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...

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 mm thick. At 37.5°C, the diffusivity through the fabric is 2 × 10⁻⁸
cm2/s, the concentration of water vapors at the surface of the body is 10⁻⁵
g/cm³, and the concentration of water vapor at the surface of the fabric is 0 g/cm3.

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

b. Find the mass flow rate across the fabric. Leave the area as As.