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)
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.