The heat and moisture transfer balance theory of garment simulation

To establish the human body model to analyze the heat and moisture transfer on body surface, a new explicit definition of rational L-recursion surface is given and the L-recursion surfaces, in Grassmann spaces, are constructed by using blossom method of the homogeneous normal pyramid form. Based on our human body model, the balance theory of garment simulation, the heat and moisture transfer balance equations, called ICAD-balance equations are obtained. The balance theory of garment simulation integrally studies the complex system of human body-fabric-environment. At the same time, the method of obtaining the heat and moisture transfer balance equations is also based on the mass conservation law, the energy conservation law and the Fish law of capillarity. A finite volume method is employed to solve the ICAD-balance equations.     

The heat and moisture transfer balance theory of garment simulation

To establish the human body model to analyze the heat and moisture transfer on body surface, a new explicit definition of rational L-recursion surface is given and the L-recursion surfaces, in Grassmann spaces, are constructed by using blossom method of the homogeneous normal pyramid form. Based on our human body model, the balance theory of garment simulation, the heat and moisture transfer balance equations, called ICAD-balance equations are obtained. The balance theory of garment simulation integrally studies the complex system of human body–fabric–environment. At the same time, the method of obtaining the heat and moisture transfer balance equations is also based on the mass conservation law, the energy conservation law and the Fish law of capillarity. A finite volume method is employed to solve the ICAD-balance equations.     

A numerical study of air–vapor–heat transport through textile materials with a moving interface

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.     

A numerical study of air-vapor-heat transport through textile materials with a moving interface

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.     

An error estimate on a Galerkin method for modeling heat and moisture transfer in fibrous insulation

We propose a Galerkin finite element method for numerically modeling the process of heat and moisture transfer in porous clothing assemblies, which takes into account radiative heat transfer and sorption of water vapor into the fibers of the medium. We prove an optimal‐order error estimate for the finite element method in energy norm. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

An inverse problem of Bilayer textile thickness determination in dynamic heat and moisture transfer

An inverse problem of bilayer textile thickness determination in dynamic heat and moisture transfer is presented satisfying the heat–moisture comfort level of human body. Heat and mass transfer law in bilayer textiles is displayed by proving the existence and uniqueness of solution to the coupled partial differential equations with initial-boundary value conditions. The finite difference method is employed to derive the numerical solution to partial differential equations. The regularized solution of the inverse problem is reformulated into solving function minimum problem through the Tikhonov regularization method. The golden section method is applied to solve the direct search problem and achieve the optimal solution to the inverse problem. Numerical algorithm and its numerical results provide theoretical explanation for textile materials research and development.     

含湿相变粗糙多孔材质的热质耦合分形研究

多孔材质复杂的内部结构和含湿状态对传热和传质特性有着重要意义,其热质耦合传递过程广泛存在于能源开发和工程隔热等领域。不同于在多孔材质理想状态下对传热和传质特性的单方面分析,该文将孔道的分布参数、粗糙表面、含湿状态和相变等因素考虑进去,运用分形理论推导出了含湿相变粗糙表面多孔材质的渗流系数和耦合等效导热系数的表达式。结果表明,渗流系数与面积分形维数、含湿饱和度呈正相关,与相对粗糙度、迂曲分形维数呈负相关;耦合等效导热系数与渗流系数、相变量呈正相关,与相对粗糙度呈负相关。此外,结果还表明,相变量以及相变引起的气体膨胀压强差对热质耦合传递也有着重要影响。     

可变形孔隙介质中热、水耦合力学问题的代数多格子分析方法

研究了孔隙介质中包括热和质量传递的全耦合多相流问题的代数多格子分析方法。数学模型包括质量、线性矩、能量平衡方程和本构方程，以位移、毛细压力、汽压和温度为基本变量，模型中采用了考虑毛细压力关系的修正有效应力概念，并考虑相变、热传导、对流和潜热交换（汽化－冷凝），气相是由易混合的干空气和水蒸气组成，视为理想气体。考虑显示出较高的计算效率。     

A simple Taylor-series expansion method for a class of second kind integral equations

A simple yet effective Taylor-series expansion method is presented for a class of Fredholm integral equations of the second kind with smooth and weakly singular kernels. The equations studied in this paper arise in a number of applications, e.g., potential theory, radiative equilibrium, radiative heat transfer, and electrostatics. The approach leads to an approximate solution of the integral equation which can be expressed explicitly in a simple, closed form. The approximate solution is of sufficient accuracy as illustrated by the numerical examples arising from radiative heat transfer and electrostatics.     

Integrodifferential equations in viscoelasticity theory

We prove the correct solvability of the initial problems for integrodifferential equations with unbounded operator coefficients in Hilbert spaces. Such equations occur in many problems of the theory of viscoelasticity with memory and the heat transfer theory.     

