Sensible heat duty from flow, specific heat, and temperature change — plus the required exchanger area from U and the LMTD.
Q = ṁ·Cp·ΔT; A = Q/(U·LMTD)
How it works
The sensible heat duty is mass flow times specific heat times temperature change. Given an overall coefficient U and the log-mean temperature difference, the rate equation Q = U·A·LMTD then gives the surface area the exchanger needs.
Worked example
10,000 kg/h of water cooled 20 °C, with U = 500 W/m²·K and LMTD = 30 °C. Q ≈ 232 kW, requiring about 15.5 m² of surface.
Inputs
Mass flow (kg/h)
Specific heat Cp (kJ/kg·K) — Liquid water ≈ 4.18, light hydrocarbons ≈ 2.0–2.5, air ≈ 1.0 kJ/kg·K.
Temperature change ΔT (K) — The stream's inlet-to-outlet temperature change.
U (optional) (W/m²·K) — Overall coefficient. Leave 0 to skip the area calculation.
LMTD (optional) (K) — Log-mean ΔT for the arrangement — get it from the LMTD tool.
Frequently asked questions
Does this cover boiling or condensing?
No — this is sensible heat only (Q = ṁ·Cp·ΔT). For a phase change, use the latent load Q = ṁ·h_fg instead, then still size the area with A = Q/(U·LMTD).
Where do I get the LMTD?
From the LMTD tool, which handles counter-current, co-current, and the 1–2 shell-and-tube F correction. Feed that value in here to size the area.
What U value should I assume?
Typical overall coefficients: water-water ≈ 800–1500, steam-water ≈ 1000–3000, gas-gas ≈ 10–50 W/m²·K. Use a table of typical U values for screening, then confirm by detailed rating.
Assumptions
Sensible heat only — no boiling or condensation. For phase change use the latent load ṁ·h_fg instead.
Constant Cp over the temperature range; use the mean Cp for wide ranges.
Required area uses a constant U and the true-countercurrent LMTD; apply the F correction factor for multi-pass shell-and-tube units.
References
Sensible-heat and exchanger rate equations — Incropera & DeWitt, Fundamentals of Heat and Mass Transfer.
Related Heat Transfer tools
Heat Exchanger LMTD — Log-mean temperature difference for a two-stream exchanger, plus duty Q if you supply U and area.
Insulated Pipe Heat Loss — Heat loss per metre and total from an insulated pipe, with the outer-surface temperature (personnel-protection check).