TRANSFER: BASICS OF MASS AND HEAT TRANSFER - Biomass as a Sustainable Energy Source for the Future - page 114

heat transferred to the droplet surface is divided into heat used for evaporation and
heat used for increasing the temperature of the droplet.

Example 4.2 Mass diffusion-controlled evaporation of a fuel droplet

The presentation of this example follows Turns (2000, p. 103) but in this case for
ethanol fuel.

Given
An ethanol droplet initially at temperature 10 or 20 K below the boiling temper-
ature is evaporating in surrounding air with a temperature of 800 K.

To be determined
Droplet lifetime, t d :

a. Assuming that the droplet temperature is constant in time
b. Solving simultaneously the equation for droplet temperature and also taking
into account a slip velocity, v s ,of10m s −1

Discussion of the solution procedure
The balance between conductive heating and evaporative cooling determines the
droplet temperature evolution. In general, the droplet temperature will change with
time. In (a), as a first approximation, it is assumed that the droplet temperature
remains constant during the evaporation process. In (b), this assumption is not
made, but instead, an additional equation for the droplet temperature is solved.

Physical properties of ethanol
Boiling temperature: T boil = 351 K
Latent heat: h fg = 855 kJ kg −1

mol −1
Diffusion coefficient in air: D = 1.02 × 10 −5 m 2

MW: MW F = 46.07 g

s −1 at 273 K

Properties of the droplet
Diameter: d d = 100 m

Surface temperature: T s =T boil −

μ

10 K or T s =T boil − 20 K

m −3 Density : ρ F = 789 kg

Properties of the surroundings
p = 1 atm
MW: MW air =29g mol − 1

Temperature: T air = 800 K

Solution
a. Assuming constant droplet temperature
The droplet lifetime can be estimated using Equation (4.41), after calculating
the evaporation constant K, from Equation (4.40).