Learning Forum

[kimjh12]

Hi, I have question about maxwell-stefan equations written in the fluent theory guide Fluent 2024 R2.

In chapter 7.1.1.3.2, there are definitions and equations related to Maxwell-Stefan equations. 

My question is the formula $M_{w,m}$ which is defined as $\sum_{i=1}^N\frac{Y_i}{M_{w,i}}$, where $Y_i$ is a mass fraction of $i$th species, and $M_{w,i}$ is a molecular weight of $i$th species.

Also, there is a remark related to the formula; 'a subscript used to define a mean molecular weight in the mixture'.

I wonder if the expression is defined properly.

In my thought, $M_{w,m}$ should be inverse of $\sum_{i=1}^N\frac{Y_i}{M_{w,i}}$. 

The proof is as follows. By using the related quantities between mass fraction $Y_i$ and mole fraction $X_i$, $\sum_{i=1}^N\frac{Y_i}{M_{w,i}}$ is equal to $\sum_{i=1}^N\frac{X_iM_{w,i}}{\sum_{j=1}^N X_jM_{w,j}}\frac{1}{M_{w,i}}$.

Since $\sum_{i=1}^N X_i=1$ by definition of the mole fraction, we can further simplify the expression. As a result, $\sum_{i=1}^N\frac{Y_i}{M_{w,i}}$ is equal to $\frac{1}{\sum_{j=1}^N\frac{X_j}{M_{w,j}}}$, which is inverse of the mean molecular weight in the mixture. 

Thank you. 

[Ahmed Hussien]

Your logic seems correct. I will further investigate and let you know. 

[Ahmed Hussien]

 

I checked this and you are right. There is a typo in the documentation and it will be fixed in the next release. However, the implementation in the code is correct. It should not affect the solution in your case.