Unsteady state heat-transfer 1

[Timewrap]

Hi All,

Here is a little problem on which I need your help.

This is a batch process.
A tank intially start with a temperature of -90 deg C and had to be heated up to -80 deg C in two hours. I'm considering a heat transfer fluid circulating through the vessel jacket at about 35 deg C, the return H-T fluid gets cooled up to 30 deg C and heated in a heater to compensate for the heat loss.

I can calculate the amount of the Heat transfer fluid required based on the heat load and physical properties.

I want to calculate the exact time required to be able to heat up the tank contents from -90 deg C to -80 deg C. Since it is a batch process, the LMTD gets lower and lower as the tank gets heated.

Assume there is a mixer in the tank to provide turbulance.

Your comments are appreciated.

Thanks in advance,

Timewrap.

 

[Latexman]

Open up your Perry's dude. This diff. eq. has an exact solution and it's in there. In my 6th Ed. "Batch Operations: Heating and Cooling of Vessels" starts on page 10-38. If you don't have Perry's, it's also in Kern's "Process Heat Transfer".

Good luck,
Latexman