CM 3120, Transport / Unit Operations 2
Concept Quiz #2
Spring 2009
Mon. Feb. 16, 2009
Closed Book
1. Mass Transfer of Species A in a Flowing Fluid
A fluid is flowing downward (z-direction only) in laminar flow between the walls of a rectangular channel as
shown in the diagram below, and the velocity varies in the x-direction. One of the chemical components in both
walls is Species A which is slightly soluble in the fluid, which is composed, initially, entirely of Species B. Due
to this slight solubility, the concentration of A in the fluid at the wall is cAo and the concentration of A in the
fluid entering the channel is zero, cA=0 at z = 0 for all values of x between x = 0 and x = W (the width of the
channel). The concentration changes in both the x- and z-directions as indicated in the diagram below due to
the actions of diffusion and convection. There is no chemical reaction occurring for species A. Please answer
the following questions.
x
Channel wall
z
Channel wall
vz
cAo
NAx
cA=0
ConvectionNAz
dominated cAo
cAo
NAx
Diffusion only
cAo
cA=0
x=0
x=W
1. Draw the molar fluxes for species A (NA) on the diagram above. If there is more than one component of NA,
indicate all of them. Indicate whether these molar fluxes are diffusion- or convection-dominated.
2. One of the assumptions for this problem is that A is very dilute. What statement was made in the description
above that justifies this assumption?
“.. Species A which is slightly soluble in the fluid…”
3. We assume that the concentration varies in the x- and z-directions only, cA = cA(x,z). Why doesn’t
concentration vary in the y-direction, which is the direction into and out of the paper?
CAo is uniform for all y at x=0 and x=W
4. Simplify the Equation of Continuity below using the information given in the problem statement above and
using the assumptions stated previously. We assume that the concentrations in the fluid are at steady-state.
𝜕𝑐𝐴0
𝜕𝑐0𝐴
𝜕𝑐
𝜕𝑐𝐴
𝜕 2 𝑐𝐴 𝜕 2 𝑐𝐴0 𝜕 2 𝑐𝐴0
0𝐴
0
+ 𝑣𝑥
+ 𝑣𝑦
+ 𝑣𝑧
= 𝐷𝐴𝐵 [ 2 +
+
] + 𝑅𝐴
2
2
𝜕𝑡
𝜕𝑥
𝜕𝑦
𝜕𝑧
𝜕𝑥
𝜕𝑦
𝜕𝑧
2
𝜕𝑐𝐴
𝜕 𝑐𝐴
𝑣𝑧
= 𝐷𝐴𝐵
𝜕𝑧
𝜕𝑥 2