Time to heat a packed bed

[dd311]

Hello,

I'm trying to determine the center line temperature of a fixed bed reactor over time during heat up. The reactor has a 6" diameter and will be heated externally by electric heaters to 700C. Two heaters are currently being considered, one providing a heat flux up to 4 W/in^2 and another up to 10 W/in^2. The bed is filled with silica sand (k=0.2 W/mK, Cp=830 J/kgK, density=1400 kg/m^3). During heat up there will be no gas flowing through the reactor, thus I expect nearly all the heat transfer to be via conduction and radiation. Therefore, I would also assume that the heaters can maintain a constant wall temperature, since the conduction into the sand is likely the limiting factor (very large Biot number). I would like to plot the centerline temperature of the reactor versus time for the different heat flux cases. Then I would also like to see how the centerline temperature versus time changes with a small purge gas flow through the sand. Does anyone have any good examples of how to calculate this?

Any help is much appreciated!

Thank you!

 

[amorrison]

I would post this question to - Chemical engineering other topics.
I think they do this all the time.

 

[Compositepro]

I can't imagine why you would use such an inappropriate way to heat a packed bed. If you have lots of time you can preheat that way, but then the purge gas you mention will cool the center while heat is applied only to the the OD. Heat the purge gas to heat the bed.

 

[dd311]

Yes, I agree this is not a very good way to heat. The application is actually somewhat different than I described, however this is the best way to think of it in simpler terms. Due to the nature of the actual setup, we may. It be able to use a hot purge gas to help heat, so I would like to get a more conservative estimate by calculating conduction only.

 

[dd311]

Sorry about the last post. Autocorrect on my phone got me. It should read:

Due to the nature of the actual setup, we may not be able to use a hot purge gas to help heat, so I would like to get a more conservative estimate by calculating conduction only.

I'd imagine radiation will also be a dominate mode of heat transfer at up to 700C, however I'm not sure how to go about estimating radiation for sand particle to particle heating. The sand will all be around 500 um diameter.

I appreciate any help!

Thanks again!