I. The "Master Equation" of Heat Exchanger Design
No matter how complex the heat exchanger, steady-state heat transfer can be written as:
Q = K · A · ΔTm
K is the overall heat transfer coefficient (W/m²·K), A is the heat transfer area, and ΔTm is the mean temperature difference (usually the logarithmic mean, covered next). This equation is the "quotation" for selection: to transfer a given amount of heat Q, either make K large, make A sufficient, or raise the temperature difference.
II. K Is the Sum of the Reciprocals of Layer-by-Layer Thermal Resistances
Heat from the hot fluid to the cold fluid passes sequentially through: hot-side convection → wall conduction → cold-side convection. The total thermal resistance is added in series:
1/K = 1/h_hot + δ/λ + 1/h_cold (+ fouling thermal resistance)
Whichever link is largest dominates the whole. Common situations:
- Air-to-air heat exchange: Both h are small, 1/h dominates; raising flow velocity and adding disturbance is most effective;
- Air-to-water heat exchange: Air-side h is far smaller than water-side, so optimization is almost entirely on the air side;
- Long-running equipment: Fouling thermal resistance gradually grows and becomes the main factor later.
III. Raise K or Add A?
| Method | Advantage | Cost |
|---|---|---|
| Raise K (speed up, disturb flow) | Compact equipment, small footprint | Rising pressure drop and fan power |
| Add A (larger plates) | Low temperature difference demand, small pressure drop | More expensive and space-consuming equipment |
Actual design is a combination: first use channel design to raise K to a reasonable level, then use A to make up the remaining heat. Blindly piling up area produces big, expensive equipment; blindly increasing speed lets fan electricity bills eat the energy-saving gains.
IV. A Quick Check
For any heat exchange scheme, first ask: What is K? How big is A? What is ΔTm? Does their product equal the Q you need? If not, the scheme is inflated. Break K into three thermal resistances and you immediately know which side is the bottleneck.