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

Abstract

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.

Keywords:

• inverse problems of thickness determination
• partial differential equations of parabolic type
• well-posedness
• regularized solution
• bilayer textile materials
• numerical algorithm

AMS Subject Classifications:

• 35R30
• 35K51
• 65M32
• 80A20

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 11071221 and 10561001), Natural Science Foundation of Zhejiang Province (No. LQ12A01024) and Science foundation of Zhejiang Sci-Tech University (No. KY2012015).