorporated to adapt to the multilayer structure and its spatially varying thermophysical properties.A novel non-contact gravimetric system was introduced to monitor mass loss in real time without disrupting vacuum,enabling accurate experimental validation.Combined with dehydration data,the model quantified critical parameters including effective thermal conductivity of the dried layer,vapor diffusivity,and sublimation mass transfer resistance.The results show that the migration of the sublimation fronts from both the inner and outer tunics toward the tunica media significantly alters the drying kinetics and heat-mass transfer characteristics.The proposed approach provides an adaptable and predictive framework for simulating freeze-drying processes in structurally heterogeneous systems with spatially varying thermophysical properties.展开更多
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 hea...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 orderis 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.展开更多
We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection beco...We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.展开更多
The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements dis...The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements display severe convergence deterioration in explicit transient heat conduction analysis with lumped heat ca-pacity matrices.This convergence decay is due to the violation of variational integration consistency by the standard Galerkin formulation with lumped heat capacity matrices.This issue is resolved by introducing the boundary-enhanced Galerkin weak form that incorporates the elemental boundary contribution in the discrete finite element formulation.Subsequently,it is theoretically proven that a direct nodal integration identically fulfills the variational integration consistency in the context of the boundary-enhanced Galerkin weak form.The proposed variationally consistent nodal integration therefore enables optimal convergence for explicit transient heat conduction analysis with lumped heat capacity matrices.The efficacy of the proposed variationally con-sistent nodal integration formulation for the 13-node quadrilateral and 39-node hexahedral cubic elements is thoroughly demonstrated via numerical examples.展开更多
An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a param...An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a parameter estimation problem)and a time-varying heat source is considered in the transient heat transfer problem(a function estimation problem).Since a general irregular 2D heat conducting body is considered,a body-fitted grid generation is used to mesh the domain.Then governing equations and associated boundary and initial conditions are transformed from the physical domain to the computational domain and finite difference method is used to solve the governing equations to obtain the temperature distribution in the body.Using an efficient,accurate,and very easy to implement sensitivity analysis incorporated in a gradient based minimization method(here,steepest descentmethod),the unknown heat source is estimated accurately.In the function estimation part,it is assumed that there is no prior information on the functional form of the heat source and the estimation process can be performed with a reasonable initial guess for the heat source.The main advantage of the proposed inverse analysis is that the sensitivity matrix(and hence,the objective function gradient with respect to the unknown variables)can be computed during the direct heat transfer solution through newyet simple explicit expressions with no need to solve extra equations such as the sensitivity and adjoint problems and impose additional computational costs comparable to the direct problem solution ones.Some test cases are presented to investigate the accuracy,efficiency,and effect of measurement error on the estimated parameter and function for the line heat source.展开更多
With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavi...With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.展开更多
Knowledge of heat flow and associated variations of temperature with depth is crucial for understanding how the Earth functions. Here, we demonstrate possible heat shielding effects that result from the occurrence of ...Knowledge of heat flow and associated variations of temperature with depth is crucial for understanding how the Earth functions. Here, we demonstrate possible heat shielding effects that result from the occurrence of mafic intrusions/layers（granulitic rocks） within a dominantly granitic middle crust and/or ultramafic intrusions/layers（peridotitic rocks） within a dominantly granulitic lower crust; heat shielding is a familiar phenomenon in heat engineering and thermal metamaterials. Simple one-dimensional calculations suggest that heat shielding due to the intercalation of granitic, granulitic and peridotitic rocks will increase Moho temperatures substantially. This study may lead to a rethinking of numerous proposed lower crustal processes.展开更多
The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the ...The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the frequency responses of the heat absorbed by the room＇s internal surfaces,inside surface temperature,indoor air temperature and outdoor synthetic temperature.The measured results match very well with the theoretical results of the zeroth and the first order values of the decay rates and time lags of heat conduction in the building construction,but the difference between the measured values and the theoretical values for the second order is too great to be accepted.It is therefore difficult to accurately test the second order value.However,it is still advisable to complete the analysis using the zeroth-and the first-orders values of the decay rates and time lags of heat conduction in building construction under field conditions,because in these cases the decay rates of heat conduction reach twenty which meets the requirements of engineering plans.展开更多
This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic fie...This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.展开更多
