Heat Exchanger | mysimulator.uk

Two ways to run two streams past each other

A heat exchanger moves thermal energy from a hot fluid stream to a cold one across a separating wall, without the streams mixing. The geometry decides everything about performance. In parallel flow, both streams enter at the same end and travel the same direction; the temperature difference between them is largest at the inlet and shrinks continuously, both streams asymptotically approaching a shared exit temperature. In counter-flow, the streams enter at opposite ends and move in opposite directions, so a substantial temperature difference is maintained along the entire length — which is exactly why counter-flow can push the hot outlet below the cold outlet temperature, something parallel flow can never achieve.

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The LMTD method

Because the temperature difference between the two streams varies continuously along the length, a single average driving force must be defined carefully — the arithmetic mean overstates heat transfer since the difference decays exponentially, not linearly. The correct average is the log mean temperature difference (LMTD):

Q = U · A · LMTD

ΔT1, ΔT2 = temperature differences between the two streams
           at each end of the exchanger

LMTD = (ΔT1 − ΔT2) / ln(ΔT1 / ΔT2)

U = overall heat transfer coefficient
A = heat transfer surface area

For the same four inlet/outlet temperatures, counter-flow's LMTD is always greater than or equal to parallel flow's, because its ΔT1 and ΔT2 are closer together and the driving force is sustained rather than front-loaded — directly translating into a smaller required area A for the same duty Q, or more heat transferred for the same area.

Effectiveness-NTU: when outlet temperatures are unknown

LMTD needs all four temperatures up front, which makes it awkward for a rating problem — an existing exchanger where you know only the inlets and must find the outlets. The effectiveness-NTU method sidesteps that by defining effectiveness ε as the fraction of the maximum thermodynamically possible heat transfer actually achieved:

ε = Q_actual / Q_max          Q_max = Cmin · (Th,in − Tc,in)

NTU = U·A / Cmin              Cr = Cmin / Cmax

Cmin, Cmax = smaller/larger of the two heat capacity rates (ṁ·cp)

Counter-flow: ε = (1 − e^[−NTU(1−Cr)]) / (1 − Cr·e^[−NTU(1−Cr)])
Parallel flow: ε = (1 − e^[−NTU(1+Cr)]) / (1 + Cr)

For a given NTU and capacity ratio Cr, the counter-flow formula always yields an equal or higher ε than the parallel-flow formula — and in the special case Cr = 1, counter-flow effectiveness rises linearly toward 100% as NTU grows, while parallel flow's is capped at 50% no matter how large the exchanger gets. That single number is the clean mathematical statement of why real-world exchangers — radiators, condensers, heat recovery ventilators — are built counter-flow whenever the geometry allows it.

Where each method is actually used

In practice engineers reach for LMTD during sizing — all temperatures are specified by the process, and the question is how much area A to build — and for effectiveness-NTU during rating or system simulation, where only inlet conditions and the exchanger's physical size are known and the outlet temperatures must fall out of the calculation without iteration. Cross-flow and shell-and-tube exchangers sit between the two idealised limits and use correction factors or dedicated ε-NTU relations for their specific geometry.

Frequently asked questions

Why can counter-flow heat exchangers outperform parallel-flow ones?

In counter-flow the hot outlet can approach the cold inlet temperature (and vice versa) because a temperature difference is maintained across the entire length. In parallel flow both streams converge toward the same shared exit temperature, capping the maximum possible heat transfer well below what counter-flow can achieve for the same inlet temperatures and flow rates.

What does NTU actually represent physically?

Number of transfer units, NTU = UA / Cmin, is a dimensionless measure of the exchanger's thermal size relative to the minimum heat capacity rate flowing through it. A small NTU means the exchanger barely has enough area or is passing fluid too fast to change its temperature much; large NTU means the exchanger has abundant transfer capacity per unit of heat capacity flow, letting the outlet approach its theoretical thermodynamic limit.

When is the LMTD method preferred over effectiveness-NTU?

LMTD is the natural choice when all four inlet and outlet temperatures are already known or specified — typically a sizing problem, computing the required area A. Effectiveness-NTU is preferred when only the inlet temperatures are known and outlet temperatures must be found, such as rating an existing exchanger, because it avoids the iterative solution LMTD would otherwise require.

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