Explicit analytical solutions of non-Fourier heat conduction equation for IC chip

Four basic explicit analytical solutions of non-Fourier heat conduction equation simulating IC chip thermal condition are derived. Some other analytical series solutions can also be derived with the above-mentioned basic solutions. Analytical solution has its own irreplaceable important meaning in theory. In addition, as the standard solution to check the accuracy, convergence and effectiveness of various numerical computational methods and their differencing schemes, grid generation ways and so on, the analytical solution is very useful also for the newly rapidly developing computational heat transfer.     

An analytical solution of non-Fourier Chen-Holmes bioheat transfer equation

An algebraically explicit analytical solution with heat wave effect is derived for the non-Fourier bioheat transfer Chert-Holmes model. Besides its important theoretical meaning （for example, to expand the understanding of heat wave phenomena in living tissues）, this analytical solution is also valuable as the benchmark solution to check the numerical calculation and to develop various numerical computational approaches.     

Non-Fourier Heat Conduction Effects During High-Energy Beam Metalworking

Non-Fourier heat conduction induced by ultrafast heating of metals with a high-energy density beam was analyzed. The non-Fourier effects during high heat flux heating were illustrated by comparing the transient temperature response to different heat flux and material relaxation times. Based on the hyperbolic heat conduction equation for the non-Fourier heat conduction law, the equation was solved using a hybridmethod co mbining an analytical solution and numerical inversion of the Laplace transforms for a semiinfinite body with the heat flux boundary. Analysis of the temperature response and distribution led to a criterion for the applicability of the non-Fourier heat conduction law. The results show that at a relatively large heat flux, such as greater than 108 W/cm2, the heat-affected zone in the metal material experiences a strong thermal shock as the non-Fourier effects cause a large step increase in the surface temperature. The results provide a method for analyzing transient heat conduction problems using a high-energy density beam, such as electron beam deep penetration welding.     

时域间断Galerkin有限元法在激光热加工过程中应用

针对半无限体和薄膜结构受多种激光热源作用下的非傅里叶热传导过程,采用时域间断Galerkin有限元法进行数值仿真.其主要特点是在时域内对温度及其时间导数分别进行三次Hermite插值和线性插值.对于半无限激光热源热传导问题,其计算结果与解析解吻合良好.算例表明,时域间断Galerkin有限元法在高频激光脉冲问题中,没有...     

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.      

一维导热反问题非级数形式的精确解

以一维线性导热反问题为研究对象，求得了在一特殊情况下的非级数形式的精确解．采用一种新的拟逆解法，它将带有测量误差的边界条件进行微小扰动而化为非局部条件．进行数值求解，通过数值解与精确解的比较，对计算误差的变化规律进行了分析研究．     

激光辐照材料表面非Fourier热传导问题的半解析解

针对有较长热驰豫时间的材料在表面受到激光脉冲照射时的非Fourier热传导问题,利用Laplace、Hankel变换及其逆变换,给出了一个半解析解.数值仿真表明,该半解析解能够清晰显示非Fourier热传导问题中的热波现象.     

Explicit analytical solutions of transport equations considering non-Fourier and non-Fick effects in porous media

Based on the method of separation variables with addition developed in recent years, new methods of separation variables are proposed, and two algebraically explicit analytical solutions to the general partial differential equation set of non-Fourier and non-Fick heat and mass transfer in porous media drying are derived. The physical meaning of these solutions is simple and clear, and they are valuable for computational heat and mass transfer as benchmark solutions.     

热传导问题的MATLAB数值计算

分析了应用MATLAB中PDE工具箱解热传导问题的方法和步骤，编制了三个难以用解析方法求解的算例。采用有限元法求解导热偏微分方程，应用PDE工具箱得到数值解。对适合圆柱坐标描述的问题，通过公式变化将其转换为能用PDE工具箱求解的形式。算例表明，用MATLAB对复杂形状和有内热源的非稳态导热问题进行数值计算和图形处理是方便高效的。     

Explicit analytical solutions fof transport equations considering non-Fourier and non-Fick effects in porous media

Dryingprocessinporousmediawidelyexistsin manyfieldssuchasenergy,chemistry,biology,medicineandarchitectonics.Researchesintothiskind ofphenomenonaretraditionallybasedonFourierlaw andFicklaw.Thesetwolawsincludethehypotheses ofinfinitepropagationofheatandmassdisturbance,respectively.Suchanapproximateapproachisprecise enoughfortheconventionalunsteadyheatandmass transfer.However,forhighintensiveandrapiddry ingprocess,itcouldleadtoerrorstosomeextent.Therefore,itisnecessarytoconsiderthenon linearrel…     

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.     

Explicit analytical solutions of transport equations considering non-Fourier and non-Fick effects in porous media

Based on the method of separation variables with addition developed in recent years, new methods of separation variables are proposed, and two algebraically explicit analytical solutions to the general partial differential equation set of non-Fourier and non-Fick heat and mass transfer in porous media drying are derived. The physical meaning of these solutions is simple and clear, and they are valuable for computational heat and mass transfer as benchmark solutions.     