The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitr...The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.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
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
The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dim...The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.展开更多
A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials （FGMs）. The model can handle a spatially varying material property field of FGMs. In...A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials （FGMs）. The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the interelement boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element （FE） model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional FEM and boundary element method （BEM）. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.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
Inverse heat conduction method (IHCM) is one of the most effective approaches to obtaining the boiling heat transfer coefficient from measured results. This paper focuses on its application in cryogenic boiling heat t...Inverse heat conduction method (IHCM) is one of the most effective approaches to obtaining the boiling heat transfer coefficient from measured results. This paper focuses on its application in cryogenic boiling heat transfer. Experiments were conducted on the heat transfer of a stainless steel block in a liquid nitrogen bath, with the assumption of a 1D conduction condition to realize fast acquisition of the temperature of the test points inside the block. With the inverse-heat conduction theory and the explicit finite difference model, a solving program was developed to calculate the heat flux and the boiling heat transfer coefficient of a stainless steel block in liquid nitrogen bath based on the temperature acquisition data. Considering the oscillating data and some unsmooth transition points in the inverse-heat-conduction calculation result of the heat-transfer coefficient, a two-step data-fitting procedure was proposed to obtain the expression for the boiling heat transfer coefficients. The coefficient was then verified for accuracy by a comparison between the simulation results using this expression and the verifying experimental results of a stainless steel block. The maximum error with a revised segment fitting is around 6%, which verifies the feasibility of using IHCM to measure the boiling heat transfer coefficient in liquid nitrogen bath.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
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.
文摘Making use of the relativistic BBGKY technique,the relativistic generalization of Landau collision integral is obtained.Furthermore,we calculate the relativistic hydrodynamic modes up to the second order in the hydrodynamic wave number.Combining Résibois' method,we present the first principle formula of the relativistic heat conductivity of Coulomb electronic plasmas for low-order corrections.
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funded by the Scientific and Technological Research Projects in Henan Province(No.252102310425)the Key Scientific Research Projects of Higher Education Institutions in Henan Province(No.23A560018).
文摘Freeze-drying of structurally heterogeneous biomaterials such as porcine aorta presents considerable modeling challenges due to their inherent multilayer composition and moving sublimation interfaces.Conventional models often overlook structural anisotropy and dynamic boundary progression,while experimental determination of key parameters under cryogenic conditions remains difficult.To address these,this study develops a heat and mass transfer model incorporating a dynamic node strategy for the sublimation interface,which effectively handles continuous computational domain deformation.Additionally,specialized fixed nodes were incorporated to adapt to the multilayer structure and its spatially varying thermophysical properties.A novel non-contact gravimetric system was introduced to monitor mass loss in real time without disrupting vacuum,enabling accurate experimental validation.Combined with dehydration data,the model quantified critical parameters including effective thermal conductivity of the dried layer,vapor diffusivity,and sublimation mass transfer resistance.The results show that the migration of the sublimation fronts from both the inner and outer tunics toward the tunica media significantly alters the drying kinetics and heat-mass transfer characteristics.The proposed approach provides an adaptable and predictive framework for simulating freeze-drying processes in structurally heterogeneous systems with spatially varying thermophysical properties.
文摘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 orderis 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.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2025B1515020077 and 2024A15150301-39)the National Natural Science Foundation of China(Grant No.12205138)the Shenzhen Science and Technology Innovation Committee(Grant No.JCYJ2022-0530113206015).
文摘We present a minimal theoretical model for self-sustained oscillations of a thin elastic sheet on a hot plate,induced by thermomechanical coupling.As the plate temperature increases,the sheet’s static deflection becomes unstable via a Hopf bifurcation at a critical temperature TC,giving rise to spontaneous periodic motion.Linear stability analysis yields analytical expressions for the critical oscillation temperature TC and the oscillation period at onset.Numerical simulations of the nonlinear equations confirm the bifurcation and reveal how key parameters(stiffness,thermal softening,thermal coupling,etc.)govern the oscillation amplitude and waveform.Finally,we demonstrate that the self-oscillating sheet can perform mechanical work as a heat engine,and we compare its performance to the Carnot efficiency limit.This work provides design principles for thermally driven selfoscillators with potential applications in soft robotics,adaptive structures,and thermal energy harvesting.
