PHYSICAL PRETREATMENT OF BIOMASS - Biomass as a Sustainable Energy Source for the Future - page 256

k ρ a h fg

h

sat

ð T − T wb Þ = ð ω − ω Þ ð Eq : 8 : 17 Þ

Thus, T wb is practically only dependent on the temperature of the surroundings and the
humidity of the air.
The analogy of Chilton and Colburn concerning heat and mass transfer under
turbulent conditions and transfer from “ fixed walls ” leads to an expression for h / k :

0 : 33 0 : 67

Nu
Re Pr 0 : 33 =

Sh
ReSc 0 : 33 ,

h

k = D

Pr
Sc

Sc
Pr

c p Le 0 : 67 = ρ c p = ρ ð Eq : 8 : 18 Þ

The physical properties in this expression are related to the surrounding air above the
vaporizing medium.

Question : Derive the expression for h/k yourself with intermediate steps.

The process of drying can be described as a sequence of transport phenomena that
occur onandwithina drying solidparticle.Dryingof different biogenicmaterials usually
occurs in two or more distinct stages. This is related to the fact that initially freemoisture
is available at the drying surface, resulting in a virtually constant drying rate. This drying
phase is also called the constant-rate period , in which the material dries from an initial
water content w i to the critical water content w c . For further drying, bound water from
capillaries/interstitial spaces is to diffuse to the surface making it just wet, which causes
retardation of the process. This phase in drying is called the first falling-rate period ,
and in this phase, the water content decreases from w c to a lower value but above
the equilibrium water content, w e , which is material dependent. Upon further drying,
the transport process from within the drying particle can no longer ensure a wetted
surface and then the process becomes not so much dependent on outer conditions,
but rather on internal molecular diffusion processes that depend on the characteristics
of the fuel. This final drying phase is called the second falling-rate period ; the process
continues till w e is reached and then the driving force forwater removal has become zero.
Figure 8.3 shows a schematic of the drying rate behavior of some biogenic
materials, illustrating different drying characteristics.
During the “ constant-rate period, ” the drying time t c can be expressed as

t c = w i −

w c
R c A

ð Eq : 8 : 18 Þ

with R c being the constant drying rate per unit area.

Question : Derive an expression for R c .

During the first falling-rate period, it can be assumed that the rate of drying is lin-
early dependent on the actual free moisture content (w

− w e ), expressed as follows:

ð w=w

= ð t=t f
t=0

1
A

dw
dt = K w

1
K A

dw

− ð − w e Þ = Kf ) − dt ð Eq : 8 : 19 Þ

ð w − w e Þ

w=w c