About Heat Exchanger LMTD Calculator
The heat exchanger LMTD calculator sizes or rates a two-stream heat exchanger using the Log Mean Temperature Difference method and cross-checks the result with the effectiveness-NTU method. Enter the four terminal temperatures (hot inlet/outlet and cold inlet/outlet), the overall heat-transfer coefficient U, and either the area to rate an existing unit or a stream flow and specific heat to size a new one.
It reports the two terminal temperature differences, the LMTD, the effective mean temperature difference F x LMTD, the heat duty Q, the required or supplied area A, and -- when stream capacity rates are known -- the effectiveness epsilon, the number of transfer units NTU, and the capacity ratio Cr. The arrangement (counter-flow or parallel-flow) changes how the terminal differences are paired and is fully accounted for.
How It Works
- Pick the flow arrangement: counter-flow (streams move in opposite directions) or parallel-flow (same direction).
- Enter the hot inlet/outlet and cold inlet/outlet temperatures, and the overall coefficient U in W/(m^2.K).
- Choose to solve for area (supply a stream mass flow and cp so the energy balance fixes the duty) or for duty (supply the area A).
- The calculator forms dT1 and dT2 for the chosen arrangement, evaluates LMTD = (dT1 - dT2)/ln(dT1/dT2), applies the optional correction factor F, then computes Q = U A F LMTD and the effectiveness-NTU figures.
Worked Example
A counter-flow exchanger cools a hot stream from 100 C to 60 C while heating a cold stream from 20 C to 50 C, with U = 500 W/(m^2.K). The hot stream has m*cp = 1000 W/K. Terminal differences are dT1 = 100 - 50 = 50 K and dT2 = 60 - 20 = 40 K, so LMTD = (50 - 40)/ln(50/40) = 10/0.22314 = 44.81 K. The duty is Q = 1000 x (100 - 60) = 40,000 W, giving required area A = Q/(U x LMTD) = 40000/(500 x 44.81) = 1.785 m^2. With Cmin = 1000 W/K and Cmax = 1333 W/K, Cr = 0.75, NTU = U A/Cmin = 0.893 and effectiveness epsilon = Q/(Cmin x (100 - 20)) = 40000/80000 = 0.50.
Formulas
- Terminal temperature differences
counter-flow: dT1 = Th_in - Tc_out, dT2 = Th_out - Tc_in | parallel-flow: dT1 = Th_in - Tc_in, dT2 = Th_out - Tc_out- Log Mean Temperature Difference
LMTD = (dT1 - dT2) / ln(dT1 / dT2) [limit: LMTD = dT1 when dT1 = dT2]- Heat duty (LMTD method)
Q = U * A * F * LMTD- Energy balance per stream
Q = m_h * cp_h * (Th_in - Th_out) = m_c * cp_c * (Tc_out - Tc_in)- Effectiveness-NTU
NTU = U A / Cmin, Cr = Cmin/Cmax | CF: eps = (1 - e^-NTU(1-Cr))/(1 - Cr e^-NTU(1-Cr)) | PF: eps = (1 - e^-NTU(1+Cr))/(1 + Cr)
Standards & References
- TEMA (Tubular Exchanger Manufacturers Association) standards
- Cengel & Ghajar, Heat and Mass Transfer
- Incropera, Fundamentals of Heat and Mass Transfer
- Kays & London, Compact Heat Exchangers (effectiveness-NTU)
Frequently Asked Questions
What is the difference between the LMTD and effectiveness-NTU methods?
LMTD is convenient when all four terminal temperatures are known (sizing): you compute the mean driving temperature and then the area. Effectiveness-NTU is convenient when outlet temperatures are unknown (rating): you compute effectiveness from NTU and capacity ratio. This tool reports both so you can cross-check.
Why does counter-flow need less area than parallel-flow?
For the same inlet and outlet temperatures, counter-flow produces a larger and more uniform temperature difference along the exchanger, so its LMTD is higher. Because Q = U A F LMTD, a larger LMTD means less area is needed for the same duty. Parallel-flow also cannot raise the cold outlet above the hot outlet.
What happens when the two terminal temperature differences are equal?
When dT1 equals dT2 the formula (dT1 - dT2)/ln(dT1/dT2) becomes 0/0. The analytic limit is simply dT1, so the calculator returns the common terminal difference instead of dividing by zero.
What is the LMTD correction factor F?
F accounts for shell-and-tube or cross-flow arrangements that are neither pure counter-flow nor pure parallel-flow. It is 1 for ideal counter-flow or parallel-flow and less than 1 otherwise, increasing the required area. Read F from TEMA charts for the chosen configuration and enter it here.