Non-Fourier heat conduction study for steady states in metallic nanofilms

As a fundamental theory of heat transfer, Fourier’s law is valid for most traditional conditions. Research interest in non-Fourier heat conditions is mainly focused on heat wave phenomena in non-steady states. Recently, the thermomass theory posited that, for steady states, non-Fourier heat conduction behavior could also be observed under ultra-high heat flux conditions at low ambient temperatures. Significantly, this is due to thermomass inertia. We report on heat conduction in metallic nanofilms from large currents at low temperatures; heat fluxes of more than 1×1010 W m 2 were used. The measured average temperature of the nanofilm is larger than that based on Fourier’s law, with temperature differences increasing as heat flux increased and ambient temperature decreased. Experimental results for different film samples at different ambient temperatures reveal that non-Fourier behavior exists in metallic nanofilms in agreement with predictions from thermomass theory.     

Molecular dynamics simulations of non-Fourier heat conduction

Unsteady heat conduction is known to deviate significantly from Fourier＇s law when the system time and length scales are within certain temporal and spatial windows of relaxation. Classical molecular dynamics simulations were used to investigate unsteady heat conduction in argon thin films with a sudden temperature increase or heat flux at one surface to study the non-Fourier heat conduction effects in argon thin films. The studies were conducted with both pure argon films and films with vacancy defects. The temperature profiles in the argon films showed the existence of mechanical waves when the thin film was suddenly heated and the wave nature of the heat propagation. The flux phase relaxation time, Zq, and the temperature phase relaxation time,τt, were calculated from the temporal variations of the energy flux and temperature distribution in the film. Comparisons of the MD temperature profiles with temperature profiles predicted by Fourier＇s law show that Fourier＇s law is not able to predict the temperature variations with time. Different film thicknesses were also studied to illustrate the variation of the time needed for the films to reach steady-state temperature profiles after a sudden temperature rise at one surface and to illustrate the finite speed of the energy waves.     

Free boundary value problems for a class of generalized diffusion equation

The transport behavior of free boundary value problems for a class of generalized diffusion equations was studied. Suitable similarity transformations were used to convert the problems into a class of singular nonlinear two-point boundary value problems and similarity solutions were numerical presented for different representations of heat conduction function, convection function, heat flux function, and power law parameters by utilizing the shooting technique. The results revealed the flux transfer mechanism and the character as well as the effects of parameters on the solutions.     

One-dimensional unsteady general solution for Wang bioheat transfer equation with heat source proportional to temperature

An analytical general solution is derived for the non-Fourier Wang bioheat transfer model with special internal heat production. It is valuable for finding the special solutions with specified conditions and for expanding the understanding of the non-Fourier heat conduction phenomena in living tissues, for example, the controversial temperature fluctuation effects. This analytical solution can also be used as the benchmark solution to check the numerical calculations and to develop various numerical computational approaches. Because there is an arbitrary function in the expression of internal heat production, this solution can actually be applied to many types of internal heat production distributions.     

Thermal wave propagation in graphene studied by molecular dynamics simulations

The transient heat conduction in both armchair and zigzag-edged graphene ribbons pulsed by local heating with a duration of 1 ps was studied using nonequilibrium molecular dynamics simulations. The results show that the heat pulse excites two waves which indicates non-Fourier heat conduction. One of the two waves is a sound wave （first sound）, which has macroscopic momentum and propagates at the speed of sound. The other is a thermal wave （second sound）, whose propagation speed is 1/√3 of the sound velocity. The sound wave excited by the heat pulse is a longitudinal wave, whose energy is only transported in the longitudinal direction. The thermal wave excited by the heat pulse is generated by transverse lattice vibrations, with the energy only having the transverse component. The observed anisotropy of the transient heat conduction suggests that the system is in a non-equilibrium state during propagation of the heat pulse. Further statistical analyses show that the displacement of the heat pulse energy is related to the time as 〈σ2〉 ∝ t^1.80, which implies that heat transport is ballistic-diffusive transport in graphene. The higher proportion of the ballistic transport will lead to stronger heat waves. At the crest of the thermal wave, energy is transported ballistically, while in the diffusive region and during attenuation of the thermal wave, the energy is transported diffusively.     

