Performance fabrics, like that shown in Figure P4.39, are known to allow only a one-way direction of water vapors, created from sweat, to move away from the body. Taking a microscopic view, assume that the human body is in contact with the fabric that is \(0.5 \mathrm{~mm}\) thick. At \(37.5^{\circ} \mathrm{C}\), the diffusivity through the fabric is \(2 \times 10^{-8} \mathrm{~cm}^{2} / \mathrm{s}\), the concentration of water vapors at the surface of the body is \(10^{-5} \mathrm{~g} / \mathrm{cm}^{3}\), and the concentration of water vapor at the surface of the fabric is \(0 \mathrm{~g} / \mathrm{cm}^{3}\).

a. Derive an expression of the concentration profile across the fabric

b. Find the mass flow rate across the fabric. Leave the area as \(A_{s}\)

Transcribed Image Text:

Air CH20=0 mole/m y=5x104 y=0m Human Body CH20 = 10 mole/m FIGURE P4.39