The full Navier-Stokes-Fourier system with mixed boundary condition that describes the motion of shear-thinning and incompressible viscous fluid in a rotating multi-screw extruder is investigated. The viscosity is ass...The full Navier-Stokes-Fourier system with mixed boundary condition that describes the motion of shear-thinning and incompressible viscous fluid in a rotating multi-screw extruder is investigated. The viscosity is assumed to depend on the shear rate and the temperature. The global existence of suitable weak solutions is established. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.展开更多
In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depen...In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.展开更多
We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the lo...We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.展开更多
The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. E...The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.展开更多
In this paper the nonlinear heat-conduction equations rhoc partial derivativew/partial derivativet = partial derivative/partial derivativex (k partial derivativew/partial derivativex) with Dirichlet boundary condition...In this paper the nonlinear heat-conduction equations rhoc partial derivativew/partial derivativet = partial derivative/partial derivativex (k partial derivativew/partial derivativex) with Dirichlet boundary condition and the nonlinear boundary condition are studied. The asymptotic behavior of the global of solution are analyzed by using Lyapuunov function. As its application, the approximate solutions are constructed.展开更多
Dependence of the thermal conductivity on the length of two armchair single-walled carbon nanotubes （SWNTs） is studied by the nonequilibrium molecular dynamics （MD） method with Brenner Ⅱ potential. The thermal co...Dependence of the thermal conductivity on the length of two armchair single-walled carbon nanotubes （SWNTs） is studied by the nonequilibrium molecular dynamics （MD） method with Brenner Ⅱ potential. The thermal conductivities are calculated for （5, 5） and （7, 7） SWNTs with lengths ranging from 22 to 155nm. The results show that the thermal conductivity of SWNTs is sensitive to the length and it does not converge to a finite value when the tube length increases up to 155nm, however it obeys a power law relation.展开更多
Using the scattering matrix method, we investigate the thermal transport m a nanostructure at low temperarures. It is found that phonon transport exhibits some novel and interesting features： resonant transmission, r...Using the scattering matrix method, we investigate the thermal transport m a nanostructure at low temperarures. It is found that phonon transport exhibits some novel and interesting features： resonant transmission, resonant reflection, and small thermal conductance. A comparison between thermal conductances is performed when stress-free and hard-wall boundary conditions are applied for acoustic modes, respectively. The result indicates that the characteristics of the thermal conductance versus temperature for different types of boundary conditions are qualitatively different.展开更多
The calculation of the temperature field of an underwater concrete tank system storing crude oil is relatively complex. Based on experimental data and optimization analysis of relative parameters, unsteady heat-transf...The calculation of the temperature field of an underwater concrete tank system storing crude oil is relatively complex. Based on experimental data and optimization analysis of relative parameters, unsteady heat-transfer is calculated by use of heat equilibrium theory. It is found that the predicted value of temperature is in good agreement with experimental data.展开更多
Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system....Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.展开更多
This paper concerns the inviscid,heat conductive and resistive compressible MHD system in a horizontally periodic flat strip domain.The global well-posedness of the problem around an equilibrium with the positive cons...This paper concerns the inviscid,heat conductive and resistive compressible MHD system in a horizontally periodic flat strip domain.The global well-posedness of the problem around an equilibrium with the positive constant density and temperature and a uniform non-horizontal magnetic field is established,and the solution decays to the equilibrium almost exponentially.Our result reveals the strong stabilizing effect of the transversal magnetic field and resistivity as the global well-posedness of compressible inviscid heat-conductive flows in multi-D is unknown.展开更多
By measuring the effective thermal conductivity, taking photos of the distribution of the nano-particles in the fluids and photos that reflect the interfacial phenomena between nano-particles and fluids, we try to exp...By measuring the effective thermal conductivity, taking photos of the distribution of the nano-particles in the fluids and photos that reflect the interfacial phenomena between nano-particles and fluids, we try to explain the possible mechanism for heat conductive enhancement.展开更多
Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study...Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study its dynamics.It is shown in this paper that the uniform boundedness of the entropy and the inhomogeneous Sobolev regularities of the velocity and temperature can be propagated for viscous and heat-conductive gases in R3,provided that the initial vacuum occurs only at far fields with suitably slow decay of the initial density.Precisely,it is proved that for any strong solution to the Cauchy problem of the heat-conductive compressible Navier-Stokes equations,the corresponding entropy remains uniformly bounded,and the L2 regularities of the velocity and temperature can be propagated,up to the existing time of the solution,as long as the initial density vanishes only at far fields with a rate not faster than O(1/|x|^(2)).The main tools are some singularly weighted energy estimates and an elaborate De Giorgi-type iteration technique.We apply the De Giorgi-type iterations to different equations in establishing the lower and upper bounds of the entropy.展开更多
By using Differential Scanning Caborimetry（DSC）,Thermogravimetric（TG） thermal analysis etc,we determined thermal physical properties,such as the heat conduction performance, specific heat capacity,heat stability a...By using Differential Scanning Caborimetry（DSC）,Thermogravimetric（TG） thermal analysis etc,we determined thermal physical properties,such as the heat conduction performance, specific heat capacity,heat stability and etc,of different metal oxide/Nylon 1010 composites.The results show that after added ZnO,CuO,Fe3O4 in PAlOlO matrix,the thermal conductivity of composites linear increases with the increasing of the quality score of metal oxide.When using ZnO as thermal conductive filler and the particle diameter ranges 35 to 40μm,heat conduction performance of the modified composites is the best.The thermal conductivity of ZnO/PA1010 composites linear increases with the temperature increasing.The heat capacity of Nylon 1010 and all kinds of metal oxide/Nylon 1010 increases gradually with the temperature rising.In the same temperature,heat capacity of the modified composites reduces gradually with the content of metal oxide increasing.The glass transition temperature of Nylon 1010 is about 47℃or so,and adding metal oxide can improve the thermal stability of composites.展开更多
基金Supported by the National Natural Science Foundation of China(No.11671027,11601031,,11471321)
文摘The full Navier-Stokes-Fourier system with mixed boundary condition that describes the motion of shear-thinning and incompressible viscous fluid in a rotating multi-screw extruder is investigated. The viscosity is assumed to depend on the shear rate and the temperature. The global existence of suitable weak solutions is established. The fictitious domain method which consists in filling the moving rigid screws with the surrounding fluid and taking into account the boundary conditions on these bodies by introducing a well-chosen distribution of boundary forces is used.
基金supported by NSFC (11171228,10801111,10971171)the fundamental Research Funds for the Central University (2010121006)the Natural Science Foundation of Fujian Province of China (2010J05011)
文摘In this paper,we prove a blow-up criterion of strong solutions to the 3-D viscous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum.This blow-up criterion depends only on the gradient of velocity and the temperature,which is similar to the one for compressible Navier-Stokes equations.
基金supported by the China Postdoctoral Science Foundation (20090450333)supported by the National Basic Research Program (2005CB321700)NSFC (40890154)
文摘We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.
基金This research was surpported by the National Natural Science Foundation , Mathematical TY Foun-dation (TY10126029) of China and the Youth Foundation of Shandong University.
文摘The model of transient behavior of semiconductor with heat-conduction is an initial and boundary problem. Alternating-direction multistep preconditioned iterative methods and theory analyses are given in this paper. Electric potential equation is approximated by mixed finite element method, concentration and heat-conduction equations are approximated by Galerkin alternating-direction multistep methods. Error estimates of optimal order in L2 are demonstrated.
文摘In this paper the nonlinear heat-conduction equations rhoc partial derivativew/partial derivativet = partial derivative/partial derivativex (k partial derivativew/partial derivativex) with Dirichlet boundary condition and the nonlinear boundary condition are studied. The asymptotic behavior of the global of solution are analyzed by using Lyapuunov function. As its application, the approximate solutions are constructed.
文摘Dependence of the thermal conductivity on the length of two armchair single-walled carbon nanotubes （SWNTs） is studied by the nonequilibrium molecular dynamics （MD） method with Brenner Ⅱ potential. The thermal conductivities are calculated for （5, 5） and （7, 7） SWNTs with lengths ranging from 22 to 155nm. The results show that the thermal conductivity of SWNTs is sensitive to the length and it does not converge to a finite value when the tube length increases up to 155nm, however it obeys a power law relation.
基金Supported by the National Natural Science Foundation of China under Grant No 10547132, and the Young Teacher Foundation of Tianjin University under Grant No 5110117.
文摘Using the scattering matrix method, we investigate the thermal transport m a nanostructure at low temperarures. It is found that phonon transport exhibits some novel and interesting features： resonant transmission, resonant reflection, and small thermal conductance. A comparison between thermal conductances is performed when stress-free and hard-wall boundary conditions are applied for acoustic modes, respectively. The result indicates that the characteristics of the thermal conductance versus temperature for different types of boundary conditions are qualitatively different.
