Calculating rate of temp increase in bulk fluid.

[wguidry]

Hello. I am trying to determine a method to calculate the rate of temperature increase in a storage sphere.

The storage sphere receives a 'hot' feed which is circulated through a chiller. We are considering a spare chiller that has a lower capacity than the existing chiller. So Qin > Qout and there will be some accumulation of Q in the sphere. I would like to know how I can calculate the rate dT/dt of the bulk fluid inside the sphere assuming a constant volume.

 

[ardilesd]

Assuming that the avergare temperature in the tank is the Output temperature, the energy Balance for the Tank:
dT
M Cp ---- = F . Cp . (Tin - T )
dt

Energy Balance for the Chiller
Q = U.A.DT = F.Cp.(Tin - T)
where DT is a function (logarithmic) of T.

There is an analitycal solution for the whole problem.
It is really challenging to reach it, but, if you are in a hurry, go to Kern, Heat trasnfer Processes, Chapter 18.
Regards

 

[wguidry]

Thanks ardilesd. I solved it analytically. The reference to Kern was helpful.

Cheers.