Problem I $($old exam problem$)$

For a chemical process, species A must be added to a stream of inert carrier gas B$.$ To do

this in a controlled manner, liquid $A$ is evaporated from a round pan into a flowing stream of $B$

$($see right figure below$).$ Unfortunately, little is known about the mass transfer coefficients for

the round pan and the diffusion coefficient of A in air, which prevents the process engineer

from optimizing the conditions.

In order to quantify the relative importance of convection and diffusion for the evaporation of

A from the pan, two laboratory experiments are performed $($see Figures below$)$ under

identical conditions $(T=293K,P=1$atm $)$:

$1/$ Evaporation of liquid A from a narrow cylindrical tube with diameter $D_{\text{t}\text{u}\text{b}\text{e}}=2cm($left figure

on next page$).$ Pure carrier gas $B$ is blown over the top of the tube at velocity $v_{}=1\frac{m}{s}.$

The distance from the liquid surface to the top of the tube is $L=25cm$ at the start of the

experiment.

$2/$ Evaporation of liquid A from the actual process device, a flat circular pan with diameter

$D_{\text{p}\text{a}\text{n}}=10cm.$ Pure carrier gas $B$ is blown across the pan at velocity $v_{}=1\frac{m}{s}($right figure$).$

An analytical balance is used to monitor evaporation in both experiments. When pseudo

steady state is reached, the mass rate of evaporation $($in $k\frac{g}{s})$ from the pan is $100$ times

larger than from the tube. The exact value of the vapor pressure of $A,p_{A,v},$ is unknown, but

$p_{A,v}1$ atm.

A$/$ Derive an equation for the molar flux of A from the narrow tube as a

function of $p_{A,v}.$ Do not insert numerical values.

B$/$ Calculate the Sherwood number for evaporation from the circular pan.