基金supported by the National Natural Science Foundation of China(Grant Nos.12372201 and 12072302).
文摘The 13-node quadrilateral and 39-node hexahedral cubic serendipity elements produce nodally integrated positive-definite lumped heat capacity matrices in higher-order finite element analysis.However,these elements display severe convergence deterioration in explicit transient heat conduction analysis with lumped heat ca-pacity matrices.This convergence decay is due to the violation of variational integration consistency by the standard Galerkin formulation with lumped heat capacity matrices.This issue is resolved by introducing the boundary-enhanced Galerkin weak form that incorporates the elemental boundary contribution in the discrete finite element formulation.Subsequently,it is theoretically proven that a direct nodal integration identically fulfills the variational integration consistency in the context of the boundary-enhanced Galerkin weak form.The proposed variationally consistent nodal integration therefore enables optimal convergence for explicit transient heat conduction analysis with lumped heat capacity matrices.The efficacy of the proposed variationally con-sistent nodal integration formulation for the 13-node quadrilateral and 39-node hexahedral cubic elements is thoroughly demonstrated via numerical examples.
文摘An inverse analysis is presented to estimate line heat source in two-dimensional steady-state and transient heat transfer problems.A constant heat source is considered in the steady-state heat transfer problem(a parameter estimation problem)and a time-varying heat source is considered in the transient heat transfer problem(a function estimation problem).Since a general irregular 2D heat conducting body is considered,a body-fitted grid generation is used to mesh the domain.Then governing equations and associated boundary and initial conditions are transformed from the physical domain to the computational domain and finite difference method is used to solve the governing equations to obtain the temperature distribution in the body.Using an efficient,accurate,and very easy to implement sensitivity analysis incorporated in a gradient based minimization method(here,steepest descentmethod),the unknown heat source is estimated accurately.In the function estimation part,it is assumed that there is no prior information on the functional form of the heat source and the estimation process can be performed with a reasonable initial guess for the heat source.The main advantage of the proposed inverse analysis is that the sensitivity matrix(and hence,the objective function gradient with respect to the unknown variables)can be computed during the direct heat transfer solution through newyet simple explicit expressions with no need to solve extra equations such as the sensitivity and adjoint problems and impose additional computational costs comparable to the direct problem solution ones.Some test cases are presented to investigate the accuracy,efficiency,and effect of measurement error on the estimated parameter and function for the line heat source.
基金Project supported by the Guangdong Basic and Applied Basic Research Foundation of China(No.2023A1515012809)the Natural Science Foundation of Shaanxi Province of China(No.2023-JC-YB-073)the Fundamental Research Funds for the Central Universities of China(No.D5000230066)。
文摘With the miniaturization of devices and the development of modern heating technologies,the generalization of heat conduction and thermoelastic coupling has become crucial,effectively emulating the thermodynamic behavior of materials in ultrashort time scales.Theoretically,generalized heat conductive models are considered in this work.By analogy with mechanical viscoelastic models,this paper further enriches the heat conduction models and gives their one-dimensional physical expression.Numerically,the transient thermoelastic response of the slim strip material under thermal shock is investigated by applying the proposed models.First,the analytical solution in the Laplace domain is obtained by the Laplace transform.Then,the numerical results of the transient responses are obtained by the numerical inverse Laplace transform.Finally,the transient responses of different models are analyzed and compared,and the effects of material parameters are discussed.This work not only opens up new research perspectives on generalized heat conductive and thermoelastic coupling theories,but also is expected to be beneficial for the deeper understanding of the heat wave theory.
基金supported by the National Natural Science Foundation of China (Nos.41530319,41374079,41374060)the State Key Laboratory of Geological Processes and Mineral Resources,China University of Geosciences (No.MSFGPMR201309)
文摘Knowledge of heat flow and associated variations of temperature with depth is crucial for understanding how the Earth functions. Here, we demonstrate possible heat shielding effects that result from the occurrence of mafic intrusions/layers（granulitic rocks） within a dominantly granitic middle crust and/or ultramafic intrusions/layers（peridotitic rocks） within a dominantly granulitic lower crust; heat shielding is a familiar phenomenon in heat engineering and thermal metamaterials. Simple one-dimensional calculations suggest that heat shielding due to the intercalation of granitic, granulitic and peridotitic rocks will increase Moho temperatures substantially. This study may lead to a rethinking of numerous proposed lower crustal processes.
