TRANSFER: BASICS OF MASS AND HEAT TRANSFER - Biomass as a Sustainable Energy Source for the Future - page 125

SHORT-ANSWER QUESTIONS

4.1 What is Fick ' s law for diffusion? For which type of mixtures is Fick ' s law an

exact law? What is meant by the generalized Fick ' s law?

4.2 What is the form of the mass transfer equation for a steady nonreactive balance

between advection and diffusion?

4.3 Give examples of radiative heat transfer processes dominated by surface-to-

surface transfer and of processes for which the effects of absorption and emis-
sion in the space between surfaces (participating medium) are essential.

4.4 Explain in what sense the set of equations Equation (4.11) provides a solution

for the surface-to-surface radiative heat transfer problem. How would you solve
the equations (a) in the case that the temperature of all surfaces is known and (b)
in the case that for some surfaces the temperature and for other surfaces the heat
flux are known?

4.5 What is the nature of Newton s law of cooling Equation (4.25)? Considering a

few examples, explain how the value of the heat transfer coefficient depends on
the properties of the system.

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What is the d 2 -law for droplet evaporation? What are the assumptions that have
to be satisfied for this law to be valid?

4.6

4.7 What is the difference between the infinite conductivity model and the finite

conductivity model for fuel droplet evaporation?

PROBLEMS

4.1 Equation (4.8) is valid when the heat conductivity is independent on the direc-

tion. How would a generalization look like for the case of heat conductivity
being different in the three coordinate directions? Which physical properties,
e.g., of biomass material, could cause such difference?

4.2 Consider a layer of biomass of thickness 2 L, with moisture removal at both

sides. In a simple modeling approach, the drying process is assumed to be mass
transfer limited and to proceed at constant or slowly changing temperature.
Assuming that the sample does not shrink during drying, moisture removal
can be expressed using Fick

s law for unsteady diffusion of moisture in the
direction orthogonal to the layer. Experimentally, it was found that the effective
moisture diffusivity D eff is temperature dependent and has the form of an Arrhe-
nius relationship:

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, depending on pre-exponential factor D 0 and the activa-
tion energy E a (Gebreegziabher et al., 2013). Let X ( x , t) denote the sample mois-
ture concentration as a function of position (distance from the symmetry plane)

E a
R u T

D eff = D 0 exp −