Required heat transfer area from duty, U, and LMTD — with full step-by-step working
kW
W/m²·K
°C
°C
°C
°C
°C
Required Heat Transfer Area:
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What is This Calculating?
The core heat exchanger sizing equation relates heat duty, area, the overall heat transfer coefficient, and LMTD:
Q = U × A × LMTD
Rearranged to solve for the required area:
A = Q / (U × LMTD)
Why It Matters
This is the final step in basic heat exchanger sizing — once you know how much heat needs to move (Q), how effectively it can transfer through the exchanger surface (U), and the driving temperature difference (LMTD), the required surface area tells you roughly how large (and how expensive) the exchanger needs to be.
This calculator assumes a pure counter-current or co-current arrangement (correction factor F = 1). For multi-pass shell-and-tube exchangers, the true area is A = Q / (U × LMTD × F), where F < 1 is found from the exchanger's specific geometry.
Typical U Values
Service
Typical U (W/m²·K)
Water to water
800 – 1500
Water to light oil
300 – 900
Steam condenser (water cooled)
1500 – 4000
Gas to gas
10 – 50
Solved Examples (Practice Problems)
Click "Try This Example" to auto-fill the calculator above and see the full step-by-step working.
Example 1 — Direct LMTD, water-to-water exchanger
A water-to-water exchanger has a duty of 500 kW, U = 850 W/m²·K, and LMTD = 45°C. Find the required area.
Example 2 — Direct LMTD, gas-to-liquid exchanger (low U)
A gas cooler has a duty of 120 kW, U = 300 W/m²·K, and LMTD = 25°C. Find the required area, and notice how much larger it is than Example 1 despite lower duty — because U is lower.
Example 3 — Calculating LMTD from temperatures first
A counter-current exchanger: hot fluid 140°C → 95°C, cold fluid 25°C → 70°C, duty 300 kW, U = 600 W/m²·K. Find the required area (this is the equal-ΔT edge case — watch the working).
Worked Solutions in Full
Three examples solved in full, followed by a complete problem that starts from flow rates and ends with an area, which is how the calculation usually arises in practice.
Example 1 — Water-to-water exchanger
Given: Q = 500 kW, U = 850 W/m²·K, LMTD = 45 °C
Step 1 — Rearrange Q = U × A × LMTD: A = Q / (U × LMTD)
Step 2 — Convert duty to watts: 500 kW = 500,000 W
Given: Hot oil, 2 kg/s, cp = 2.1 kJ/kg·K, cooled from 150 °C to 90 °C. Cooling water enters at 30 °C and leaves at 80 °C (cp = 4.18 kJ/kg·K). Counter-current, U = 400 W/m²·K.
Step 3 — Temperature differences: ΔT₁ = 150 − 80 = 70 °C, ΔT₂ = 90 − 30 = 60 °C
Step 4 — LMTD: (70 − 60) / ln(70/60) = 64.87 °C. This is Example 1 of the LMTD Calculator.
Step 5 — Required area: A = 252,000 / (400 × 64.87) = 9.71 m²
Answer: Duty 252 kW, water flow 1.21 kg/s, required area ≈ 9.7 m².
Practical Notes and Common Mistakes
This equation is the last step in a preliminary exchanger sizing. The duty comes from an energy balance, the LMTD from the terminal temperatures (see the LMTD Calculator), and U from tables or a detailed film-coefficient calculation. The area you get is a first estimate that a full thermal design will refine.
Mistakes that give wrong answers
kW versus W. U is in W/m²·K, so duty must be converted to watts. Skipping this makes the area 1,000 times too small.
Using a clean-surface U. Fouling lowers U over time. Use a fouled (dirty) U, or add a fouling allowance, so the exchanger still works after months of service.
Skipping the correction factor. For multi-pass or cross-flow exchangers, A = Q / (U × F × LMTD), with F below 1, so the true area is larger.
Inconsistent duty. The hot side and cold side must give the same Q. If they do not, the temperatures or flow rates are inconsistent.
A U value from the wrong service. Gas-side services have U values ten to a hundred times lower than liquid-to-liquid, which changes the area enormously.
No design margin. The result is the theoretical minimum. Add an allowance for uncertainty in U and for future capacity.
Frequently Asked Questions
Where do I get the overall heat transfer coefficient (U)?
U depends on the fluids, the exchanger type, and fouling — it's usually taken from published tables of typical values (like the one above) for a first estimate, or calculated in detail from individual film coefficients and wall/fouling resistances for final design.
Why does a lower U require a much bigger exchanger?
Because A = Q / (U × LMTD) — U sits in the denominator, so halving U doubles the required area for the same duty and LMTD. Gas-side services (low U) often need dramatically more surface area than liquid-side services for the same heat duty.
Does this area include a design margin?
No — this gives the theoretical minimum required area. Real designs typically add 10-20% margin for fouling, uncertainty in U, and future capacity, similar to the margin convention used in pump motor sizing.
What if my exchanger isn't pure counter-current or co-current?
Multi-pass shell-and-tube or cross-flow exchangers need a correction factor F (always ≤ 1) applied as A = Q / (U × LMTD × F). This calculator gives the true counter-current/co-current case; F is found separately from charts based on the exchanger's specific temperature ratios and geometry.
Related Tool
Need to calculate LMTD on its own first? Use the LMTD Calculator — or just switch to "Calculate LMTD from Temps" above.