A droplet of substance A is suspended in a stream of gas B. The droplet radius is
Question:
A droplet of substance A is suspended in a stream of gas B. The droplet radius is r 2 – We postulate that there is a spherical stagnant gas film of radius r 2 .
The concentration of A in the gas phase is x A1 at r = r 1 and x A2 at r = r 2 .
a. By a shell balance, show that for steady-state diffusion r 2 N Ar is a constant and set the constant equal to r 1 2 N A+1 , the value at the droplet surface.
b. Show that Eq. 17.0–1 and the result in (a) lead to the following equation for x A :
r 1 2 N A+1 = – c D AB /1–x A r 2 dx A /dr (17.G–1)
c. Integrate this equation between the limits r 1 and r 2 and get
N A+1 = c D AB /r 2 – r 1 (r 2 /r 1 ) ln x B2 /x B1 (17.G–2)
d. If a mass transfer coefficient k p is defined by N A+1 = k p (p A1 – p A2 ), show that when
r 2 → ∞ k p = 2cD AB /D/(p B )ln (17.G–3)
in which D is the droplet diameter. Discuss the significance of this result as applied to a droplet evaporating into a large body of gas that is not in motion.
Expert Answer:
Principles of heat transfer
ISBN: 978-0495667704
7th Edition
Authors: Frank Kreith, Raj M. Manglik, Mark S. Bohn
