Temperature profile through a Steel cylinder vs time

[yukipilas]

I am having trouble developing an algorithm to solve this problem required for a warming up procedure. I have a steel cylinder (hollow) which is being heated up with a gas from the outside and I wish to know the temperature distribution of the gas as it cools down and from the steel cylinder as its being heated up, assumption is a one dimensional heat transfer (vertically) , axial heat transfer is considered uniform.
The process conditions are that the gas (70t/h) cp: 2,15 kj/kg*k heats up the cylinder from 250°c to 350 with an initial wall temperature (tw) of 240°c at a rate of 15°c /h. I have already calculated the required heat to heat up my cylinder (M.cp.dt) 800kw, and selected a heat transfer coefficient from the literature. The approach I’ve been trying to take is using the equation Q=UA(tw-tgas) and dividing the area (cylinder) in 40 sections, therefore 40 different heat transfer areas. I also multiplied my equation by Dt giving me 1 point in time.
This is apparently a quasi-transient heat transfer problem. My problem is:
- If i divide my cylinder in 40 different sections i wish to calculate the temperature profile and therefore the heat transfer through each section, with the formula Q=UA(Tw-tgas) I cannot do this, I have 2 unknowns which are tgasout (which is the temperature leaving each section) and twout (temperature of the cylinder leaving each section)

I would really appreciate any suggestions on how to approach this

best regards,

yukipilas

 

[racookpe1978]

1. What dimensions?
2. What is the direction of the centerline of the cylinder? Vertical or horizontal?
3. What is the direction of the (350 C ???) gas flow, and how fast is it flowing, and
4. What is the temperature of whatever wall or surface is retaining the gas AWAY from the cylinder?
5. Is the cylinder at a uniform 240 deg C when the gas flow starts?

 

[yukipilas]

Thank you for your questions,

the cylinder is in vertical position (20m long) with an initial temperature of 240°C, imagine a shell and tube heat exchanger where the gas flow enters (initial temperature 250°C) through the top (shellside) flowing downward heating up the outside surface of hollow tubes, remember the tubes are hollow therefore no heat transfer from inside to the outside of the tubes is considered (no cooling medium inside the tubes). Number of tubes n=300. The gas velocity I do not have but the flow rate is 70t/h. To question 4 i did not understand what did you mean, question 5 yes 240 °C is the initial temperature of the cylinder.

to simplify the problem we could also consider heating the surface of a wall with a gas at a certain time range. The gas would flow vertically along the wall losing its heat as it leaves it, the heat would distribute itself on the wall and produce a temperature gradient,
- at t=x what is the temperature on the different points of the wall?

i hope this clears up better the idea?

The Ti represent the temperatures at eeach section of the wall at time =X
time =x Wall
Tgas> I I
T1 =?I I
T2 =?I I
T3 =?I I
T4 =?I I
T5 =?I I
I I Tgasout=?
Best regards,

 

[yukipilas]

Sry sketch did not turn out well in the post, the I´s are supposed to be the wall

 

[racookpe1978]

The reason I asked nbr 4 (what is the diameter and temperature profile of the very hot "outside tube" holding the gas flowing around your steel pipe) is that radiation from that outside tube through the gas to the steel pipe is going to be a significant heating force on the steel pipe being heated by the gas by convection and conduction directly. you cannot ignore it if you think all of the heat energy from the gas is going "inside" to the steel pipe.

At these gas speeds (1.16 tons per minute flowing from top to bottom) natural convection is, of course, at least not any concern at all. You will certainly be turbulent! Gas pressure and the gas properties at THAT pressure and temperature (at 250, at 350, and at appropriate values in between!) DO matter. What are you using for those values?

How are you interpolating (or are you linearly extrapolating or using some sort of properties lookup table) between 250 and 350?

thoroughly insulating the outside of the outer tube will help reduce the "wasted" heat lost cooling of the gas from top to bottom, but not eliminate it by any means.

 

[yukipilas]

I am taking the fluid properties out of Aspen, i am not extrapolating.

I would appreciate any recommendations on the procedure to calculate the temperature distribution across a cylinder or wall

 

[prex]

Please post a sketch of your setup.
I don't understand what you mean by 'axial heat transfer is considered uniform' and 'at a rate of 15°c /h'.
What I guess is that you want to know the axial temperature distribution in the cylinder and how this changes over time. Depending on the thickness of the tube this could really be a quasi static problem, where each state of temperature in time is the static temperature distribution corresponding to the gas inlet temperature at the same instant. Whether you can treat this as quasi static depends also on what kind of estimate you want and on the goal of the calculation. Anyway a static calculation for a given gas temperature would be the best point to start with.
This is quite different from the temperature distribution in a sphere that you pointed out in another thread. Also what I don't understand is how you can determine a heat transfer coefficient without knowing the velocity of the gas flow.

prex
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