Numerical Solution
Numerical Example of a system with Water Vapor (A) diffusing through Nitrogen. (T0=40 F, Td=90, xAd=0.025) based on Example 18.5-1: Simultaneous Heat and Mass Transfer
The goals- to create equations for the Temperature and Concentration profiles & to determine the ratio of (heat tranfer alone) : (heat transfer with mass transfer)
This shows that the flux NAz(z) is only dependant on delta (the thickness of the layer). We can then justify using only a variable, rather than a function, for the value of NAz for the remainder of the calculations. The following equation is one that shows the chosen concentration profile (xA(z)) works according to our analytic approach.
This equation is proven because the imaginary term (2nd term, LHS) is negligible (magnitue 10^(-8)). Just in case you still don't belive the concentration profile xA(z), the following equation will work if we have chosen satisfactory xA(z) and NAz(z).
Here again we see that the imaginary term (2nd term, LHS) is negligible(10^(-7)) and remaining terms are identical. Now we must develop expressions for the temperature profile.
Now that we have an equation for the temperature profile, lets verify that it works.
So it works appropriately. These equations T(z) and xA(z) can be plotted to show the concentration profiles. The final step in solving this problem is to investigate the relationship between heat and mass transfer when they occur simultaneously. We have already seen that Maas flux is not affected by simultaneous heat transfer, but is heat transfer affected by simultaneous mass transfer? We will do this by solving for the ratio of (heat transfer alone) : (heat transfer with mass transfer). The formula for the ratio is given in the section regarding the analytical derivation of the temperature profiles.
So the effect of the mass transfer on the heat transfer is about 10%, relatively significant in this case.
Go back to the Main Page or the analytical solution of the Concentration Profiles or the Temperature Profiles