# Process dynamics modelling for heated tank, differential equations

#### maistral

I can't seem to model this properly. This isn't an assignment, I'm just curious how this will go, lol.
So I have this tank with an incoming feed stream with temperature Ti, and an output stream T. It has a jacket where q would be modified depending on the desired output stream T.

So I assembled this:

ρ*cp*vdT/dt = q + m*cp*(T-Ti)

I can't seem to assemble the differential equation required for q.

Thanks!

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#### Chestermiller

Mentor
I can't seem to model this properly. This isn't an assignment, I'm just curious how this will go, lol.
So I have this tank with an incoming feed stream with temperature Ti, and an output stream T. It has a jacket where q would be modified depending on the desired output stream T.

So I assembled this:

ρ*cp*vdT/dt = q + m*cp*(T-Ti)

I can't seem to assemble the differential equation required for q.

Thanks!
Hey maistral. Let me understand what you are trying to do. You are looking as a well-mixed CST. The inlet temperature may be a function of time, and you are trying to control the outlet temperature. You measure the outlet temperature as a function of time, and compare it to the desired set point. The question is, based on these measurements, what strategy do you use to control q to minimize the deviation from the desired set point. Correct?

Chet

#### maistral

Yes. That's what I'm after, and I can't seem to set the differential equations for it :|

#### Chestermiller

Mentor
Yes. That's what I'm after, and I can't seem to set the differential equations for it :|
You already have the differential equation. The only thing you are missing is how the heat flux is controlled to try to maintain the set point. For example, if it is a proportional controller, then q = k(Ts-T), where k is a constant of proportionality and Ts is the set point temperature.