基金The Advance Research Projects of Southeast Universityfor the National Natural Science Foundation of China(No.XJ0701262)the National Key Technologies R&D Program of China during the 11th Five-Year Plan Period(No.2008BAJ12B04,2008BAJ12B05,2006BAJ03A04)
文摘The field measurements of decay rates and time lags of heat conduction in a building construction taken in Nanjing during the summer of 2001 are presented.The decay rates and time lags are calculated according to the frequency responses of the heat absorbed by the room＇s internal surfaces,inside surface temperature,indoor air temperature and outdoor synthetic temperature.The measured results match very well with the theoretical results of the zeroth and the first order values of the decay rates and time lags of heat conduction in the building construction,but the difference between the measured values and the theoretical values for the second order is too great to be accepted.It is therefore difficult to accurately test the second order value.However,it is still advisable to complete the analysis using the zeroth-and the first-orders values of the decay rates and time lags of heat conduction in building construction under field conditions,because in these cases the decay rates of heat conduction reach twenty which meets the requirements of engineering plans.
基金supported by the National Natural Science Foundation of China(12401279,12371219)the Double-Thousand Plan of Jiangxi Province(jxsq2023201115)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027).
文摘This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.
基金Projects(41530637,41877222,41702290)supported by the National Natural Science Foundation of China
文摘The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.
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The heat transfer coefficient in a multidimensional heat conduction problem is obtained from the solution of the inverse heat conduction problem based on the thermographic temperature measurement. The modified one-dimensional correction method （MODCM）, along with the finite volume method, is employed for both two- and three-dimensional inverse problems. A series of numerical experiments are conducted in order to verify the effectiveness of the method. In addition, the effect of the temperature measurement error, the ending criterion of the iteration, etc. on the result of the inverse problem is investigated. It is proved that the method is a simple, stable and accurate one that can solve successfully the inverse heat conduction problem.
基金supported by the Special Fund for Basic Scientific Research of Central Colleges,Chang'an University(Project No.CHD2011JC150)the National Natural Science Foundation of China(No.11102059)
文摘A novel hybrid graded element model is developed in this paper for investigating thermal behavior of functionally graded materials （FGMs）. The model can handle a spatially varying material property field of FGMs. In the proposed approach, a new variational functional is first constructed for generating corresponding finite element model. Then, a graded element is formulated based on two sets of independent temperature fields. One is known as intra-element temperature field defined within the element domain; the other is the so-called frame field defined on the element boundary only. The intra-element temperature field is constructed using the linear combination of fundamental solutions, while the independent frame field is separately used as the boundary interpolation functions of the element to ensure the field continuity over the interelement boundary. Due to the properties of fundamental solutions, the domain integrals appearing in the variational functional can be converted into boundary integrals which can significantly simplify the calculation of generalized element stiffness matrix. The proposed model can simulate the graded material properties naturally due to the use of the graded element in the finite element （FE） model. Moreover, it inherits all the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional FEM and boundary element method （BEM）. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show a good numerical accuracy.
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 Natural Sciences Foundation of China (No. 50776075)
文摘Inverse heat conduction method (IHCM) is one of the most effective approaches to obtaining the boiling heat transfer coefficient from measured results. This paper focuses on its application in cryogenic boiling heat transfer. Experiments were conducted on the heat transfer of a stainless steel block in a liquid nitrogen bath, with the assumption of a 1D conduction condition to realize fast acquisition of the temperature of the test points inside the block. With the inverse-heat conduction theory and the explicit finite difference model, a solving program was developed to calculate the heat flux and the boiling heat transfer coefficient of a stainless steel block in liquid nitrogen bath based on the temperature acquisition data. Considering the oscillating data and some unsmooth transition points in the inverse-heat-conduction calculation result of the heat-transfer coefficient, a two-step data-fitting procedure was proposed to obtain the expression for the boiling heat transfer coefficients. The coefficient was then verified for accuracy by a comparison between the simulation results using this expression and the verifying experimental results of a stainless steel block. The maximum error with a revised segment fitting is around 6%, which verifies the feasibility of using IHCM to measure the boiling heat transfer coefficient in liquid nitrogen bath.
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.
