Heat Exchanger Sizing: How to Calculate Area and Flow Rate

Heat exchangers are critical equipment in chemical plants, refineries, HVAC systems, power plants, and food processing. Sizing a heat exchanger involves calculating the heat duty, the driving temperature difference (LMTD), and the required heat transfer area.

Under-sized exchangers cannot achieve the required process temperatures. Over-sized ones waste capital and may cause control problems. This guide covers the LMTD method — the standard approach for heat exchanger preliminary design.

Heat duty is the rate of heat transfer between the two fluid streams.

**Q = m × Cp × ΔT**

Where: - Q = heat duty (kW or W) - m = mass flow rate (kg/s) - Cp = specific heat capacity (kJ/kg·K) - ΔT = temperature change of the fluid (K or °C)

This must be equal for both hot and cold sides (energy balance): **Q_hot = Q_cold → m_h × Cp_h × (T_h_in – T_h_out) = m_c × Cp_c × (T_c_out – T_c_in)**

LMTD is the effective average temperature difference driving heat transfer across the exchanger.

**LMTD = (ΔT₁ – ΔT₂) / ln(ΔT₁/ΔT₂)**

Where ΔT₁ and ΔT₂ are the temperature differences at each end of the exchanger.

**Counter-flow arrangement** (most efficient — hot and cold fluids flow in opposite directions): - ΔT₁ = T_h_in – T_c_out (hot inlet vs cold outlet) - ΔT₂ = T_h_out – T_c_in (hot outlet vs cold inlet)

**Parallel-flow arrangement:** - ΔT₁ = T_h_in – T_c_in - ΔT₂ = T_h_out – T_c_out

Counter-flow always gives a higher LMTD than parallel-flow — meaning less area is required. Always use counter-flow unless process constraints prevent it.

**Q = U × A × LMTD × F**

Rearranged for area: **A = Q / (U × LMTD × F)**

Where: - A = heat transfer area (m²) - U = overall heat transfer coefficient (W/m²·K) - F = LMTD correction factor (1.0 for pure counter-flow; 0.75–0.95 for shell-and-tube multi-pass)

The overall heat transfer coefficient U accounts for the resistance of both fluid films and the wall: **1/U = 1/h_hot + wall resistance + 1/h_cold + fouling factors**

Cool 10 kg/s of process water from 70°C to 40°C using cooling water entering at 28°C and leaving at 38°C. Shell-and-tube heat exchanger, counter-flow.

**Step 1 — Heat Duty:** Q = 10 × 4.18 × (70 – 40) = **1,254 kW**

Check cooling water flow rate: m_cw = Q / (Cp × ΔT) = 1,254 / (4.18 × 10) = **30 kg/s**

**Step 2 — LMTD (counter-flow):** ΔT₁ = 70 – 38 = 32°C (hot in, cold out) ΔT₂ = 40 – 28 = 12°C (hot out, cold in) LMTD = (32 – 12) / ln(32/12) = 20 / 0.981 = **20.4°C**

**Step 3 — Heat Transfer Area:** Use U = 1,500 W/m²·K, F = 0.88 (two-pass shell) A = 1,254,000 / (1,500 × 20.4 × 0.88) = **46.4 m²**

Add 20% fouling margin: **Design area = 56 m²** This equates to approximately a 450 mm shell × 4.8 m tube length, with 19 mm OD tubes.

Fouling is the deposition of scale, biofilm, corrosion products, or process deposits on heat transfer surfaces. It reduces U over time and must be accounted for in design.

The fouling factor R_f is added to the resistance in the U calculation: **1/U_design = 1/U_clean + R_f_hot + R_f_cold**