基金This project was financially supported by the National Natural Science Foundation of China(Grant No.59895410)
文摘The calculation of the temperature field of an underwater concrete tank system storing crude oil is relatively complex. Based on experimental data and optimization analysis of relative parameters, unsteady heat-transfer is calculated by use of heat equilibrium theory. It is found that the predicted value of temperature is in good agreement with experimental data.
基金The NNSF.MTYF(10126029)of China and the YF of Shandong University.
文摘Collocation method is put forward to solve the semiconductor problem with heat-conduction, whose mathematical model is described by an initial and boundary problem for a nonlinear partial differential equation system. One elliptic equation is for the electric potential, and three parabolic equations are for the electron concentration, hole concentration and heat-conduction. Using the prior estimate and technique of differential equations, we obtained almost optimal error estimates in L2.
基金the National Natural Science Foundation of China(11771360,12171401)the Natural Science Foundation of Fujian Province of China(2019J02003).Z.P.Xin was supported by Zheng Ge Ru Foundation,Hong Kong RGC Earmarked Research Grants CUHK14305315,CUHK14302819,CUHK14300917,CUHK14302917,CUHK14300819,and Basic and Applied Basic Research Foundation of Guangdong Province(2020B1515310002).
文摘This paper concerns the inviscid,heat conductive and resistive compressible MHD system in a horizontally periodic flat strip domain.The global well-posedness of the problem around an equilibrium with the positive constant density and temperature and a uniform non-horizontal magnetic field is established,and the solution decays to the equilibrium almost exponentially.Our result reveals the strong stabilizing effect of the transversal magnetic field and resistivity as the global well-posedness of compressible inviscid heat-conductive flows in multi-D is unknown.
基金The project is financially supported by the National Nature Science Foundation of China with Grant number(No.59995550-3)Thanks also for the valuable suggestions from Prof Yuqin Gu of the Department of Engineering Mechanics, Tsinghua University and Pr
文摘By measuring the effective thermal conductivity, taking photos of the distribution of the nano-particles in the fluids and photos that reflect the interfacial phenomena between nano-particles and fluids, we try to explain the possible mechanism for heat conductive enhancement.
基金supported by National Natural Science Foundation of China(Grant No.12131010)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310002)+2 种基金supported by National Natural Science Foundation of China(Grant Nos.11971009 and 11871005)the Guangdong Basic and Applied Basic Research Foundation(Grant Nos.2019A1515011621 and 2020B1515310005)supported by the Zheng Ge Ru Foundation and the Hong Kong RGC Earmarked Research Grants(Grant Nos.CUHK-14305315,CUHK-14300917 and CUHK-14302819).
文摘Due to the high degeneracy and singularity of the entropy equation,the physical entropy for viscous and heat-conductive polytropic gases behaves singularly in the presence of vacuum,and it is thus a challenge to study its dynamics.It is shown in this paper that the uniform boundedness of the entropy and the inhomogeneous Sobolev regularities of the velocity and temperature can be propagated for viscous and heat-conductive gases in R3,provided that the initial vacuum occurs only at far fields with suitably slow decay of the initial density.Precisely,it is proved that for any strong solution to the Cauchy problem of the heat-conductive compressible Navier-Stokes equations,the corresponding entropy remains uniformly bounded,and the L2 regularities of the velocity and temperature can be propagated,up to the existing time of the solution,as long as the initial density vanishes only at far fields with a rate not faster than O(1/|x|^(2)).The main tools are some singularly weighted energy estimates and an elaborate De Giorgi-type iteration technique.We apply the De Giorgi-type iterations to different equations in establishing the lower and upper bounds of the entropy.
基金Natural Science Foundation of Jiangsu Province,China(Grant No.SBK201121291)
文摘By using Differential Scanning Caborimetry（DSC）,Thermogravimetric（TG） thermal analysis etc,we determined thermal physical properties,such as the heat conduction performance, specific heat capacity,heat stability and etc,of different metal oxide/Nylon 1010 composites.The results show that after added ZnO,CuO,Fe3O4 in PAlOlO matrix,the thermal conductivity of composites linear increases with the increasing of the quality score of metal oxide.When using ZnO as thermal conductive filler and the particle diameter ranges 35 to 40μm,heat conduction performance of the modified composites is the best.The thermal conductivity of ZnO/PA1010 composites linear increases with the temperature increasing.The heat capacity of Nylon 1010 and all kinds of metal oxide/Nylon 1010 increases gradually with the temperature rising.In the same temperature,heat capacity of the modified composites reduces gradually with the content of metal oxide increasing.The glass transition temperature of Nylon 1010 is about 47℃or so,and adding metal oxide can improve the thermal stability of composites.
