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Engineering Reference

Heat Exchanger NTU Effectiveness Reference

Reference-style context for the NTU/effectiveness method — common flow arrangements, typical ε–NTU relationships, dimensionless groups (NTU, C*), and how NTU concepts support preliminary heat exchanger checks. Not a design chart and not a calculator.

TypeEngineering reference — NTU/effectiveness concepts

Caution

This is a reference for preliminary checks only.

The relationships on this page describe idealised flow arrangements with constant fluid properties and uniform flow distribution. They are useful for sanity-checking sizes, rating existing exchangers, and building intuition — they are not a substitute for a complete thermal-hydraulic rating or vendor design. There is no NTU calculator on ProcessConvert; the values here are reference relations, not an interactive chart.

Purpose

The NTU/effectiveness method expresses heat exchanger performance through two dimensionless groups — the number of transfer units NTU = UA / C_min and the capacity rate ratio C* = C_min / C_max — combined into an effectiveness ε = Q / Q_max. It is mathematically equivalent to the LMTD method but is often easier when outlet temperatures are unknown (typical of rating, off-design analysis, or checks against an existing exchanger). This reference summarises the dimensionless groups, the most common ε–NTU relations, and the boundaries within which they are useful.

Dimensionless variables

Number of transfer units
NTU = U × A / C_min

A measure of the exchanger's heat-transfer size relative to the smaller capacity stream. Higher NTU means a larger exchanger relative to the flow.

Capacity rate ratio
C* = C_min / C_max, C = ṁ × Cp

Ratio of the smaller stream capacity rate to the larger. C* = 1 means balanced flow; C* = 0 means one side is changing phase (condenser or evaporator).

Effectiveness
ε = Q / Q_max, Q_max = C_min × (T_h,in − T_c,in)

Ratio of actual duty to the maximum thermodynamically possible duty for the given inlet temperatures and flow rates. Always between 0 and 1.

Typical ε–NTU relationships

Flow arrangementε(NTU, C*) relationC* = 1 limit
Counter-current (single pass)
Best effectiveness at a given NTU and C*; F = 1 in LMTD equivalent.
ε = (1 − exp(−NTU × (1 − C*))) / (1 − C* × exp(−NTU × (1 − C*)))ε = NTU / (1 + NTU)
Parallel-flow (co-current, single pass)
Maximum effectiveness ≈ 0.5 even at very high NTU when C* = 1.
ε = (1 − exp(−NTU × (1 + C*))) / (1 + C*)ε = (1 − exp(−2 × NTU)) / 2
Shell-and-tube, 1 shell – 2 tube passes
Equivalent to LMTD × F correction; F-charts published for this arrangement.
ε = 2 × {(1 + C*) + (1 + C*²)^½ × (1 + exp(−NTU × (1 + C*²)^½)) / (1 − exp(−NTU × (1 + C*²)^½))}⁻¹Use the general relation with C* = 1
Cross-flow, both fluids unmixed
Approximate correlation; vendor rating required for design.
ε ≈ 1 − exp{(1/C*) × NTU^0.22 × [exp(−C* × NTU^0.78) − 1]} (approximate)Use chart or numerical solution
Cross-flow, one fluid mixed, one unmixed
Two sub-cases (mixed = C_min vs mixed = C_max) give different ε relations.
C_mixed = C_max: ε = (1/C*) × (1 − exp(−C* × (1 − exp(−NTU))))ε = 1 − exp(−(1 − exp(−NTU)))
Phase change (condenser or evaporator)
Independent of flow arrangement when C* = 0.
ε = 1 − exp(−NTU)N/A — C* approaches 0

Relations summarised from standard heat transfer references (Incropera; Kays & London; Coulson & Richardson Vol. 6). Compact correlations for cross-flow arrangements are approximate; vendor rating uses tabulated charts or numerical solutions.

