# Crossflow HX tube and fin, derive Tout hot side as a function of mdot hot side in

## Apparatus:

Crossflow Tube and fin HX. (liquid-to-air Intercooler),

Hot Side: Tube side, gas flowing internally

Cold Side: fin side, water flowing in crossflow

## Goal:

Generate an environment in "OpenAI gym" where the agents actions:

are moving the valve (1),(0) fully open, fully closed on the inlet stream.

Observation:

outflow temperature

## Problem:

Generate a formula for the change in

$$\Delta{\dot V in} = \Delta{Tout}$$

where:

$$\Delta{\dot V in}$$ is the flow rate inside the tube &

$$\Delta{Tout}$$ is the temperature out of the tube.

Its understood that this is one of the most common process control problems: feedback or feedforward valve that controls inlet flowrate to regulate outlet temperature. Temperature is sensed by a thermocouple.

F-F = 0

## Energy balance:

$$V \cdot \rho\cdot c_p \cdot \frac{dT_{out}}{dt} = F \cdot \rho \cdot c_p \cdot T_{out} - F \cdot \rho \cdot c_p \cdot T_{in}$$ This can be rearranged to make $$T(out)=f(T(in))$$ Its further understood that the change in Tin can be proportional to the pressure or height change at the valve.

Im looking for a solution that ties this whole process together. Better yet if someone knows a textbook (process control, instrumentation engineering, Linear models etc.) where this problem similar to this is solved and the logic is stepped out would be even better. Thank you all for your time.

• Shows no effort towards a solution and looks like homework. Any decent text book covers this, my favorite is Heat Transfer by Simonson. – Solar Mike Aug 24 '20 at 10:58
• My apologies I am electronics embedded engineering student doing a thesis on using RL instead of PID. I really have little process knowledge background and any assistance in direction of a textbook showing the solving of this problem would be of great benefit and appreciation. My apologies for lack of knowledge in this field, any guidance would be appreciated. – Lone_Dingo Aug 24 '20 at 11:03
• Thank you for your comment Solar Mike, I have a copy of that textbook could you please guide me to the chapter you are referring to? – Lone_Dingo Aug 24 '20 at 11:32
• I improved the formatting of your energy balance with MathJax, please check if the equation is correct how I wrote it or change it otherwise. Also, please explain your problem a bit more (Section apparatus is atm only 2 half-sentences) and most important, add info on what you already figured out and where exactly you still struggle. Then you can get precise answers that help you at the points where you need help. – OpticalResonator Aug 24 '20 at 11:39

First, find the energy balance - basically mass flow x thermal capacity x delta T is the same on both sides.

Edit to add There's an error in your energy balance: on the left hand side it's simply $$\Delta T$$, not the derivative. Also make sure to use the correct values for $$c$$ as you have two different media.

Then, find something like this for your valve: Assuming a constant pressure, this allows you to write the mass flow on one side as a function of the stem position of the valve - the value you are actually controlling. Then you should be set.

Image source is this by Spirax Arco, might be worthwhile to read anyway when you are dealing with HX.

• Thank you @mart, this link was most helpful. still trying to link the Temp out with flow in but I will study this link in detail today, thanks again. – Lone_Dingo Aug 24 '20 at 20:44
• @Lone_Dingo if in doubt draw a P&ID sketch of your setup including the valve – mart Aug 25 '20 at 6:02