TRANSFER: BASICS OF MASS AND HEAT TRANSFER - Biomass as a Sustainable Energy Source for the Future - page 115

To calculate the evaporation constant, the Spalding mass coefficient, B M ,
which requires knowledge of the fuel mass fraction at the surface, has to be
estimated first. The Clausius Clapeyron equation Equation (4.34) gives the

vapor mole fraction at the given droplet surface temperature, and then the
vapor mass fraction follows from Equation (4.35):

-

= exp =0

h fg
R u =

X s = p sat

1
T boil −

1
T sat

855, 000
8, 315

1
351 −

1
341 p atm = exp

: 6732

MW F = 46 : 07

MW F
X s MW F +1

:

Y s =X s

MW air =0

7659

ð − X s Þ

The Spalding mass coefficient, B M , is then evaluated fromEquation (4.39) as

B M = Y s −

Y ∞

=3 : 2718

1 − Y s

Here, Y ∞ is the vapor mass fraction at infinity (i.e., far away from the drop-
let). To evaluate the evaporation constant, we need to estimate ρ D , which we

ðT = 800K

treat as ρ air D Þ . Extrapolating the diffusivity from 273 to 800

K using

0 1

3 = 2

D T = D T 0 T

@ A

T 0

0 1

3 = 2

800
273

@ A

02 × 10 −5 m 2 s −1 =5 12 × 10 −5 m 2 s −1 =1 : :

and using the ideal gas law to evaluate ρ air ,

p 101, 325

8, 315

T air

m −3 =0 m −3

ρ air = =

800 kg

: 4417 kg

ð = 29 Þ R u

= MW air

Thus,

K= 8

ρ air D
ρ F

ln B M +1 ð Þ

12 × 10 −5

= 8×0

: 4417 × 5 :

328 × 10 −7 m 2 s −1 ln 3 ð : 2718 + 1 Þ =3 :

789

and the droplet lifetime is

2

100 × 10 −6 m

t d = d d 0

ðÞ
K

= =0 : 030 s

K