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This is my first post here. I explain the big picture of my current circumstances, I am a software engineer currently making a platform for evaluating process equipment in plants. I do not really know the technical details since it is not my area of expertise and I apologize if this question does not make any sense.

Basically, the engineer who used to help me build this software found these formulas to calculate effectiveness of a shell and tube heat exchanger:

$$ Cmin = m_1*C_{p 1} $$

$$ Cmax = m_2*C_{p 2} $$

Then we'd have to choose which one of the two is the minimum and the maximum. Then we'd have to do this:

$$ C = \frac{Cmin}{Cmax} $$

However, the engineer said that when there is a phase change Cmax would be considered as infinity and therefore C would equal 0.

If C equals 0 then that would mean the formula that would be used for effectiveness would be the following:

$$ \epsilon = 1-e^{-NTU} $$

And NTU would be:

$$ NTU= \frac{U*A}{Cmin} $$

First of all, is this logic true? If not, what is the right logic? And how should I calculate Cmin in the NTU formula? And would this still be true even if there is phase change in both sides of the sell and tube exchanger?

Again, I'm sorry if I wasn't clear enough, this is not my area of expertise...

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  • $\begingroup$ It's just about input and output. Phase change just puts a huge step (up or down depending on which way you go) an already nonlinear energy vs temp and energy vs pressure curve. $\endgroup$
    – Abel
    Commented Nov 17, 2023 at 11:23
  • $\begingroup$ don't feel bad, we spend weeks on the concept in ME Thermo. You need to include the energy used per unit mass to change phases; if it partially changes then it's according to the percent that does. If it's 100% then it's all of it plus the new temp change of the new phase. $\endgroup$
    – Tiger Guy
    Commented Nov 17, 2023 at 14:06

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First of all, I feel sorry about that I did not see your question earlier.
Your reasoning is suitable for most cases, but since you are not a chemical or mechanical engineer we can forget about messy details and pointless scenarios.
Your inference that if \begin{equation} c=0 \end{equation} Then for all heat exchangers \begin{equation} \epsilon=1-e^{(-NTU)} \end{equation} is absolutely correct. Also you can calculate $C_{min}$ by comparing following two: \begin{equation} C_{hot}=\dot{\mathbf{m_{hot}}}*C_{p,hot}\\ C_{cold}=\dot{\mathbf{m_{cold}}}*C_{p,cold} \end{equation} Where $\dot{\mathbf{m_{cold}}}$ is mass flow rate of cold fluid and $\dot{\mathbf{m_{hot}}}$ is mass flow rate of hot fluid, notation is the same for specific heats. $C_{min}$ is the smaller one from $C_{hot}$ and $C_{cold}$. Mass flow rate can be calculated by many ways. For example one can calculate mass flow rate if cross sectional area, density of the fluid and velocity of fluid is known, by the formula for steady flow $\dot{\mathbf{m}}=\rho*v*A_{c}$.
The specific heats are obtained from tables for most cases, so you will not calculate them.
For the last question I have less to say. It's a troublesome question to develop a clear answer, for me. But I believe we would use some other techniques to analyse the situation with phase change in both sides, or we would divide the analysis of process in order to account for all physical phenomena respectively, or maybe we would at least add some extra terms for phase change. Also I think the answer of this question would be case-specific. Therefore it would be best for you to consult the engineer you work with.

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