LMTD calculator (log mean temperature difference)
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Result
For a shell-and-tube exchanger with several passes, multiply the counterflow LMTD by the correction factor F from the exchanger charts.
Calculate the log mean temperature difference (LMTD) of a heat exchanger from the inlet and outlet temperatures of the hot and cold fluids, for counterflow or parallel flow. With the overall heat transfer coefficient U you can also find the heat duty from the area, or the area needed for a given duty.
Step-by-step solution
Temperature differences at the two ends
LMTD
Heat duty
Key formulas
- Heat duty
- Q = U·A·ΔTlm
- Log mean temperature difference
- ΔTlm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2)
- Stream balance
- Q = ṁcp(Tin − Tout)
How to calculate the LMTD
- Find the temperature difference at each end of the exchanger. Counterflow: ΔT₁ = T_h,in − T_c,out and ΔT₂ = T_h,out − T_c,in. Parallel flow: ΔT₁ = T_h,in − T_c,in and ΔT₂ = T_h,out − T_c,out.
- LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂). If ΔT₁ = ΔT₂, the LMTD equals that difference.
- Heat duty: Q = U·A·LMTD, with U in W/(m²·K) and A in m².
- Required area: A = Q/(U·LMTD).
Questions and answers
Why is counterflow better than parallel flow?
For the same four temperatures the counterflow LMTD is larger, so less area is needed. Counterflow also allows the cold outlet to become hotter than the hot outlet, which parallel flow can never do.
Why use a logarithmic mean instead of the average?
The temperature difference along the exchanger changes exponentially, not linearly. The arithmetic mean overestimates the driving force; it is only close when ΔT₁ and ΔT₂ are similar.
What about shell-and-tube exchangers with several passes?
Compute the counterflow LMTD and multiply it by the correction factor F, read from charts using the dimensionless ratios P and R. F is 1 for pure counterflow and below 1 otherwise.
Can I use °C instead of K?
Yes. Only temperature differences enter the formula, and a difference of 1 °C equals 1 K.
Practise it yourself
Practise Heat exchangers (LMTD)
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.