Page 179 - Industrial Ventilation Design Guidebook

4,3 HEAT AND MASS TRANSFER I 4 I

and

Substituting these into Eq. (4.315) after grouping terms,

The term

is the resistance factor caused by the material. Using Eq. (4.317), the diffusion
flow is

The term p/(p-pA) derives from assumption (4.313) representing the ef-
fects of Stefan flow. If e = 1, Eq. (4.318) gives the diffusion flow in a free
space.
Equation (4.318) indicates that if k—> °°, the diffusion resistance re-
mains under 1, namely, ej = <j). This is easy to understand, as <£ represents
that part of the material cross-sectional surface through which the vapor dif-
fuses.

4.3.9 Example of Drying Process Calculation
The problems experienced in drying process calculations can be divided
into two categories: the boundary layer factors outside the material and hu-
midity conditions, and the heat transfer problem inside the material. The
latter are more difficult to solve mathematically, due mostly to the moving
liquid by capillary flow. Capillary flow tends to balance the moisture differ-
ences inside the material during the drying process. The mathematical dis-
cussion of capillary flow requires consideration of the linear momentum
equation for water and requires knowledge of the water pressure, its depen-
dency on moisture content and temperature, and the flow resistance force
between water and the material. Due to the complex nature of this, it is not
considered here.
We will cover a simple drying model to examine the radiation drier of
coated paper. We assume there are no major temperature or humidity varia-
tions in the direction of the paper web thickness, and that temperature T and
humidity u are constant in the direction of thickness. This assumption requires
that the capillary action be ignored, and the pressure gradient of water is zero
on the assumption du/dx = dT/dx = 0. How is it possible that the humidity
distribution remains uniform?
The only approach is to ignore the capillary flow and to assume water
vaporization takes place evenly in the thickness of the paper web. With a