Let us next analyse the coupled problem during ironing of textiles, that is, the heat is transported with mass whereas the mass transport with heat is negligible. It is necessary to define both physical and mathematical models. Introducing two-phase system of mass sorption by fibres, the transport equations are introduced and accompanied by the set of boundary and initial conditions. Optimisation of material thickness during ironing is gradient oriented. The first-order sensitivity of an arbitrary objective functional is analysed and included in optimisation procedure. Numerical example is the thickness optimisation of different textile materials in ironing device.
Head is the most sensitive body part of neonate. Head that is considerably uncovered causes the significant heat and moisture loss from the skin to the surrounding areas. The main goal is to optimise the thickness of a multilayer composite textile bonnet to secure the optimal skin parameters. Problem is solved using both sensitivity analysis and material derivative concept. An arbitrary objective functional is introduced, its first-order sensitivity is formulated by means of a direct approach. Numerical application is the thickness optimisation of a composite bonnet made of different textile materials.