Compact Heat Exchanger
Theory: large area in a small volume
Overview
Why do heat exchangers like radiators have such fine, closely packed fins?
Air's heat transfer coefficient is tens of times lower than water's, so the air side must make up with area. Fine, densely packed fins exceed 1,000 m²/m³ of area per volume. Cutting fins into offset strips also breaks up boundary layers and raises h — but makes flow harder, increasing pressure drop. Organising heat transfer and pressure drop as two numbers, j and f, is the basis of compact heat exchanger design. Let's calculate an offset strip fin.
j and f factors
$G$ is mass velocity at the minimum flow area and $D_h$ the hydraulic diameter, 2.33 mm for this offset strip fin (1.5 mm spacing, 6 mm height, 0.1 mm thickness, 3 mm length). j and f come from the Manglik–Bergles correlations.
Crossflow effectiveness
An approximation for crossflow with both fluids unmixed — the arrangement of most radiators and air-conditioning coils.
Kays and London's data book
Compact heat exchanger design advanced greatly with Kays and London's Compact Heat Exchangers, compiled in the US in the 1950s. They measured many fin geometries and charted j and f against Reynolds number, so designers could pick a similar geometry and estimate performance immediately. The Manglik–Bergles correlations for offset strip fins (1995) express much of that experimental data in single formulas.
Worked examples
Example 1: offset strip fin (air, 50 °C)
| Reynolds number | Velocity | j | f | h | vs plain plates | Pressure gradient |
|---|---|---|---|---|---|---|
| 300 | 2.3 m/s | 0.0272 | 0.131 | 88 W/m²K | 1.2 | 0.66 kPa/m |
| 500 | 3.9 m/s | 0.0210 | 0.090 | 113 W/m²K | 1.5 | 1.26 kPa/m |
| 1,000 | 7.7 m/s | 0.0150 | 0.056 | 161 W/m²K | 2.1 | 3.14 kPa/m |
| 2,000 | 15.4 m/s | 0.0109 | 0.042 | 234 W/m²K | 3.1 | 9.31 kPa/m |
| 3,000 | 23.2 m/s | 0.0091 | 0.037 | 294 W/m²K | 3.9 | 18.4 kPa/m |
"Plain plates" compares with 76 W/m²K for a plain 1.5 mm channel in fully developed laminar flow (Nu = 8.23). Area density is about 1,560 m²/m³ of passage volume.
Example 2: crossflow (both unmixed) effectiveness
| NTU | Ratio 0.5 | Ratio 1 | Counterflow, ratio 1 |
|---|---|---|---|
| 0.5 | 0.352 | 0.315 | 0.333 |
| 1 | 0.545 | 0.469 | 0.500 |
| 2 | 0.739 | 0.615 | 0.667 |
| 3 | 0.828 | 0.684 | 0.750 |
| 5 | 0.905 | 0.749 | 0.833 |
Raising air speed increases h, but pressure drop rises much faster.
From Re = 1000 to 3000, h rises 1.8 times but pressure gradient 5.9 times; fan power, the product of pressure drop and flow, rises about 18 times. So compact exchangers are normally run at low air speed, adding area or frontal width rather than speed. Offset strip fins beat plain fins because they transfer more heat for the same pressure drop, but the advantage shrinks at low Reynolds number (1.2 times at Re = 300). Near a capacity ratio of 1, crossflow effectiveness levels off: even NTU 5 gives only 0.75.
Design tips
- Choose fins using j and f, comparing at equal pressure drop (fan power).
- Include fin efficiency in the effective area.
- Use the ε-NTU relation for the actual flow arrangement (counterflow, crossflow).
- Consider frontal velocity maldistribution; uneven flow lowers performance.
- Fouling or frost blocking the gaps sharply increases pressure drop.
“Fins blocked by frost”
In a cold-store evaporator, cooling deteriorated over time: moisture in the air frosted on closely spaced fins, blocking the gaps and greatly reducing airflow. Compact, narrow fins are vulnerable to frost and fouling. Widening the spacing only on the frost-prone inlet side and adding periodic defrost cycles solved it. Designing for small volume can backfire unless the operating environment is considered.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Comparing heat transfer only | Excessive fan power | Compare at equal Δp |
| Using frontal area for G | Wrong Re and h | Minimum flow area |
| Ignoring flow arrangement | Wrong effectiveness | Crossflow relation |
| Fin efficiency = 1 | Area overrated | Compute efficiency |
| Ignoring frost and fouling | Performance loss | Allow margin in spacing |
I'd like to learn related topics.
Try the ε-NTU tool and heat exchanger design tool. Related pages include pin-fin arrays, microchannel cooling and two-phase heat exchangers.
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