Research on inverse problems of textile material design, which are motivated from functional clothing industry, is an inspiring and promising research field in the inverse problems family. It is important to reveal heat and moisture transfer characteristics in the system of human body-clothing-environment, which directly determines clothing heat-moisture comfort level. We present a comprehensive description on the mixed problems for coupled partial differential equations (in abbreviation, Direct Problems) based on dynamic heat and moisture transfer law with condensation in porous fabric. More importantly, we mathematically formulate novel inverse problems of textile material determination (in abbreviation, IPTMD) based on heat-moisture comfort indexes. The unique existence for the direct problems and numerical algorithms for IPTMD is reviewed. The further research topics are concluded to promote more fruitful achievements in the research of IPTMD in the near future.
Background of the inverse problems of textile material determinationTextile materials should be designed and engineered to possess specific attributes or properties for different end-uses. People hold a common sense that better clothing, happier life; smarter clothing, more upgraded industries. Compared to other materials, such as metal, plastics, and electronics, engineering of textile materials presents a much greater challenge, owing to the lack of the precise relationships between material-processingstructural variables on one hand and properties and performance on the other as well as the nonlinear nature of the multivariable interactions. This is however changing, thanks to the efforts of generations of textile scientists. More luckily, we can now predict the properties and performance of textile materials by applying theoretical models and empirical relations. However, it would be further desirable to quantify the material, processing, and structural parameters from the anticipated *