共查询到20条相似文献,搜索用时 31 毫秒
1.
Wei-zhongDai RajaNassar 《计算数学(英文版)》2003,21(5):555-568
Heat transport at the microscale is of vital importance in microtechnology applications.The heat transport equation is different from the traditional heat transport equation since a second order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time are introduced. In this study,we develop a hybrid finite element-finite difference (FE-FD) scheme with two levels in time for the three dimensional heat transport equation in a cylindrical thin film with submicroscale thickness. It is shown that the scheme is unconditionally stable. The scheme is then employed to obtain the temperature rise in a sub-microscale cylindrical gold film. The method can be applied to obtain the temperature rise in any thin films with sub-microscale thickness, where the geometry in the planar direction is arbitrary. 相似文献
2.
S.H. Momeni‐Masuleh A. Malek 《Numerical Methods for Partial Differential Equations》2007,23(5):1139-1148
This research aims to develop a time‐dependent pseudospectral‐finite difference scheme for solving a 3D dual‐phase‐lagging heat transport equation in a submicroscale thin film. The scheme uses periodic pseudospectral discretization in space and a fully second‐order finite difference discretization in time. The three consecutive time steps model is then solved explicitly, by using a preconditioned conjugate gradient method. The scheme is illustrated by an example which is used to investigate the heat transfer in a gold submicroscale thin film. Comparisons are made with available literature. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
3.
Weizhong Dai Lixin Shen Raja Nassar 《Numerical Methods for Partial Differential Equations》2004,20(1):60-71
Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation is different from the traditional heat diffusion equation since a second‐order derivative of temperature with respect to time and a third‐order mixed derivative of temperature with respect to space and time are introduced. In this study, we consider the heat transport equation in spherical coordinates and develop a three‐level finite difference scheme for solving the heat transport equation in a microsphere. It is shown that the scheme is convergent, which implies that the scheme is unconditionally stable. Results show that the numerical solution converges to the exact solution. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 60–71, 2004. 相似文献
4.
Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation differs from the traditional heat diffusion equation in having a second‐order derivative of temperature with respect to time and a third‐order mixed derivative of temperature with respect to space and time. In this study, we develop a high‐order compact finite difference scheme for the heat transport equation at the microscale. It is shown by the discrete Fourier analysis method that the scheme is unconditionally stable. Numerical results show that the solution is accurate. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 441–458, 2000 相似文献
5.
A. A. Belolipetskii A. M. Ter-Krikorov 《Computational Mathematics and Mathematical Physics》2014,54(1):74-82
A mixed problem for a linear parabolic equation with a small parameter multiplying the time derivative and with nonlinear boundary conditions is solved. Such boundary conditions arise in some heat and mass transfer problems, for example, in cooling thin spherical gas-filled shells or in the case of a gas filling such shells with gas-permeable walls. 相似文献
6.
就各向同性的无限弹性体,具有一个球形空腔时,从双温广义热弹性理论(2TT)角度,研究三相滞后热方程的热弹性相互作用问题.在三相滞后理论中,热传导方程是一个含时间四阶导数的、双曲型的偏微分方程.假设无限介质初始时静止,通过Laplace变换,将基本方程用向量矩阵微分方程的形式表示,然后通过状态空间法求解.将得到的通解应用于特殊问题:空腔边界上承受着热荷载(热冲击和坡型加热)和力学荷载.使用Fourier级数展开技术,实现Laplace变换的求逆.计算了铜类材料物理量的数值解.图形显示,两种模型:带能量耗散的双温Green-Naghdi理论(2TGNIII)和双温3相滞后模型(2T3相)明显不同.还对双温和坡型参数的影响进行了研究. 相似文献
7.