高温作用下混凝土热-水-力耦合损伤分析模型

以混合物理论为基础建立了高温作用下混凝土的热-水-力耦合损伤分析模型.将混凝土视为由固体骨架、液态水、水蒸气、干燥气体和溶解气体共5种组分构成的混合物,模型的宏观平衡方程包括各组分的质量守恒方程、整体的能量守恒方程及动量守恒方程,模型所需的状态方程及本构关系全部给出,最后给出基于4个主要参数(固体骨架位移、气压力、毛细压力和温度)的控制方程.模型考虑了混凝土在高温作用下,水分的蒸发与冷凝、胶结材料的水化及脱水、溶解气的溶解与挥发等相变过程;从材料变形破坏过程中能量耗散特征入手,基于Lemaitre应变等价性假说和能量守恒原理得到力学损伤演化方程,并考虑了高温引起的热损伤对材料力学性能及力学损伤演化规律的影响,建立了热-力耦合损伤本构模型.     

齐次平衡法和浅水波中WBK方程的精确分析解

Based on the homogenous balance method and with the help of mathematica, the Backlund transformation and the transfer heat equation are derived. Analyzing the heat-transfer equation, the multiple soliton solutions and other exact analytical solution for Whitham-Broer-Kaup equations(WBK) are derived. These solutions contain Fan‘s, Xie‘s and Yan‘s results and other new types of analytical solutions, such as rational function solutions and periodic solutions. The method can also be applied to solve more nonlinear differential equations.     

Asymptotic solution of some singularly perturbed Fredholm integral equations

A formal approach is described for obtaining the asymptotic solution to a class of singularly perturbed Fredholm integral equations. The approach is illustrated through application to some example problems which arise in heat transfer, diffraction theory, crack mechanics, Markov processes and low order eigenvalue problems.     

A general class of evolutionary equations

Using observable quantities and state variable of a dynamical process, a general evolutionary equation is defined which unifies classical ordinary differential equations, partial differential equations, and hereditary systems of retarded and neutral type. Specific illustrations are given using transmission lines nearest-neighbor coupled at the boundary and the theory of heat transfer in solids. Some spectral theory for linearization of the equations is also discussed. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 2, pp. 268–288, February, 2007.     

On Analytical Results for the Optimal Control of the quasi-stationary Radiative Heat Transfer System

We state an optimal control problem of the coupled quasi-stationary radiative heat equations consisting of the radiative transfer equation and the instationary heat transfer equation that model radiative-conductive heat transfer. We give an existence and uniqueness result for the state equations and the adjoint equations of the quasi-stationary radiative heat transfer system. For the optimal control problem the existence of a minimizer is proven. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of stochastic heat transfer in a solid

The unsteady partial differential equations for expectation and correlation distributions of the stochastic temperature distribution in a solid are obtained, when the coefficients and the source term in the stochastic heat transfer equations are white Gaussian processes. Some solutions of the unsteady partial differential equations for expectation and correlation distributions of stochastic heat transfer are presented.     

Adjoint equations and iterative algorithms in problems of variational data assimilation

Based on the theory of adjoint equations, iterative algorithms for solving one class of data assimilation problems for the reconstruction of the initial condition are developed and substantiated. The iterative processes are optimized with the use of the spectral properties of control operators. The results are illustrated by the example of a quasi-local model of turbulent oceanic heat transfer.     

A phenomenological and kinetic description of diffusion and heat transport in multicomponent gas mixtures and plasma

Different forms of expressing diffusion and heat fluxes in multicomponent mixtures, obtained by methods of non-equilibrium thermodynamics and the kinetic theory of gas mixtures, are analysed and compared. It is shown that an alternative representation of the linear relations of non-equilibrium thermodynamics is possible, which enables them to be written in a form similar to that of the well-known Stefan–Maxwell equations. A relation between the phenomenological coefficients of non-equilibrium thermodynamics and the corresponding transport coefficients obtained in kinetic theory is established, with a confirmation that the Onsager reciprocity relations are satisfied. It is shown that there is an advantage in writing the transport relations on the basis of the “forces in terms of fluxes” representation, compared with the classical “fluxes in terms of forces” representation, used in standard schemes of phenomenological non-equilibrium thermodynamics and the Chapman–Enskog method, traditional for kinetic theory. A generalization of the Stefan-Maxwell equations and the equation for the heat flux is considered, which takes into account the contribution to these equations of the time and space derivatives of the fluxes. The relaxation form of the equations obtained enable one to approach the analysis of the propagation of small heat and concentration perturbations in gas mixtures to be justified, which, within the framework of classical transport relations, propagate with infinitely high velocity. The results presented in this review enable one to determine the areas of effective application of different methods of describing diffusion and heat transfer in multicomponent gas mixtures when solving specific gas-dynamic problems.     

重建极性连续统理论的基本定律和原理(Ⅱ)--微态连续统理论和偶应力理论

重建微态连续统理论和偶应力理论的动量和动量矩均衡定律以及能量守恒定律，并由这些定律自然地推导出相应的局部和非局部均衡方程．这些结果可由耦合型微极连续统理论过渡和归结而得到．把推导出的结果和传统的质量和微惯性守恒定律以及熵不等式结合在一起就构成微态连续统理论和偶应力理论的基本均衡定律和方程体系．还弄清了以前的各种连续统理论的不完整性层次．最后，给出了几种特殊情形．