How long to heat up a vessel? 1

[jrjones]

I am stretching my memory on heat transfer from university...but I am trying to figure out how long it would take to heat up a pressure vessel (the steel) to steady state.

The vessel is refractory lined and I have all the conductivities, surface films, etc. I know that I have to use the specific heat and density of the materials, but can't wrap my head around the set up of the equations.

The reason I want to do this?- I don't believe the output from a FEA heat transfer analysis and want to do a 1-D check to validate what the model is doing.

 

[MintJulep]

Heat in = heat out + heat stored.

 

[desertfox]

Hi jrjones

If your simply heating the steel up uniformly then you could use this for an estimate:-


Q= m*Cp*(T2-T1)

where m= mass of vessel
Q= heat input in joules
Cp= specific heat of steel

T1 & T2 =intial and final temperatures.

Of course you will lose heat while heating up through
convection, radiation and conduction which the above will not account for.
Once you know the heat input to go from T1 to T2 decide how
long it will take from the power of your heat source ie oven
or whatever your using to heat it

regards

desertfox

 

[jrjones]

Okay what I have is a reactor that is lined with 6.5 inches of refractory (dual layer), 2" 1-1/4 Cr shell, and external insulation of varying thicknesses. I want to figure out how long it will take for the system to get to steady state from an initial temperature of 70 F with a 800 F gas on the ID and an assumed external ambient temperature of 70 F.

thanks,

Ryan

 

[desertfox]

Hi jrjones

The problem is different to what I understood in the your first post.
You need a transient heat transfer to get the time to reach
steady state, by doing a transient heat transfer by conduction through the multi-layers and then heat transfer by convection to the surrounding atmosphere but sadly I can't relate it to time its years since I did any transient heat transfers.
I remember a book which might help "intoduction to heat transfer" by Frank P Incropera and David P DeWitt.

regards

desertfox

 

[IRstuff]

I'm not convinced that your 1-D model will agree or disagree with your FEA. Just consider that you're going to have to swag a net area, net thickness, net conductivity, convection coeff, emissivity, effective heat input, etc.

TTFN

FAQ731-376

 

[jrjones]

I was hoping a quick 1D approach would get me in the right order of magnitude. Was planning to use the infinite cylinder type approach...if that would work.

It has been a while for me with transient stuff as well!

 

[desertfox]

Hi jrjones

I found this free software you can download to do a transient conduction analysis:-

http://www.faculty.virginia.edu/ribando/modules/OneDTransient/index.htm

regards

desertfox

 

[magicme]

if you doubt the FEA results, possibly you should talk thru the boundary conditions you used (maybe over on the finite element forum?).

if you check the incroprera text recommended by desertfox, section 3.3 gives the overall U for a multilayered pipe.

after calculating U, you could probably get in the ballpark using this equation...

time = - {(m * Cp)/(U * A)} * ln {(Tx- Tf) / (Tx - Ti)}

m = mass of metal
Cp = specific heat (bulk metal)
A = internal surface area exposed to heat
Tx = hotside temperature (800F in this case ?)
Ti = intitial temperature (bulk metal, 70F ?)
Tf = final temperature (bulk metal)

this is a WAG (not even a SWAG ! ) ... so don't bet the farm on this.

regards,

magicme





------------------------------------
there's no place like gnome.

 

[magicme]

after more minutes of thought...

during the transient, the heat transfer out of the insulated metal wall would be much much less than the heat into the wall from the internal side.

possibly you can rationalize that all the heat transfer (only) during the transient is simply from the hot internals into the wall.

you might also be able to approximate that the conduction thru the metal layer of the wall is high, and the metal layer is at a uniform temperature at any instant.

then U simply equals the internal convection coefficient (from your FE model).... that is U = h .

i'd run that thru the equation above and see how it compares to your FEA, before making it any more complicated.

regards

------------------------------------
there's no place like gnome.