Mixed gas flow through a uniform pipe 2

[Resistom]

Hello!

I have also started working in an engineering company.
I was given the task to solve the following problem:

Mixed gas (mainly CO, CO2, H2, N2) is flowing through a uniform steal pipe, the gas pressure is approximately 1 mbar (the gas is being pumped out to create vacum conditions). The initial temp of the gas is 1000c. The ambient temp is assumed to be constant in ~40c.
I need to find out the temperature of the gas in the pipe as the factor of its length. The pipe can be horizontal, vertical and may contain elbows.

How to begin solving this problem?
Should I take heat convection, radiation and conduction in account?
Please give me some clues.

 

[Latexman]

Resistom,

I am having trouble picturing your process in my mind. You say it is initially at 1000 C. What is the initial pressure? Please explain your process from the beginning to the end. If it is a continuous process, it'll be the beginning step to the end step. If it is a batch process, it'll be the beginning time to the end time. Be sure to tell us the T and P at the beginning and at each step/time you know. What are the concentrations of each gas in the mixture?

When you come to the part of the process that has the pipe that you have to find the temperature of the gas in the pipe as the factor of its length, be as detailed as possible. What is just before this pipe? Is it insulated or bare? What is the T and P here just before the pipe? How is it connected to the pipe? Is the pipe insulated or bare? How long is the pipe? What is the diameter and schedule or internal diameter? What is the flow rate of the gas mixture?

Good luck,
Latexman

 

[Resistom]

Latexman- thank you very much for the respond.
The pipe is actually a duct, leading gas from an almost vacuum conditioned vasal (1mbar), where a metal melt is. to the atmosphere, using a pump.
The pump is connected to the pipe through a filter that functions in temperatures below 250c.
The solution must be generic, while the initial temperature of the gas is known, and the initial pressure is known. Nevertheless, the initial pressure, is assumed to be around 1mbar, as said, and the initial temperature is 1000c.
The gases relations are subject to change as function of the melt, but for practical reasons, it is assumed to have about 50% CO and 50% from the other gases.
The length of the pipe is the factor which has to be found-
what is the temperature of the gas in the pipe, just next to the pump, after x meters of vertical/horizontal/diagonal/elbowed pipe system.
The pipe is bare, not insulated. The ambient temp is reffered as constant at 40c.
There're of course pressure losses in the pipe. We already have an excel program to calculate them, but it counts an estimated temperature decreasing graph. The pressure in the pump is considered to be constant as well, while the pressure loses may be taken in account, while we have already an input about them.

Thanks in advance, hope I made it clear.

 

[BigInch]

The generic solution of T(x) is a logrithmic function of (Temp_gas - T_pipe_wall) with length and flowrate, pipe diameter. This is a very basic problem well discussed in any thermo text, complicated from the typical examples only by the actual mixture of your gases. Normally the textbook problems are given and solved with only one liquid or gas in the pipe.

Suggest you find a copy of one or all of the following,

REA's Problem Solvers on "Heat Transfer",
"Heat Transfer", J.P. Holman,
"Principles of Heat Transfer", Keith & Bohn

where you will find many exact examples (single fluid) of your problem worked out in great detail. You will only need to calculate the heat transfer properties of your gas mixture. Since that is the only difference from a typical problem of this type found in any thermo textbook, do you need a tip on how to calculate the properties of your gas mixture, or are you expecting somebody to give you a magic equation?

Going the Big Inch!

http://virtualpipeline.spaces.msn.com

 

[ReactingFlows]

While BigInch's observation is correct for moderate temperatures and adiabatic conditions, the distribution of temperature of the gas T(x) along the duct will be affected by two others things at such high temperatures: (1) radiation heat losses, (2) heat losses through the conducting walls.

There is further complication if the gases are reacting? In that case you may need to consider chemical kinetics and heat of reactions etc. (But I suspect that at such low pressures as 1 mBar reaction rates may be negligible in at such high temperatures?)

This problem interests me, and I will be glad to give futher advice where I can.


The effect of the tortuosity of the pipes is difficult problem, and simulations may have to be carried out.

ReactingFluids
London

 

[Resistom]

ReactingFluids, thank you for your reaction!
Neglecting the reaction of the gases, where and how should I start looking for an initial solution? I don't have access to the suggested books, but if you say that one has a solution to my problem, I might consider ordering it (or the company would).
I am a little bit confused from all the information and the references I have!

Resistom,
Essen, Germany.

 

[Resistom]

BTW,

The Reynolds number I have calculated suggest that this flow is rather Turbulent.

I found a solution which combines radiation and convection:
HANDBOOK of Heat Transfer Fundamentals, Ronsenow, Hartnett, Ganic.
Page 14-116:

"...The coupling between radiation and convection is weak enough that the two effects can be added, or if the coupling isn't weak, radiation dominates. In either eventan engineering correlation was found to be:

Nu= Nuc+Nur
"

and so on...
but the solution is given in a way of a column, and I don't understand what to do with it.

They refer to one article that seem to have a numeri solution, maybe I can look for that article, but I am not sure if it is the right thing I am looking for...
"D.K. Edwards, Radiation Heat Transfer Notes, Hemisphere, Washington, 1981."

Resistom,
Essen, German.

 

[Resistom]

What about this one I found:

Combined Convective and Radiative Heat Transfer in Turbulent Tube Flow

C. K. Krishnaprakas; K. Badari Narayana; Pradip Dutta
Journal of Thermophysics and Heat Transfer 1999
0887-8722 vol.13 no.3 (390-394)

This can be ordered from the internet.

Plus I am not looking for radition of the gas! just the radiation of the pipe, the gasses are assumed to be non-radiating.

 

[BigInch]

Do the conductive heat transfer first by itself. Superimpose the radiation heat loss to it, if its significant.

Going the Big Inch!

http://virtualpipeline.spaces.msn.com

 

[sailoday28]

The text book The Dynamics and Thermodynamics of Compressible Flow or similar wording by ASChER SHAPIRO will give excellent approaches to solving your problem.
As a first approach I would neglect effects of elevation except when calculating local heat transfer coefficients.

Regards