Heat Transfer in a Square Duct

[ismith3636]

I am trying to figure out how to model heat transfer in a square duct. Specifically, this is a honeycomb of channels within a duct of flowing hot air. The flow through the channels is laminar, and the entire mass of the honeycomb is heating up from the hot air flow.

Any suggestions on where to start? Initially I was thinking of just using the heat capacity of the material. However, I think the answer really depends on conductive and convective heat transfer. Since the honeycomb is heating up, it's transient heat transfer. However, with an undergraduate understanding of heat transfer mechanics, I'm having trouble coming up with the equations of non-steady state heat transfer.

Thank you in advance for the help!

 

[IRstuff]

Are you wanting the transient, or the steady state? What are you trying to analyze, the temperature of the honeycomb, or something that's attached to the honeycomb?

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[ismith3636]

It's a honeycomb structure of length L in a turbine exhaust pipe, so think of a catalytic converter on a car?

As the turbine is starting up, the exhaust temperature is changing. As this heated exhaust passes through the honeycomb, the honeycomb heats up. I would like to find the temperature of the honeycomb at different points in time.

I think that I can assume the T[sub]in[/sub] and T[sub]out[/sub] of the honeycomb structure are roughly equal. Additionally, the walls of the honeycomb structure are very thin, so I believe I can assume the T[sub]surface[/sub] is equal to the T[sub]bulk[/sub]

Thanks!

 

[srfish]

The ASHRAE Fundamentals Handbook has a whole chapter on duct design.

 

[IRstuff]

If the Biot number is <1, then it can be treated as a lumped thermal mass. If it's sufficient thin, the transient might be quite short

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[ismith3636]

Thanks IRstuff!

So to find the temperature change of the overall mass in that case, I'm going to use the lumped method to find the amount of heat transfer, and then use the heat capacity to calculate the temperature change of the honeycomb?

 

[racookpe1978]

You've got to start someplace with some approximations.

Then, look at the approximate answer you got. Decide if that is good enough (Hint: It probably won't be) then use the approx result to start your second and third iterations.

It will never be "exact" and at some point in time, the effort of the extra calculations (and the approximations you are making in each calculation) will not increase accuracy of the result. First, do the start and end points of the time interval.

 

[IRstuff]

You use the aggregate surface area, forced convection coefficient, and a mean temperature difference to calculate the average heat flow into the comb during the warming. Specific heat times the change in temperature required divided by the average heat flow results in time.

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