Practical guidance

  • •Sizing job (terminal temperatures known): the LMTD method is usually faster. NTU is not required.
  • •Rating job (area known, outlets unknown): NTU/effectiveness is the natural fit because it gives the outlet temperatures in one pass without iteration.
  • •Off-design check: given the same exchanger at a new flow rate or inlet temperature, NTU lets you predict new outlets quickly.
  • •Diminishing returns: for any C* > 0, effectiveness asymptotes well below 1. Doubling NTU from 4 to 8 typically gains only a few percent in ε.
  • •Pure-condenser shortcut: when one side is condensing or evaporating, C* → 0 and ε = 1 − exp(−NTU) regardless of flow arrangement.
  • •Balanced flow: at C* = 1 with counter-current flow, ε = NTU / (1 + NTU). For NTU = 4, ε ≈ 0.80; for NTU = 8, ε ≈ 0.89.

Units / dimensionless variables

  • •NTU: dimensionless. Computed from U × A / C_min; U in W/(m²·K), A in m², C in W/K — or any consistent set.
  • •C*: dimensionless. Bounded between 0 (one-sided phase change) and 1 (balanced flow).
  • •ε: dimensionless. Bounded between 0 and 1.
  • •C = ṁ × Cp: capacity rate in W/K or BTU/(h·°F).
  • •Q_max: C_min × (T_h,in − T_c,in), in W or BTU/h.

Assumptions

  • •Constant overall heat transfer coefficient U across the exchanger.
  • •Constant specific heat capacity Cp for each stream (no large temperature ranges with strong Cp variation).
  • •Steady-state operation; no heat losses to the environment.
  • •Idealised flow arrangement matching the chosen ε–NTU relation (e.g., pure counter-current, true cross-flow with the assumed mixing).
  • •Uniform flow distribution — no bypassing, maldistribution, or leakage.
  • •Single-phase on each side (except in explicit phase-change cases where C* = 0 applies).

Boundaries and exclusions

  • •This page does not include an interactive ε–NTU chart. The relations are listed for reference, not as a design tool.
  • •Cross-flow correlations are approximations — production rating uses tabulated charts or numerical solutions.
  • •Multi-pass shell-and-tube arrangements have arrangement-specific ε–NTU forms; mixing relations across arrangements gives wrong answers.
  • •Phase-change behaviour (boiling, condensation, partial vaporisation) generally needs zone-by-zone treatment or specialised correlations.
  • •Fouling, pressure drop, vibration, and mechanical design are not part of NTU/effectiveness — they belong to detailed rating and mechanical design.
  • •No standards-grade design accuracy is implied — these relations are for preliminary checks.

How to use in calculations

  1. 01Identify which side is C_min — the stream with the lower ṁ × Cp. Compute C* = C_min / C_max.
  2. 02For a sizing job with all terminal temperatures known, prefer the LMTD route. Use the LMTD Calculator for ΔTₘ and the Heat Exchanger Area Calculator for A.
  3. 03For a rating job (area known, outlets unknown), compute NTU = U × A / C_min and pick the ε relation for the actual flow arrangement.
  4. 04Compute Q_max = C_min × (T_h,in − T_c,in) and Q = ε × Q_max.
  5. 05Back out the outlet temperatures: T_h,out = T_h,in − Q / C_h, T_c,out = T_c,in + Q / C_c.
  6. 06Cross-check the result against the LMTD method using the computed outlets — they should agree.
  7. 07For multi-pass or cross-flow arrangements outside the listed relations, use vendor rating software or the tabulated charts in Kays & London or Incropera.

Source / context notes

  • •Kays & London, Compact Heat Exchangers — standard tabulated ε–NTU charts for all common flow arrangements.
  • •Incropera, Bergman, Lavine, DeWitt, Fundamentals of Heat and Mass Transfer — textbook derivation of ε–NTU relations.
  • •Coulson & Richardson's Chemical Engineering Volume 6, Chapter 12 — process-engineering treatment of LMTD and NTU.
  • •Perry's Chemical Engineers' Handbook, Section 11 — summarised relations and worked examples.

The relations here are summarised for reference. Use the original sources or vendor rating software when chart-level accuracy matters.

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