Average temperature of a sphere

[petersjohn]

Hello;

I made axisymmetric calculations and, among other things, found the temperature distribution in a sphere after an hour of heating. I need to estimate the average temperature of the entire sphere, how can I do it based on the node's temperature?

With much appreciation,
Sincerely,

John

 

[cbrn]

Hi,
why not get the nodal results "TEMP" over all the nodes, and average them? ;-)
OK, I understand: you have unevenly-spaced nodes so that the arithmetic average does not necessarily reflects the "true" average temperature of the body. The simplest workaround, if you have 2D-axisymmetric model, is to build a mapped mesh with a regular pattern of nodes, evenly spaced. You can enhance the mesh regularity by imposing a certain number of divisions on the bounding lines of the quarter-of-circle. Please refer to the Help on the rules to follow in order to map-mesh a 3-sided area.

Regards

 

[Struct71]

How about getting first the average temperature of each element by analyticallly averaging nodal temperatures.

Then calculating average volume temperature by sum(element temps x element volumes)/total volume

This way the locations with smaller elements and higher nodal density will have a smaller impact on the average temperature.

 

[Struct71]

Made this routine in a few minutes.
It is not tested as I have no thermal model at hand.
Might need a little tweeking.


esel, [...] !select relevant elements

cm,allelements,elem
eee=elnext(0)
vvv=0

*dowhile,eee
esel,s,,,eee
nsle
teltemp=0
nnn=ndnext(0)

*dowhile,nnn
teltemp=teltemp+temp(nnn)
nnn=ndnext(nnn)
*enddo

*get,nonodes,node,0,count
*get,vv,elem,nnn,volume

aveltemp=teltemp/nonodes
tovoltemp=aveltemp*vv
vvv=vvv+vv

esel,s,,,allelelments
eee=elnext(eee)
*enddo

avtemp=tovoltemp/vvv !here is your average body temp

 

[petersjohn]

Thank you very much.

cbrn: that's what I tried first, but the answer I've got doesn't look right

eelco71: I'll try to implement this today.

Sincerely,

John

 

[meshparts]

Hello,

I think, the average temperature is the temperature of the sphere after a very long time in an adiabatic state of the sphere. In this case the sphere will aim an uniform temperature, and this will be the average temperature. Of course you will have to simulate this for a few steps more, but it would be a very good way to check the accuracy of other methods discussed here.

Regards
Alex

 

[Struct71]

Indeed Alex,
and should also be equal to time*power*mass*C.

I just realised: a transient thermo-elastic-plastic sphere,
with temperature dependant C,KXX,ALPX,EX,KINH, very intresting.

Grab every opertunity you have to check your results.