Page 182 - Industrial Ventilation Design Guidebook

I 44 CHAPTER 4 PHYSICAL FUNDAMENTALS

The humidity change due to vaporization is

The negative sign in Eq. (4.328) is due to the fact that (du/dt) < 0 repre-
sents the net vaporization to the surroundings.
Calculating the temperature rise at each time t with Eq. (4326) and Eq.
(4.328) gives the corresponding change in humidity. As the function G and the
pressure p(T, u) are complex, numerical solutions are used.

Example 6
Calculate the humidity change and the temperature rise in a paper web at
the time when the web humidity u — 0.20 and temperature 9 — 70 °C. As-
1
2
sume the heat transfer factor on the web surface is a = 40 W m" K" and the
humidity of the surrounding air is x = 0.05 kg H 2O/kg dry air. The radiation
2
power density absorbed by the web surface is 250 kW m~ .
The vaporization heat of water, which depends on the humidity, is accu-
rately determined by

where
/ 0(T) is the vaporization heat of free water
r(T,u) is the required auxiliary heat (sorption heat)

The sorption heat for the newsprint is calculated as

3
1
2
where A 2 =-1.3820, A 3 = 7.557, A 4 =-3.372, A 6 = 8.633 x 10~ kj kg" K~ ,
A 7 = 696.0 K, and T cr = 647.3 K. Substituting u = 0.20 and T = 343 K in this
1
1
equation gives r = 21.1 kjkgr . Table 4.7 gives 1 0(B = 70 °C) = 2333.3 kj kg- ;
1
3
hence, /(T, u} = 2354 x 10 J kg- .
The partial pressure of the surrounding air p A(y] is calculated using the
humidity x — 0.05 kg H 2O/kg dry air:
The steam pressure inside the paper web p A(T, u) calculated in the previ-
ous example was p A(T, u) = 27.7x10 Pa and the diffusion resistance fac-
tor e = 0.50. If the thickness of the paper web s = 0.09 mm, the mean
diffusion distance inside the paper is Ax = s/4 = 0.0225 mm.
Substituting the numerical values in Eq. (4.323) to determine the conductance,