Question

A “cooling bag” is commonly used for storing water in hot, arid outdoor environments. The bag made of a thin porous fabric that allows water vapor, but not liquid water, to pass through it. A small amount of water (species A) diffuses through the fabric and evaporates from the surface of the bag. The rate of evaporation is controlled by convective mass transfer from the outer surface of the fabric to the surrounding dry air. The energy for evaporation is supplied by the hot air surrounding the outer surface of the bag. The evaporation of the water cools the remaining liquid water within the bag and a steady-state temperature driving force is established. If the surface temperature of the bag is 283 K, determine the temperature of the surrounding hot air. It may be assumed that the surrounding arid air contains no moisture

Answer 1

At 293 K, the latent heat of vaporization of water is ∆Hv,A = 2.45 kJ/g H2O, and the vapor pressure of water is PA.= 2.34 × 103 Pa.

Let species A and B be denoted for and air respectively.
From the appendix of mass-transfer diffusion coefficients in binary systems, obtain the mass diffusivity of species A in species B, as .
From the appendix of physical properties of gases and liquids, select the air property at a temperature of 293 K and obtain the Prandtl number , kinematic viscosity, air density, and heat capacity.

Answer 2

At 293 K, the latent heat of vaporization of water is ∆Hv,A = 2.45 kJ/g H2O, and the vapor pressure of water is PA.= 2.34 × 103 Pa.

Let species A and B be denoted for and air respectively.
From the appendix of mass-transfer diffusion coefficients in binary systems, obtain the mass diffusivity of species A in species B, as .
From the appendix of physical properties of gases and liquids, select the air property at a temperature of 293 K and obtain the Prandtl number , kinematic viscosity, air density, and heat capacity.