How to use the LMTD Heat Exchanger Calculator
- 1. Pick the arrangementCounter, parallel, 1-shell-pass shell and tube, or enter F from a chart.
- 2. Enter temperaturesInlets and outlets. Leave one outlet unknown and give both flow rates.
- 3. Get the areaHeat duty, LMTD, F and the area A = Q / (U·F·LMTD).
LMTD method
The heat duty is Q = U·A·F·ΔTlm, where the log mean temperature difference is ΔTlm = (ΔT1 − ΔT2) / ln(ΔT1/ΔT2).
- Counter flow: ΔT1 = Th,in − Tc,out and ΔT2 = Th,out − Tc,in.
- Parallel flow: ΔT1 = Th,in − Tc,in and ΔT2 = Th,out − Tc,out.
- Energy balance: Q = ṁh·cph·(Th,in − Th,out) = ṁc·cpc·(Tc,out − Tc,in).
- Shell and tube or cross flow: multiply by the correction factor F (F = 1 for pure counter flow). The tool works out F for one shell pass from P and R.
Use the LMTD method when all four temperatures are known or can be found from the energy balance.
Worked example and exam tips
Water (1.2 kg/s, cp 4.18) is heated from 20 °C to 80 °C by geothermal water entering at 160 °C at 2 kg/s (cp 4.31) in a counter-flow exchanger with U = 640 W/m²K. Q = 1.2 × 4.18 × 60 = 301 kW, so the hot water leaves at 125.1 °C. ΔT1 = 80 and ΔT2 = 105.1, so ΔTlm = 91.9 °C and A = 301 000 / (640 × 91.9) = 5.11 m².
- For the same temperatures, counter flow always gives a larger LMTD than parallel flow, so it needs less area.
- In parallel flow the cold outlet can never be hotter than the hot outlet.
- If F drops below about 0.75, add another shell pass.
Frequently asked questions
Why a log mean and not an average?
The temperature difference changes along the exchanger in an exponential way. Integrating the heat flow gives the logarithmic mean.
What happens if ΔT1 equals ΔT2?
The formula becomes 0/0, but the limit is simply ΔT1. The tool handles this case.
When should I use NTU instead?
When outlet temperatures are unknown and the area is known (a rating problem). Then the LMTD method needs trial and error, but NTU does not.
Is this calculator free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. Every calculation runs in your browser and nothing you type is sent anywhere.