非牛顿幂律流体试井模型的一种简明解析解

 在实际油藏的三元复合驱条件下,三元复合体系多表现出非牛顿幂律流体的渗流特征。将三元复合体系假定为非牛顿幂律流体所得到的均质试井模型是非线性的,难以求得解析解,通常只用数值方法求得其近似解。本文使用加法分离变量法,求解尚未有解析解的非定常非线性试井方程,导出了一系列简明（无特殊函数和无穷级数）的解析解,以发展非Newton幂律流体的理论;而且还可以作为标准解来检验相应的数值解的准确度、收敛性与稳定性,以发展数值方法。此外,应用常规分离变量法也得到了一些显式解析解。     

摄动法用于冷冻生物组织的热分析

本文提出了用于预测球形低温冷刀周围被损伤组织增长速率的一阶摄动解.模型中包括有血流和代谢热的影响,且允许生物组织的初始温度高于其相变温度.在求解过程中,冻结相和未冻结相的热容影响均被考虑.结果表明,本文所提出的一阶摄动解比Cooper解更接近实验值和数值解.     

Some non-Fourier heat conduction characters under pulsed inlet conditions

Through simulating one-and two-dimensional non-Fourier heat conduction problems under different pulsed inlet conditions, this paper numerically predicts some different non-Fourier heat conduction characters arose from different pulse types and different pulse frequencies. Meanwhile, the differences among thermal wave, non-Fourier and Fourier heat conduction are also showed.     

不同拉压模量弹性地基梁的解析解

采用拉压不同模量理论,推导了不同模量弹性地基梁的解析解.研究得到的解析解拓展了经典力学理论,并且当拉压模量相同时,该解可以退化到经典理论解.将结果与经典力学同模量理论比较表明:研究得到的解析解能很好地考虑了拉压不同模量效应.为此,合理设计材料的拉压模量比值,可以显著的改变地基梁的弹性特征值、内力及挠度值.该理论遵循材料实际的力学行为,在实际工程设计中大大提高了材料的利用率,达到节约能源的目的,具有重要的工程意义.     

稳态胞晶生长控制方程的解析解及其传输行为

建立了稳态胞晶生长温度场数学模型.通过在复数域内应用分离变量法对控制方程进行求解,得到了问题的解析解.讨论了在某些特定情形下的能量传输特性.     

Analytical Research of Temperature Distribution and Thermal Stresses within Circular Micro-hotplates

Micro-hotplate(MHP) technology is one key part in the manufacturing of gas sensors.The pursuit of analytical solutions for the temperature distribution and also thermal stresses within the MHP is of intrinsic scientific interest.In this study,analytical solutions for the temperature field,and both radial and tangential stresses and von Mises stress for circular MHP were obtained.Two geometries were considered:one had a circular heater at the center and the other had a circular heater at the center and an annular heater within the membrane part.Internal heat generation was incorporated in the energy equation for the MHP and different values of convection heat transfer coefficient were used at the upper and lower surfaces of the MHP.It has been shown that the MHP with two heaters can provide more uniform temperature field compared with the MHP with one heater.The main objective of this work is to provide an exact analytical solution for thermal stresses within the circular micro-heater with a simple geometry as a benchmark,from mathematical point of view,against which the accuracy of new numerical schemes can be checked.To make sure that the analytical procedure is correct,the analytical results are checked against numerical solutions derived from finite element simulation.Since the analytical models for the temperature field and especially for the thermal stresses of MHP are seldom investigated in the literature,the obtained results are believed to facilitate the design and performance evaluation of MHPs as well.     

Explicit analytical solutions of axisymmetric laminar natural convection along vertical tubes

There are many natural convection processes in various fields, and it is still valuable to investigate the fluid dynamics and heat transfer of natural convection. The analytical solutions are meaningful in both theoretical investigation and practical applications. Specially, they can be used as the benchmark solutions to check the numerical solutions and to develop numerical differencing schemes, grid generation methods and so on. Two explicit analytical solutions of axisymmetric steady laminar natural convection along a vertical tube with porous wall and between two vertical concentric tubes are derived for better understanding of the flow and heat transfer as well as promoting the computational fluid dynamics and computational heat transfer.     

多涂层各向异性短纤维复合材料热弹性解

建立了包含任意层同轴圆柱壳体模型,并得到了热载荷作用下的空间轴对称控制方程.利用局部/总刚度矩阵方程方法,在假定材料的性质与温度无关的情形下获得了具有任意涂层正交各向异性单向短纤维复合材料的热弹性解析解.相比于经典的弹性力学方法--根据界面应力和位移连续联立方程组求解,所用方法极大地减少了未知量的个数,便于计算机编程.最后,针对具体的算例,给出了多涂层单向短纤维增强复合材料在热载荷作用下的位移场和应力场,分析了纤维体积含量Vf对复合材料位移和应力分布的影响.