TRANSFER: BASICS OF MASS AND HEAT TRANSFER - Biomass as a Sustainable Energy Source for the Future - page 127

TABLE 4.2 Thermal conductivity λ [W m −1 K −1 ] of air and ethanol

as function of temperature
250 K 300 K 400 K 500 K 600 K 800 K 1000 K

Air 0.0223 0.0267 0.0331 0.0395 0.0456 0.0569 0.0672

Ethanol 0.0092 0.0147 0.0245 0.0327

From Kaviany (2002).

balance between incoming and outgoing radiative heat flux at the surface of a
pond of stagnant water when the sun is at an angle of 30 from the zenith. The
total hemispherical emissivity of water is known to vary from 0.95 to 0.963
in the temperature range from 273 to 373 K (Kaviany, 2002).
c. The absorption coefficient κ λ of clear water is known to depend on wave-

length. In the visible range (0.4

m), it varies from 0.02 to 0.6 m −1
(Modest 2003, p. 416). By solving the radiative transfer equation, determine
the decrease of intensity of incoming sunlight in a water layer with a depth
0.1 m for the case that the sun is at an angle of 30

- 0.7 μ

from the zenith.

4.5 For purposes of engineering calculations, the most appropriate reference

state for the evaluation of properties determining heat and mass transfer during
evaporation of a fuel droplet is a simple 1/3 rule, wherein the reference
temperature and species mass fractions are, respectively, T r =T s + 1

3 T b −

ð T s Þ

, with subscripts b and s referring to bulk and
surface (Hubbard et al. 1975). An ethanol droplet at an initial temperature
T s = 273 K is heated by surrounding air at temperature T air = 500 K. What is
the value of the thermal conductivity to be used according to the 1/3 rule? Phys-
ical data on the thermal conductivity of air and ethanol are given in Table 4.2.

and Y i , r =Y i , s + 1

3 Y i , b −

Y i , s

PROJECTS

P4.1 Using an appropriate software package, solve the model equations for an eva-
porating ethanol droplet for a range of conditions and plot the properties of the
solutions. Consider varying droplet temperature and the effect of convective
heat transfer.

P4.2 Using the kinetic data and properties data available in the literature, create an
implementation of the model for particle devolatilization described in
Section 4.5.2. Compare your results with those presented in Lu et al.
(2010), and discuss the sensitivity of the predictions to different aspects such
as wood material properties, kinetic rate coefficients, and particle size
and shape.