L.M.T.D. Correction factors

Estimation of the “true temperature difference” from the logarithmic mean temperature difference by applying a correction factor to allow for the departure from true counter-current flow:

ΔT m = Ft ΔT tm                          (eq – 1.10)

Where ΔT m = true temperature difference, the mean temperature difference for use in the design eq. 1.3.

Ft      = the temperature correction factor.

The correction factor is a function of the shell and tube fluid temperatures, the number of tube and shell passes. It is normally correlated as a function of two dimensionless temperature ratios:

R   = (T1 – T2)                (eq – 1.11)

(t2 – t1)

and

S   =  (t2 – t1)                (eq – 1.12)

(T1 – t1)

R is equal to the shell-side fluid flow-rate times the fluid mean specific heat; divided by the tube-side fluid flow-rate times the tube-side fluid specific heat.

S is a measure of the temperature efficiency of the exchanger.

For a 1 shell: 2 tube pass exchanges, the correction factor is given by:

Ft  =  .                       √(R2 + 1)  ln [(1 – S)/(1 – RS)]                      .      (eq  – 1.13)

(R – 1) ln [(2 – S (R + 1 – √(R2 + 1))/ (2 – S (R + 1 – √(R2 + 1))]

The derivation of equation 1.9 is for a 1 shell : 2 tube pass exchanger can be used for any exchanger with an even number of tube passes. Plots of the same can be seen in the books.