Heat-transfer rate Q̇
Heat-transfer rate from Q̇ = FUAΔTₗₘ.
Thermal engineering · Heat transfer · conduction
Heat exchanger LMTD — duty, area and U
Calculate the logarithmic mean temperature difference from four terminal temperatures, apply correction factor F, then solve Q̇, A or U.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
ΔTₗₘResults
Heat-transfer area A
Required or entered heat-transfer area.
Overall heat-transfer coefficient U
W/(m²·K)
Required or entered overall heat-transfer coefficient.
LMTD ΔTₗₘ
K
Logarithmic mean temperature difference calculated from the two terminal differences.
Corrected LMTD FΔTₗₘ
K
LMTD multiplied by the explicit correction factor F.
Terminal difference ΔT₁
K
First terminal temperature difference for the selected flow arrangement.
Terminal difference ΔT₂
K
Second terminal temperature difference for the selected flow arrangement.
Steady operation with known terminal bulk-fluid temperatures. The hot stream cools and the cold stream warms; both terminal differences must remain strictly positive.
01Formulas and symbols
Formulas used
↔
ΔT₁ = Tₕ,in − T𝒸,out ; ΔT₂ = Tₕ,out − T𝒸,inCounterflow→→
ΔT₁ = Tₕ,in − T𝒸,in ; ΔT₂ = Tₕ,out − T𝒸,outParallel flowΔTₗₘ
(ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂)LMTD ΔTₗₘFΔTₗₘ
F · ΔTₗₘCorrected LMTD FΔTₗₘQ̇
F · U · A · ΔTₗₘHeat-transfer rate Q̇A
Q̇ / (F · U · ΔTₗₘ)Heat-transfer area AU
Q̇ / (F · A · ΔTₗₘ)Overall heat-transfer coefficient U02Assumptions and limits
Scope of validity
- Steady operation with known terminal bulk-fluid temperatures.
- The hot stream cools and the cold stream warms; both terminal differences must remain strictly positive.
- The overall coefficient U is treated as constant over the whole heat-transfer area.
- Heat loss to surroundings, energy storage and property variation are not modeled.
- Correction factor F is an explicit engineering input between 0 and 1; this calculator does not derive F from multipass geometry.
- Phase change, ε-NTU analysis, mass flow rates, heat capacities and pressure drop are outside scope.
03Validation example
Reference numerical case
- Counterflow reference: Tₕ,in = 120 °C, Tₕ,out = 80 °C, T𝒸,in = 20 °C and T𝒸,out = 60 °C.
- ΔT₁ = 60 K and ΔT₂ = 60 K; the analytical limit gives ΔTₗₘ = 60 K.
- With F = 1, U = 500 W/(m²·K) and A = 10 m², Q̇ = 300 kW.
- Inverse modes return A = 10 m² and U = 500 W/(m²·K) for Q̇ = 300 kW.
04References
Technical references
- Incropera et al. — Fundamentals of Heat and Mass Transfer: logarithmic mean temperature difference method.
- Kern — Process Heat Transfer: LMTD heat-exchanger sizing.
- NIST Special Publication 811 — SI units and temperature intervals.