Determining the flow on the counter-flow heat exchanger

[_kon]

I am trying to design a control system for a simple heating system (I am not en expert in this area) and I want to set the mass flow on both sides of the counter-flow heat exchanger at a given moment (in a simplified way for now). The cold water stream has temperature T[sub]1[/sub] and the mass flow is m[sub]1[/sub]. I want to heat it to T[sub]final[/sub] temperature. The warm water stream has a temperature T[sub]2[/sub]>T[sub]final[/sub] and the question is what should be the mass flow of the warm stream m[sub]2[/sub]? I want to assume (for now) an ideal exchanger, which means that the overall heat transfer coeffisient OHTC can be as big as I want. For now, I used a simple equation:
m[sub]1[/sub]*cp_water*(T[sub]final[/sub]-T[sub]1[/sub]) = m[sub]2[/sub]*cp_water*(T[sub]2[/sub]-T[sub]x[/sub])

I have two unknowns: m[sub]2[/sub] and T[sub]x[/sub]. I assumed that T[sub]x[/sub] can go down to T[sub]1[/sub], hence I can estimate (T[sub]x_min[/sub] = T[sub]1[/sub]) that:
m1*(T[sub]final[/sub] - T[sub]1[/sub])<= m[sub]2[/sub](T[sub]2[/sub]-T[sub]1[/sub])
hence:
m[sub]2[/sub] >= m[sub]1[/sub]*(T[sub]final[/sub]-T[sub]1[/sub])/(T[sub]2[/sub]-T[sub]1[/sub])

However, this is only an estimate (and I don't know if it is corrent)and does not take into account the flows in the exchanger.
Could someone help me (give me the right equation) or point me to a source that would allow me to correctly calculate m[sub]2[/sub]?

 

[EdStainless]

Do you have a specific HX that you are working with?
Get the HEI (Heat Exchanger Institute) design manual for HX and use the sizing/rating equations there.

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P.E. Metallurgy, consulting work welcomed

 

[georgeverghese]

If you have a theoretical pure countercurrent HX with infinite exchange area and /or infinite U, then your min value for m2 is correct.

 

[_kon]

thank you for your answers!

@EdStainless

Do you mean the book:
"STANDARDS FOR SHELL AND TUBE HEAT EXCHANGERS, 5TH EDITION" from:

https://www.heatexchange.org/products/hei-standards

?

@georgeverghese

I'm glad my estimates are right. Where would you recommend looking to be able to calculate the actual case for a concentric tube architecture exchanger?

 

[georgeverghese]

Think you mean a double pipe exchanger, which is a pipe inside a pipe HX. These are pure countercurrent units. Thermal design of these is well covered in DQ Kern's Process Heat Transfer textbook.
Can you describe your service requirements ? Flows, max operating pressures, inlet / exit temperatures, service fluid type, total thermal duty, potential for fouling, corrosivity all play a role in HX selection.

 

[EdStainless]

Kern is a great source for these HX.
You can also find some manufactures web sites with sizing information
These are commonly used in sanitary service such as pasteurizers.
They are usually built serpentine because of how long they get.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed