Effectiveness-NTU Calculator

Use the effectiveness-NTU calculator to perform either a design calculation or a performance assessment of a heat exchanger.

Effectiveness42.859%of the thermodynamic maximum. The NTU method needs NO outlet temperatures, which is why it is used for design where LMTD is used for rating

Log mean temperature difference42.4509 Kfrom end differences of 45 K and 40 K — always BELOW their arithmetic mean of 42.5 K, which is why using the average overestimates the duty

Arithmetic mean difference42.5 K0.116% higher — the two converge as the end differences approach each other

Hot end difference45 K

Cold end difference40 K

Arrangementcounterflowthe cold outlet may legally exceed the hot outlet, which parallel flow can never achieve

Heat duty from the streams120 kWboth sides agree, as an energy balance requires

Heat duty from UA × LMTD120.0088 kWwith UA = 2,827 W/K

UA required for these temperatures2,826.79 W/Kq/LMTD — this is the rating question, and it is what LMTD exists to answer

NTU0.70675UA/C_min — a dimensionless size. Above about 5 the returns diminish sharply

Capacity ratio C_r0.83333C_min/C_max — at 0 one stream is condensing or boiling and holds its temperature

Maximum possible duty280 kWC_min × (T_h,in − T_c,in) — limited by the SMALLER capacity rate, because that stream runs out of ability to absorb or give up heat first

Actual duty by NTU120.0053 kW

Counterflow effectiveness at this NTU42.859%

Parallel flow at the same NTU39.616%always lower — parallel flow cannot exceed 50% effectiveness at C_r = 1 however large you build it, while counterflow approaches 100%

Effectiveness at double the size61.448%twice the area buys only 18.589 more points — the diminishing return that sets the economic size

The formula

LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂); ε = f(NTU, C_r)

Why the LOG mean

The temperature difference between two streams varies continuously along an exchanger, so the driving force is not the same everywhere. Integrating the local difference over the area produces the log mean, not the arithmetic mean, and the log mean is always the smaller of the two. Using the average therefore overestimates the duty and undersizes the exchanger — by a few percent when the end differences are similar, and badly when they are not.

The formula divides by ln(ΔT₁/ΔT₂), which is zero when the two end differences are equal. That is not a singularity in the physics: the limit is simply the common value, and this calculator returns it rather than dividing by zero.

Counterflow beats parallel flow, always

In parallel flow both streams enter at the same end and approach a common temperature from opposite sides, so the cold outlet can never exceed the hot outlet no matter how large the exchanger. Effectiveness is capped at 50% when the two capacity rates are equal.

Counterflow holds a more even difference along the whole length and permits the cold stream to leave hotter than the hot stream does — a temperature cross that parallel flow cannot produce. Its effectiveness approaches 100% as the exchanger grows.

Two methods, two jobs

LMTD needs all four temperatures and tells you the area required: it is the rating method. The effectiveness-NTU method needs only the two INLET temperatures and the capacity rates, so it can predict performance for an exchanger that does not exist yet: it is the design method. Above about NTU = 5 the returns diminish so sharply that further area is rarely worth its cost.