2 replies to this topic

[peet_dk]

Hi
I am about to make some calculations for a fermenter which have to be cooled down, with internal coils and dimple jackets.

I have found the correlations for the convective heat transfers. But how do I find the overall heat transfer coefficient? Do I have to find a U-value for both the jacket and coils, or only one U-value?

Will it look like this?

1/U_ij*A_i = 1/h_i*A_i + 1/h_j*A_j + 1/h_fc*A_f

1/U_ic*A_i = 1/h_i*A_i + delta_x/k + 1/h_c*A_c

And then calculate Q_ij and Q_ic?

Where:

h_i = heat transfer coefficient inside the fermenter
h_j = heat transfer coefficient inside the dimple jacket.
h_c = heat transfer coefficient inside the coils
h_fc = free convection coefficient.

A_j = Dimple jacket plate area.
A_c = Coil surface area.
A_f = Fermenter area
A_i = A_j + A_c

delta_x = thickness of pipe in coil.
k_c = cond. pipe material.

And then a question about the Delta_T:
I found this way to calculate the Delta_T in a book:

Delta_T = (2*T_fermenter-(T_inlet +T_outlet)) / (2)

But another place I can see they calculate it as:

Delta_T = T_fermenter – T_j.mean

Which way is correct when I want to use Q = U * A * Delta_T?

[ankur2061]

Peek,

Suggest you take a look at the following section in the book "Handbook of Chemical Engineering Calculations" 3rd Edition by Nicholas P.Chopey.

Section 7.16; the section gives an equation for outside heat transfer coefficient (h_outside)from coils in agitated vessels

For inside heat transfer coefficient from a coil you can use the Sieder-Tate equation as given in D. Q. Kerns book by equation 6.1 for laminar flow and equation 6.2 for turbulent flow. For helical coils the heat transfer coefficient will require correction as given on Page 721 of D. Q. Kerns book. This may be designated as h_{inside,corrected}.

Next you need to calculate the clean overall HTC by:

1/U_clean = 1/h_outside + 1/h_{inside,corrected}

The next step involves calculating the Dirty HTC

U_dirty = U_clean / (1 + U_clean*(R_di + R_do))

where

R_di = Inside fouling factor
R_do = Outside fouling factor

Once you have calculated the Udirty, you can use this value to calculate the heat transfer area. If your application is a "agitated batch cooling", considering a "coil-in-tank, non-isothermal medium" you can use equation 18.11 in D.Q. Kern to calculate your heat transfer area.

It is important to note that heat transfer from dimpled jackets may have a different methodolgy for calculating HTC and the method only describes batch cooling for coil and an ordinary jacket

The whole calculation process is tedious but then so is your assignment. Perform your calculation steps systematically and you will not miss. Good Luck!

Regards,
Ankur.

[peet_dk]

hi Ankur, thanks for the input.

I use this one inside the dimple jacket: http://www.cheresour...l_design3.shtml (have found the CEP magazine)

Inside the coils, I found one in Incropera's Introduction To Heat Transfer (Gnielinski's eq)

And inside the fermenter I found on in Basic Biotechnology by Colin Ratledge and Bjørn Kristiansen, the renoyld number is very high, I will look at the one you posted, to see if the %-error is lower for turbulent flow.

Anyway, thats not the problem.

The problem is the overall heat transfer coefficient, U.

The one you use:

1/U_clean = 1/h_outside + 1/h_{inside,corrected}

Do not take the dimple jacket into consideration, or do it?