batch heat transfer question 1

[hollerg]

Kern's book on Heat Transfer shows computing the time to cool a tank using an external cooler, but it does not account for a concurrent heat source.

I have seen, but can't recall an alternative method (Max Jakob? or Carslaw and Jaeger?) which accounts for a constant energy load added (reaction or mechanical) during the cool down. If someone would share the method I would be most grateful.

Or how would one modify the kern computation to accomplish the same thing?

Thank you for your time

 

[speco]

Hollerg,

I don't know if there is a simple answer to this problem. I have encountered similar problems in the past, where I needed to generate a complex cooling curve with an additional heat source. The basic formula for batch cooling is not complicated. It normally uses a fixed batch mass, and uses a simple natural log function of the temperatures to calculate the cooling time.

My solution for the complex cooling curve was to write a BASIC program to solve calculate the time for each temperature increment (an input variable). It adds to the heat load per increment based on the time, then adjusts the effective mass of the batch to account for the additional heat. Then it reiterates until it converges within a given percent. Once that's done, the calculation is the same as the normal batch cooling time calculation.

I would imagine that you could do the same with an Excell spreadsheet if you are good with Excell. BASIC is my weapon of choice for such problems.

Regards,

SPECO (

http://www.stoneprocess.com)

 

[FredRosse]

I evaluate similar thermal transients all the time in EXCEL. I often use time variable heat input and temperature variable heat transfer coefficients, this is difficult with classical solutions, easy with a PC plus EXCEL (or FORTRAN if you are a real old engineer).

In EXCEL the problem is setup with a single row of data performing an energy balance for the thermal mass (the batch) over a short time step (dt). The first column is the time step number (integers), the second is the problem time (= step number * dt), the third column is the batch mass temperature, and following columns contain computations for all of the energy inputs/outputs. The basic energy balance sums all energy inputs and outputs during the time step, then the change in the batch temperature (dT)is calculated, (dT = energy flow rate * dt / batch mass / batch specific heat). Time steps must be small enough that the dT value is small. On the following row, the batch temperature is updated (batch temp = previous batch temp + dT) and the energy balance is computed again, giving a new dT, etc.

In some cases, heat transfer to ambient is relevant, and the ambient temperature is also time variable, in which case each row also has an ambient temperature entry.

If you would like I could e-mail an example.

 

[IRstuff]

You could just post it on the Engineering.com upload site

TTFN

FAQ731-376