Zhi‐Zhong Sun Weizhong Dai 《Numerical Methods for Partial Differential Equations》2014,30(4):1291-1314
Heat conduction in multilayered films with the Neumann (or insulated) boundary condition is often encountered in engineering applications, such as laser process in a gold thin‐layer padding on a chromium thin‐layer for micromachining and patterning. Predicting the temperature distribution in a multilayered thin film is essential for precision of laser process. This article presents an accurate finite difference (FD) scheme for solving heat conduction in a double‐layered thin film with the Neumann boundary condition. In particular, the heat conduction equation is discretized using a fourth‐order accurate compact FD method in space coupled with the Crank–Nicolson method in time, where the Neumann boundary condition and the interfacial condition are approximated using a third‐order accurate compact FD method. The overall scheme is proved to be convergent and hence unconditionally stable. Furthermore, the overall scheme can be written into a tridiagonal linear system so that the Thomas algorithm can be easily used. Numerical errors and convergence rates of the solution are tested by an example. Numerical results coincide with the theoretical analysis. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1291–1314, 2014 相似文献
8.
《Nonlinear Analysis: Hybrid Systems》2008,2(1):121-143
Hyperbolic two-step microscale heat transport equations have attracted attention in thermal analysis of thin metal films exposed to ultrashort-pulsed lasers. Exploration of temperature-dependent thermal properties is absolutely necessary to advance our fundamental understanding of microscale (ultrafast) heat transport. In this article, we develop a finite difference scheme, by obtaining an energy estimate, for solving the hyperbolic two-step model with temperature-dependent thermal properties in a double-layered microscale thin film with nonlinear interfacial conditions irradiated by ultrashort-pulsed lasers. The method is illustrated by investigating the heat transfer in a gold layer on a chromium layer. 相似文献
9.
The inverse problem of determining a spacewise dependent heat source, together with the initial temperature for the parabolic heat equation, using the usual conditions of the direct problem and information from two supplementary temperature measurements at different instants of time is studied. These spacewise dependent temperature measurements ensure that this inverse problem has a unique solution, despite the solution being unstable, hence the problem is ill-posed. We propose an iterative algorithm for the stable reconstruction of both the initial data and the source based on a sequence of well-posed direct problems for the parabolic heat equation, which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for a typical benchmark test example, which has the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure gives accurate numerical approximations in relatively few iterations. 相似文献
10.
11.
Cui-Cui Ji & Weizhong Dai 《高等学校计算数学学报(英文版)》2023,16(2):511-540
Nanoscale heat transfer cannot be described by the classical Fourier law
due to the very small dimension, and therefore, analyzing heat transfer in nanoscale
is of crucial importance for the design and operation of nano-devices and the optimization of thermal processing of nano-materials. Recently, time-fractional dual-phase-lagging (DPL) equations with temperature jump boundary conditions have
showed promising for analyzing the heat conduction in nanoscale. This article
proposes a numerical algorithm with high spatial accuracy for solving the time-fractional dual-phase-lagging nano-heat conduction equation with temperature jump
boundary conditions. To this end, we first develop a fourth-order accurate and unconditionally stable compact finite difference scheme for solving this time-fractional
DPL model. We then present a fast numerical solver based on the divide-and-conquer
strategy for the obtained finite difference scheme in order to reduce the huge computational work and storage. Finally, the algorithm is tested by two examples to verify
the accuracy of the scheme and computational speed. And we apply the numerical
algorithm for predicting the temperature rise in a nano-scale silicon thin film. Numerical results confirm that the present difference scheme provides ${\rm min}\{2−α, 2−β\}$ order accuracy in time and fourth-order accuracy in space, which coincides with the
theoretical analysis. Results indicate that the mentioned time-fractional DPL model
could be a tool for investigating the thermal analysis in a simple nanoscale semiconductor silicon device by choosing the suitable fractional order of Caputo derivative
and the parameters in the model. 相似文献
12.
This paper investigates the inverse problem of determining a spacewise dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from a supplementary temperature measurement at a given single instant of time. The spacewise dependent temperature measurement ensures that the inverse problem has a unique solution, but this solution is unstable, hence the problem is ill-posed. For this inverse problem, we propose an iterative algorithm based on a sequence of well-posed direct problems which are solved at each iteration step using the boundary element method (BEM). The instability is overcome by stopping the iterations at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented for various typical benchmark test examples which have the input measured data perturbed by increasing amounts of random noise. 相似文献
13.
