Shell diameter for ST-type exchanger equation

In summary, the speaker has discovered new information about ST-type exchangers and plans to use it to build a reactor. They had trouble finding an equation from Ludwig's writings but eventually found it in a different book. The equation can be found in "Applied Process Design for Chemical and Petrochemical Plants" under equation 10-2.
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TL;DR Summary
Formula for shell diameter.
Hello. I have figured out a few things about ST-type exchangers and I intend to build a reactor with this new knowledge. I have a rather... small problem.

So I searched for shell diameter correlations given the pitch and number of tubes and I found this from a writeup:
apparentlyfromludwig.png


Apparently, it's from Ludwig, but the writeup did not say where the equation is, exactly. I have been staring and scanning at Ludwig for five long hours now and I am unable to find this equation (lol, I swear my eye nerves are going to burst). Is someone familiar with this equation? Thank you.
 
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Nevermind, found it. Apparently it's in another Ludwig book. Applied Process Design for Chemical and Petrochemical Plants; eqn 10-2; for people who might need this.
 
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1. What is the equation for calculating the shell diameter for an ST-type exchanger?

The equation for calculating the shell diameter for an ST-type exchanger is: D = (Q / 0.22)^0.5, where D is the shell diameter in meters and Q is the heat duty in kW.

2. How do I determine the heat duty for an ST-type exchanger?

The heat duty for an ST-type exchanger can be determined by using the equation: Q = U x A x LMTD, where Q is the heat duty in kW, U is the overall heat transfer coefficient in W/m^2K, A is the heat transfer area in m^2, and LMTD is the log mean temperature difference in K.

3. What is the log mean temperature difference (LMTD) and how is it calculated?

The log mean temperature difference (LMTD) is a measure of the temperature difference between the hot and cold fluids in a heat exchanger. It is calculated using the equation: LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2), where ΔT1 is the temperature difference between the hot and cold fluids at the inlet and ΔT2 is the temperature difference at the outlet.

4. How does the overall heat transfer coefficient (U) affect the shell diameter for an ST-type exchanger?

The overall heat transfer coefficient (U) is a measure of the overall resistance to heat transfer in a heat exchanger. A higher U value means a smaller shell diameter is needed to achieve the desired heat duty, while a lower U value requires a larger shell diameter.

5. Are there any other factors that should be considered when calculating the shell diameter for an ST-type exchanger?

Yes, other factors that should be considered include the fluid properties, such as viscosity and thermal conductivity, as well as the design pressure and temperature of the exchanger. It is also important to consider any fouling or corrosion that may occur, as this can affect the overall heat transfer coefficient and therefore the required shell diameter.

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