Study In Mathematical Model On Heat And Moisture Transfer Through Textiles

Textile material design is a kind of inverse problem in mathematical physical field. In this paper, from the point of clothing comfort, we study the textile material design problem by the theories and methods of inverse problems based on a steady-state model of coupled heat and moisture transfer through parallel pore textiles, which can not only be used to predict and guide the experiments of textile material design and clothing equipment design scientifically, but also to provide theoretical support and scientific explanation for textile material design.In this paper, we mainly consider the formulation of direct problem and inverse problem of thickness design for parallel pore textiles, meanwhile some numerical methods are presented to solve the direct and inverse problems.In chapter 2, a steady-state model of heat and moisture transfer through parallel pore textiles where their boundary and initial conditions are presented reasonably. By decoupling of coupled ODEs and the finite difference method (FDM), we design the numerical methods for the direct problem. Numerical simulation is achieved for down and polyester material in order to verify the validity of methods, and numerical results are well matched with the experimental data on the"Walter"Manikin. The algorithm is proved convergent with the convergence rate of the first order theoretically.In chapter 3 and 4, we propose an inverse problem of thickness design both for single layer textile material and bilayer textile material under low temperature respectively. Introducing a regularized function of thickness variable, solving the inverse problem can be formulated into a function minimization problem. Combining the finite difference method for ordinary differential equations with direct search method of one-dimensional minimization problems, we derive three kinds of iteration algorithms of regularized solution for the inverse problems of thickness design. Numerical simulation is achieved in order to verify the validity of proposed methods.We overcome the difficulties of solving nonlinear coupled ordinary differential equations by decoupling skill. Subsequently we obtain the numerical solutions of ordinary differential equations by the finite difference method, and corresponding convergence rate is obtained and proved. Most importantly, it is the first time that we propose inverse problems of thickness design for textile materials design based on thermal and moisture comfort. Adopting the idea of regularization method, we construct a regularized function of thickness variable and define a kind of regularized solution, and subsequently iteration algorithms of regularized solution for the inverse problems are derived.