LBE–DEM simulation of inter-phase heat transfer in gas–solid cross jets

Lattice-Boltzmann equation(LBE)–Discrete element method(DEM)coupled simulation of a twodimensional gas–solid cross jet is performed,focusing on the gas-particle two-way coupling effect on heat transfer characteristics.The Reynolds number is 1000,and particle Stokes numbers are 10,25,and 50 under the same number flow rate of particles.The gas phase temperature field and particle distribution as well as the inter-phase heat transfer characteristics are studied and analyzed.The dominating effects,i.e.the mean temperature difference and mean heat transfer coefficient between the gas–solid phases,for the pre-and post-collision stages of the cross jets are illustrated respectively.The change of dominating roles is related to the dynamical response characteristics of particles.     

Modeling and simulation of heat transfer for glass bulb mold

Cooling system design in glass bulb pressing operation can greatly affect the productivity and the quality of the final product. The concept of cyclic-averaged steady temperature field is proposed in modeling. Heat transfer in the mold region is considered to be a cyclic-steady, three-dimensional conduction; heat transfer within the glass melt region is treated as a transient, one-dimensional conduction; heat exchange between the cooling system surface and coolant is treated as a steady heat convection. A hybrid model consisting of a three-dimensional boundary element method for the mold region and a finite-difference method with a variable mesh for the melt region is used for numerical simulation. Compared with the experimental data, the numerical model developed here is computationally efficient and sufficiently accurate.     

Studies of the process of moisture exchange across a membrane using irreversible thermodynamics

On the basis of non-equilibrium thermodynamic theory,the coupling phenomena of heat and mass transfer during the process of moisture exchange across a membrane were studied and the relevant physical and mathematical models were established.Formulae for calculating the four characteristic parameters included in the non-equilibrium thermodynamic model were derived,and the dependences of these parameters on the temperatures and concentrations on the two sides of the membrane were analyzed,providing a basis for calculating the heat and mass fluxes.The effects of temperature and concentration differences between the two sides of membrane and the membrane average temperature on the transmembrane mass and heat fluxes were investigated.The results show that for a given membrane average temperature,a larger concentration difference or a smaller temperature difference leads to a higher mass flux.For fixed concentration and temperature differences and with the mass flux predominantly caused by the concentration difference,a higher membrane average temperature yields a higher mass flux.The ratio of the heat of sorption induced by mass flow to total heat relates not only to the temperature and concentration differences between the two sides of membrane but also to the membrane average temperature and the ratio increases when the temperature difference is reduced.     

Effects of sub-lithospheric small-scale convection with a Newtonian rheology on the seafloor topography and heat flux

Scafloor topography and heat flux show clear dependence on the age of seafloor. A half-space cooling (HSC)model can reproduce seafloor topography and heat flux data for younger seafloor, but for older seafloor the observations show reduced variations with the age in comparison with the HSC model predictions. The deviation was attributed to the sub-lithospheric small-scale (SSC) convection first by Parsons and McKenzie (1978). While there is little doubt that the SSC can enhance heat flux at relatively old seafloor, questions were raised as to whether or not the SSC can actually lead to a reduced topography. In this study, the effects of SSC on scafloor topography and heat flux are investigated by formulating a 2-D thermal convection model that is parallel to plate motion. Instead of using closed boundary conditions,which will bring large pressure effects because of return flow,a flow through boundary condition is adopted. The results show that although the SSC enhances the surface heat flux, it has little effects on topography for the fluids with a more realistic rheology. The reason for this is that the SSC transports the heat from the bottom to the top and cools down the whole fluids, and with the existence of a stagnant lid, the whole effects on topography are negligible.     

Influence of size effect and boundary conditions on temperature overshooting in nanoscale thermal conduction

The temperature overshooting phenomenon in one-dimensional nanoscale heat conduction in thin films is studied for various boundary conditions.The results show that when ballistic heat transport strongly affects the heat transport process,temperature overshooting is more likely to occur.A sudden increase of temperature on only one surface of a thin film cannot trigger temperature overshooting,while symmetric boundary temperature perturbations lead to the largest temperature overshooting.Twodimensional heat conduction is also studied in a nanoscale area.The analytic results show that Fourier’s law may severely underestimate the temperatures in nanofilms as well as in nanoareas when temperature overshooting occurs.     

