Page 175 - Industrial Ventilation Design Guidebook

4.3 HEAT AND MASS TRANSFER I 3 7

in which

The dimensionless quantity Sh is called the Sherwood number.
The heat transfer factor a is defined by

where q is the heat flow density from the surface to the surroundings. Using di-
mensionless variables ® and TJ from Eqs. (4.284d) and (4.284f), Eq. (4.295) gives

where the dimensionless quantity Nu is the Nusselt number.
According to Eqs. (4.289) and (4.292) it is seen that with constant £or x

which leads to the important results

The above shows how the dimensionless numbers are used to provide the
most accurate solution. Collecting these definitions together,

Note the diffusion factor appearing in the Schmidt number, D AB =
(M B/M)D AB (Eq. (4.275)).
The preceding discussion has attempted to formulate the situation for
laminar boundary layer flow as accurately as possible and to obtain precise
correlation between the heat transfer and mass transfer factors.
It is not possible to translate the above reasoning to turbulent flow, as tur-
bulent flow equations are not reliable. However, in practice it is typical to as-
sume that the same analogy is also valid for turbulent flow. Because of this
hypothesis level, it is quite futile to use the diffusion factor D' AB in the
Schmidt number; instead we will directly use the number D AB as in the Sher-
wood number. Hence in practical calculations Sc = v/D AB.

Example S
n
m
Heat transfer is defined by Nu = AR Pr . The function G( • ) is given as