Log Mean Temperature Difference
Effective average temperature gap driving heat across an exchanger.
Formula
Variables
Example
ΔT₁=40, ΔT₂=20: LMTD = 20/ln2 ≈ 28.9
How it works
In a heat exchanger, the temperature difference between the hot and cold streams usually changes from one end to the other, so a simple arithmetic average can misrepresent the true driving force for heat transfer. The log mean temperature difference (LMTD) is the mathematically correct average that comes from integrating the local temperature difference along the exchanger length under steady flow assumptions. It gives the single constant temperature gap that would transfer the same total heat as the real, varying profile.
When to use it
Use this formula when analyzing or sizing heat exchangers such as condensers, evaporators, shell-and-tube units, or plate exchangers. It is especially useful whenever the inlet and outlet temperatures of the two fluid streams are known and you need the effective temperature driving force for heat transfer calculations.
Worked example, step by step
Given: ΔT₁ = 75°C, ΔT₂ = 25°C Step 1: Substitute into the LMTD formula LMTD = (ΔT₁ - ΔT₂) / ln(ΔT₁ / ΔT₂) Step 2: Compute the numerator 75 - 25 = 50 Step 3: Compute the ratio inside the log 75 / 25 = 3 Step 4: Take the natural log ln(3) ≈ 1.0986 Step 5: Divide LMTD = 50 / 1.0986 ≈ 45.5°C Final answer: LMTD ≈ 45.5°C
Common mistakes to avoid
- Using log base 10 instead of the natural logarithm
- Swapping ΔT₁ and ΔT₂ without keeping the order consistent
- Using this formula when one temperature difference is zero or negative without checking the exchanger arrangement and sign convention
Did You Know?
LMTD is used because the temperature difference along a heat exchanger changes non-linearly.
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