Heat Exchangers

Heat exchangers transfer heat between two fluids. Learn types (double-pipe, shell-and-tube, plate, finned), parallel vs counter-flow, overall U, LMTD and effectiveness–NTU methods, fouling and sizing.

Car radiators, air-conditioner coils, power-plant condensers, milk pasteurisers and CPU liquid coolers are all heat exchangers: one fluid warms or cools another through a wall.

Designing one means answering two questions: how much area is needed for a given duty (sizing, LMTD), or what outlet temperatures will an existing unit give (rating, ε-NTU)?

An analogy

Two people walking side by side in opposite directions passing a warm object back and forth: in counter-flow, each meets the other at every stage of the journey, so heat is swapped most effectively.

Types

Double-pipe (simple, small duties), shell-and-tube (the refinery workhorse, high pressure), plate (compact, efficient, easy to clean — food and HVAC), finned-tube (air coolers, radiators), and regenerators (rotating wheels, glass furnaces).

Counter-flow vs parallel flow

In counter-flow the fluids move in opposite directions: the cold outlet can get hotter than the hot outlet and the mean temperature difference is larger, so less area is needed. Parallel flow gives more uniform wall temperatures but is less effective.

LMTD method (sizing)

When inlet and outlet temperatures are known, compute Q̇ from an energy balance, ΔT_lm from end temperature differences, then A = Q̇/(U ΔT_lm). Multipass and cross-flow units use a correction factor F ≤ 1.

ε-NTU method, fouling and design trade-offs

When only inlets are known, ε-NTU gives outlets directly: Q̇ = ε C_min (T_h,in − T_c,in). Fouling (scale, biofilm) adds resistance R_f — designs add 10–25 % area margin and plan cleaning. Designers balance area, pressure drop, cost, cleanability and vibration (TEMA standards).

Formulas

• Duty: Q̇ = ṁ_h c_ph ΔT_h = ṁ_c c_pc ΔT_c
• Rate equation: Q̇ = U A ΔT_lm (× F for multipass)
• LMTD: ΔT_lm = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂)
• Overall U (thin wall): 1/U = 1/h_i + R_f + t/k + 1/h_o
• Counter-flow effectiveness: ε = [1 − e^(−NTU(1−C_r))] / [1 − C_r e^(−NTU(1−C_r))]

Worked example: Sizing with LMTD

Given: Hot water 2 kg/s, 150 → 90 °C; Cold 30 → 70 °C, counter-flow; U = 800 W/m²·K

Find: Duty and area.

• Q̇ = 2 × 4.18 × 60 = 501.6 kW
• ΔT₁ = 150 − 70 = 80, ΔT₂ = 90 − 30 = 60
• ΔT_lm = 20/ln(80/60) = 69.5 K
• A = 501 600/(800 × 69.5) = 9.0 m²

Answer: 502 kW, ≈ 9.0 m²

Worked example: Rating with ε-NTU

Given: Hot 2 kg/s water at 150 °C; Cold 3 kg/s water at 30 °C; UA = 8000 W/K, counter-flow

Find: Heat duty.

• C_min = 8360 W/K, C_r = 0.667
• NTU = 8000/8360 = 0.957
• ε = 0.530
• Q̇ = 0.530 × 8360 × 120 = 532 kW

Answer: ≈ 532 kW

Common mistakes

• Wrong: Using arithmetic mean ΔT. — Right: Use LMTD (arithmetic overestimates when end ΔTs differ).
• Wrong: Forgetting fouling. — Right: Add fouling resistances or area margin.

Applications

• Power & process plants: Condensers, feedwater heaters, reboilers and coolers (shell-and-tube).
• Automotive: Radiators, intercoolers, oil coolers and battery chillers.
• HVAC & food: Plate exchangers for district heating substations and pasteurisation.

Key takeaways

• Q̇ = UAΔT_lm; counter-flow is most effective.
• LMTD for sizing, ε-NTU for rating.
• 1/U sums film, wall and fouling resistances.
• Balance area, pressure drop and cleanability.

Going further

• Pinch analysis: Composite curves of all hot and cold streams in a plant find the minimum utility and optimal exchanger network.
• Compact exchangers: Brazed plate-fin and microchannel exchangers reach > 1000 m²/m³ for aerospace and automotive.
• Design standards: TEMA and ASME Section VIII govern mechanical design; HTRI/Aspen EDR handle thermal-hydraulic rating.