Heat Exchanger LMTD Calculator
Calculates the Log Mean Temperature Difference (LMTD) for counter-flow or parallel-flow heat exchangers, then uses it to find the required heat transfer area or rate. Used in the design and rating of industrial heat exchangers.
About this calculator
The LMTD method determines an effective mean driving temperature difference across a heat exchanger. For counter-flow or parallel-flow configurations, define ΔT₁ = T_h,in − T_c,out and ΔT₂ = T_h,out − T_c,in. The log mean temperature difference is LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂). When ΔT₁ ≈ ΔT₂, the arithmetic mean is used instead to avoid division by near-zero values. The heat transfer rate is then Q = U · A · F · LMTD, where U is the overall heat transfer coefficient, A is the heat transfer area, and F is a correction factor (F = 1 for pure counter-flow or parallel-flow; tabulated values apply to shell-and-tube configurations). The LMTD accounts for the fact that temperature differences vary along the exchanger length, giving a single representative value.
How to use
A counter-flow water-to-water exchanger: hot fluid enters at 90 °C, exits at 60 °C; cold fluid enters at 20 °C, exits at 50 °C. ΔT₁ = 90 − 50 = 40 °C; ΔT₂ = 60 − 20 = 40 °C. Since ΔT₁ = ΔT₂, LMTD = (40 + 40)/2 = 40 °C (arithmetic mean applies). If U = 800 W/(m²·K) and A = 2 m², then Q = 800 × 2 × 1.0 × 40 = 64 000 W = 64 kW. Now change cold outlet to 55 °C: ΔT₁ = 90 − 55 = 35 °C, ΔT₂ = 60 − 20 = 40 °C. LMTD = (35 − 40)/ln(35/40) = −5/ln(0.875) = −5/(−0.1335) ≈ 37.5 °C.
Frequently asked questions
What is the difference between counter-flow and parallel-flow LMTD in heat exchangers?
In a counter-flow heat exchanger, hot and cold fluids flow in opposite directions, which maintains a more uniform temperature difference along the entire length and produces a higher LMTD for the same inlet and outlet conditions. In a parallel-flow arrangement, both fluids enter at the same end, the temperature difference is largest at the inlet and smallest at the outlet, yielding a lower LMTD and therefore requiring more area for the same duty. Counter-flow is thermodynamically superior and is the preferred configuration whenever space and pressure-drop constraints allow. The LMTD formula is the same for both; only the assignment of ΔT₁ and ΔT₂ changes.
When should I use the LMTD correction factor F in heat exchanger calculations?
The correction factor F is needed whenever the flow arrangement deviates from ideal counter-flow, such as in multi-pass shell-and-tube exchangers, cross-flow heat exchangers, or mixed-flow configurations. F is always ≤ 1, and values below 0.75 are generally considered inefficient and a signal to reconsider the exchanger geometry. F is determined from standardised charts or correlations based on two dimensionless temperature ratios (P and R) that compare the thermal effectiveness to the theoretical maximum. For a single-pass pure counter-flow or parallel-flow exchanger, F = 1 exactly.
How do I use LMTD to find the required heat transfer area for a new heat exchanger?
Rearrange the fundamental equation to A = Q / (U · F · LMTD). First calculate the required duty Q from energy balances on both fluid streams (Q = ṁ · cp · ΔT for each side). Then estimate or look up the overall heat transfer coefficient U, which depends on fluid types, flow velocities, and fouling factors — typical values range from 200 W/(m²·K) for gas-to-gas to 2000 W/(m²·K) for liquid-to-liquid exchangers. Calculate LMTD from the four terminal temperatures and apply the appropriate F factor. The resulting area guides initial sizing before detailed mechanical design begins.