Textile material design is of paramount important in the study offunctional clothing design. It is therefore important to reveal heatand moisture transfer characteristics in the system of humanbody-clothing-environment, which directly determinethermalcomfort/safety level of human body. Based on the parabolic model ofdynamic heat and moisture transfer with condensationin porous fabric under low temperature, we present inverseproblems of textile parameters determination (IPTPD), including thickness, thermal conductivity and porosity determination. Moreover we mathematically formulate a new space-fractional parabolic model of heat-moisture transfer within thermal protective clothing under high environmental temperature-humidity, and the corresponding inverse problems of textile material design are put forward.

Adopting the idea of regularizationapproaches,we formulate the IPTPDinto functionminimization problems. Developing efficient numerical methods for coupled PDEs, sideways parabolic problems and direct search methods for optimization problems, we construct iterative algorithms of approximated solution for the IPTPD. Theoretical study and numerical simulation results validatethe formulation of the IPTPD and demonstrate effectiveness ofthe proposed numericalalgorithms.