I. Known Conditions
| Parameter | Hot side (exhaust) | Cold side (make-up air) |
|---|---|---|
| Air volume | 12000 m³/h | 12000 m³/h |
| Inlet temperature | 140°C | 20°C |
| Outlet temperature (target) | 90°C | 70°C |
| Air density (mean temp) | ≈ 0.95 kg/m³ | |
| Specific heat cp | ≈ 1.005 kJ/kg·K | |
II. Calculate Mass Flow and Recovered Heat
Mass flow m = (12000/3600) × 0.95 ≈ 3.17 kg/s. Cold side temperature rise 70−20 = 50 K:
Q = m·cp·ΔT = 3.17 × 1005 × 50 ≈ 159 kW
Hot side temperature drop 140−90 = 50 K, releasing the same 159 kW; energy balance is self-consistent.
III. Calculate LMTD (Counter Flow)
Counter-flow end temperature differences: ΔT₁ = 140−70 = 70 K, ΔT₂ = 90−20 = 70 K.
ΔTm = (70 − 70) / ln(70/70) → ends equal, so ΔTm = 70 K
In this example the two end temperature differences happen to be equal, a simplification of the symmetric condition.
IV. Calculate the Required Area
Take the overall heat transfer coefficient of the air-to-air plate heat exchanger K ≈ 25 W/m²·K (including two-side convection and thin wall):
A = Q / (K · ΔTm) = 159000 / (25 × 70) ≈ 90.9 m²
Adding a 10%~15% margin, select a plate pack of about 100 m². This result can be taken directly for quotation or to check equipment samples.
Selection is not guessing; it is settling the four accounts of Q, K, ΔTm, and A one by one.