超快速强热流加热半无限体瞬态温度场理论分析

计及超快速加热引起传热过程的非傅立叶效应,建立了第二类边界条件下的半无限体的动态温度场方程组。用拉普拉斯变换法对方程进行求解;结果表明,强热流快速加热在半无限体内产生一个温度波。波面通过之处引起局域温度突然升高。     

脉冲热流作用下球体内的非傅立叶热传导

分析了球形物体表面遭受一随时间变化脉冲热流时的双曲型非傅立叶热传导问题．给出了此类超急速传热情形下的热传导方程、边界条件及初始条件的无量纲形式,采用Ｌａｐｌａｃｅ变换技术,求得了任意时刻球体内部温度分布的解析解．作为算例,计算了方波脉冲这类随时间变化热流作用下球体内的温度变化,结果表明,该类超急速热传导问题与常规的傅立叶热传导相比具有明显不同的特征     

由激光辐照固体表面引起的非Fourier三维传热问题的解析解

针对激光束瞬间加热物体表面时,材料表面附近温度场变化的问题,建立了基于非傅里叶热传导理论的三维热传导数学模型. 考虑了激光束的聚焦特征,即热量或高温主要集中在光束中心附近的局部区域,且沿材料表面切向呈非均匀分布. 利用积分变换技巧,得到了问题Laplace逆变换的解析形式,从而给出了新的温度场解析解,并据此分析了传热过程中固体内部的温度场演化规律及特征. 数值计算结果显示,该问题的温度场呈现出明显的非傅里叶传热特征,与经典的热传导的扩散形式不同,它是以波的形式进行传热的.      

按非Fourier定律分析陶瓷薄膜受热沉积作用的热力耦合问题

考虑热传导的非Fourier定律,并且在温度控制方程中计入应变和应力变化的热效应,在应力本构方程中计入了温度变化的影响,得出了各向同性线性热弹性温度梯度非Fourier物质的热力双向耦合方程,且对有限厚度陶瓷薄膜,给出了边界受单一脉冲热沉积的典型一维瞬态问题的数值结果.讨论了延迟时间对温度增加量和应力分布的影响.主要结论:对陶瓷类介质,由于热渡波速和膨胀波波速有极大的数量级差异,热力耦合对传播速度影响甚微,即以十分接近热波波速和膨胀波波速传播.由于外加作用是以热学量给出的脉冲热沉积,因此传播的主要控制速度是热波波速.传播的力学量属高阶小量.     

调制激光束的温度效应

研究聚焦的调制激光束照射团体材料表面时所引起的温升分布。根据固体对光的吸 收和材料的热传导过程建立了数学模型。在柱坐标系下用Ｈａｎｋｅｌ积分变换方法求解一般 形式的热传导方程得出了直流温升和交变温升空间分布的积分表达式。通过计算机模拟 得到了不同材料的温升分布与激光束参数之间的关系。     

冲击热流快速加热半无限体热冲击问题非傅立叶效应研究

基于热量传播速度为有限值的双曲线型导热微分方程式,对实际中常见的冲击热流快速加热半无限体所产生的动态热应力问题进行了理论研究,分析了动态温度效应和热;中击期间动态热应力的变化规律。所得结果对完善发展热冲击理论及分析其机理都具有重要的意义。     

基于傅立叶级数解的导温系数现场测定

将路面温度场抽象为1维瞬态热传导方程,由分离变量法导出满足方程的傅立叶级数,推导出在已知界面温度时确定1维层状体瞬态温度分布的解答.基于路面温度场实测数据,提出用牛顿法反算路面材料导温系数的方法.在路面降温过程中路面温度沿深度单调变化时,傅立叶级数解取50项就能够达到0.01℃的精度.实测数据分析结果表明:路面沥青层中上部导温系数较下部稍大,中面层AC-16导温系数为0.002 4m2.h-1,底面层AC-25为0.001 6m2.h-1,比大多实验室测定值低.