考虑到薄膜表面的热通量主要是来自辐射,因而采用一个依赖时间的拟二维拟线性扩散方程的Stefan问题(混合初边值问题)作为该问题的数学模型。用一种具有Crank-Nicholson格式的无条件稳定的有限差分析来求解抛物型偏微分方程的定解问题。用追赶法求解离散化的三对角方程组,然后用预估校正法求解拟线性扩散方程,从而避免了示解非线性差分方程组,琥珀亚硝酸酯在纵向自由薄膜凝固期内的温度分布数值计算结果和 相似文献
14.
The inverse problem of determining a spacewise-dependent heatsource for the parabolic heat equation using the usual conditionsof the direct problem and information from one supplementarytemperature measurement at a given instant of time is studied.This spacewise-dependent temperature measurement ensures thatthis inverse problem has a unique solution, but the solutionis unstable and hence the problem is ill-posed. We propose avariational conjugate gradient-type iterative algorithm forthe stable reconstruction of the heat source based on a sequenceof well-posed direct problems for the parabolic heat equationwhich are solved at each iteration step using the boundary elementmethod. The instability is overcome by stopping the iterativeprocedure at the first iteration for which the discrepancy principleis satisfied. Numerical results are presented which have theinput measured data perturbed by increasing amounts of randomnoise. The numerical results show that the proposed procedureyields stable and accurate numerical approximations after onlya few iterations. 相似文献
15.
This paper is concerned with a heat diffusion problem in a half-space which is motivated by the detection of material defects
using thermal measurements. This problem is solved by inverting the Laplace transform with respect to time on a contour in
the complex plane using an exponentially convergent quadrature rule. This leads to a finite number of time-independent problems,
which can be solved in parallel using boundary integral equation methods. We provide a full numerical analysis of this scheme
on compact time intervals. Our results are formulated in a way that they can easily be used for other diffusion problems in
exterior or interior domains. 相似文献
16.
Cho Lik Chan 《Applied Mathematical Modelling》1993,17(12):650-657
An efficient algorithm is proposed to solve the steady-state nonlinear heat conduction equation using the boundary element method (BEM). Nonlinearity of the heat conduction equation arises from nonlinear boundary conditions and temperature dependence of thermal conductivity. Using Kirchhoff's transformation, the case of temperature dependence of thermal conductivity can be transformed to the nonlinear boundary conditions case. Applying the BEM technique, the resulting matrix equation becomes nonlinear. The nonlinearity, however, only involves the boundary nodes that have nonlinearboundary conditions. The proposed local iterative scheme reduces the entire BEM matrix equation to a smaller matrix equation whose rank is the same as the number of boundary nodes with nonlinear boundary conditions. The Newton-Raphson iteration scheme is used to solve the reduced nonlinear matrix equation. The local iterative scheme is first applied to two one-dimensional problems (analytical solutions are possible) with different nonlinear boundary conditions. It is then applied to a two-region problem. Finally, the local iterative scheme is applied to two cavity problems in which radiation plays a role in the heat transfer. 相似文献
17.
《Journal of Computational and Applied Mathematics》2012,236(5):819-833
This paper focuses on the numerical study of heat and moisture transfer in clothing assemblies, which is described by a multi-component and multiphase air–vapor–heat flow with a moving interface. A splitting semi-implicit finite volume method is applied for the system of nonlinear parabolic equations and an implicit Euler scheme is used for the interface equation. In terms of classical Dirichlet to Neumann map, the implicit system can be solved directly and no iteration is needed. Two types of clothing assemblies are investigated and the comparison with experimental measurements is also presented. 相似文献
18.
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation, is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term. 相似文献
19.
A compact finite difference scheme is developed to the three-dimensional microscale heat transport equation. This new scheme is fourth order in space and second order in time. It is proved to be unconditionally stable with respect to initial values. Numerical results are provided for comparison testing purpose. 相似文献
20.
The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed. 相似文献