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Q = U·A·LMTD

Heat Exchanger Area
Calculator

Size a heat exchanger from heat duty, overall U, and LMTD, with full step-by-step solutions.

Formula

A=QU×LMTDA = \dfrac{Q}{U \times \text{LMTD}}

Quick Answer

Heat exchanger area sizing comes from Q = U·A·LMTD, rearranged to A = Q/(U·LMTD). Given the heat duty Q, the overall heat transfer coefficient U, and the log mean temperature difference (LMTD, use the LMTD calculator to get this from your four stream temperatures), this calculator solves directly for the required heat transfer area A.

Heat Exchanger Area Calculator

A=QU×LMTDA = \dfrac{Q}{U \times \text{LMTD}}

Don't have your LMTD yet? Get it from the LMTD calculator first.

How to Use the Heat Exchanger Area Calculator

  1. 1

    Get the LMTD

    If you don't already have it, compute the log mean temperature difference from your four stream temperatures using the LMTD calculator.

  2. 2

    Enter the heat duty Q

    Enter the required heat duty Q, the rate of heat that must be transferred between the two streams.

  3. 3

    Enter the overall heat transfer coefficient U

    Enter U, the overall heat transfer coefficient, from equipment data, a correlation, or a typical range for your fluid pairing.

  4. 4

    Enter the LMTD

    Enter the LMTD value and click Calculate to get the required heat transfer area A.

Need the LMTD first? Use the LMTD Calculator, or see the full Heat Transfer topic guide.

What Is Heat Exchanger Area Sizing?

Every heat exchanger design problem eventually asks the same question: how much heat transfer surface area do I need to move a given amount of heat between two streams? The answer combines three quantities, the required heat duty Q, how effectively heat crosses the surface (the overall heat transfer coefficient U), and the average temperature driving force (the log mean temperature difference, LMTD).

This calculator solves the rearranged design equation A = Q/(U·LMTD) directly. If you don't have your LMTD yet, compute it first from your four stream temperatures with the LMTD calculator.

Two large industrial cooling towers at a chemical plant
Heat transfer equipment at plant scale — the area this calculator sizes is a real, purchasable, capital-cost number. Mike Birkenshaw, CC BY-SA 2.0, via Wikimedia Commons.

Derivation: From Rate Equation to Area

The basic heat transfer rate equation states that the total heat duty equals the overall conductance (U·A) times the average driving temperature difference:

Q=UA ΔTlmQ = U A \,\Delta T_{lm}

Since the temperature difference between the two streams varies continuously along the exchanger length (not linearly), the log mean temperature difference is the exact effective average, using it in place of a simple arithmetic mean is what makes this equation valid for the whole exchanger, not just one point along it. Rearranging for the unknown area gives the sizing form:

A=QU×ΔTlmA = \dfrac{Q}{U \times \Delta T_{lm}}

Required Area vs U

A = Q/(U·LMTD) is a hyperbola, not a straight line — for this page's own worked example (Q = 500 kW, LMTD = 40°C), here's how required area actually falls as U improves.

100100052550100200Overall U (W/m²K)Required area A (m²)worked example: A = 25 m²
For Q = 500 kW and LMTD = 40°C, area falls fast at low U (where fouling or gas-side resistance dominates) but flattens out at high U — past a point, a better U barely shrinks the exchanger further.

When You Need This Calculation

  • New exchanger sizing. Given a required heat duty and stream temperatures, this is the first-pass calculation to estimate how large the exchanger must be.
  • Checking an existing exchanger against a new duty. Compare the area an existing unit provides against the area a new, higher heat duty would require.
  • Comparing U estimates. Since required area scales inversely with U, this calculator makes it easy to see how sensitive the design is to your assumed heat transfer coefficient.

Worked Example

Sizing a Shell-and-Tube Exchanger

Problem: A process needs a heat duty Q = 500 kW transferred with an overall heat transfer coefficient U = 500 W/m²K and an LMTD of 40°C. Find the required area.

A=QU×ΔTlm=500,000500×40A = \dfrac{Q}{U \times \Delta T_{lm}} = \dfrac{500{,}000}{500 \times 40}
A=500,00020,000=25 m2A = \dfrac{500{,}000}{20{,}000} = 25\ \text{m}^2

Answer: A = 25 m²

Common Mistakes

  • Using arithmetic mean ΔT instead of LMTD. This overstates the driving force and undersizes the exchanger, always use the log mean temperature difference.
  • Mixing units between Q and U. Q is commonly quoted in kW while U is in W/m²K, convert to consistent units (this calculator converts Q from kW to W internally) before dividing.
  • Ignoring the correction factor for multi-pass exchangers. For shell-and-tube units with multiple tube or shell passes, Q = U·A·F·LMTD needs a correction factor F < 1, or the calculated area will be undersized.
  • Using a clean-surface U for a long-term design. Fouling reduces effective U over time, size with a fouled or design U, not the clean-tube value, unless the exchanger will be cleaned very frequently.

Key Takeaways

  • A = Q/(U·LMTD), the core heat exchanger sizing equation.
  • Get LMTD first from stream temperatures, not an arithmetic average.
  • Required area scales inversely with U, a better estimate of U matters as much as Q.
  • Multi-pass shell-and-tube exchangers need a correction factor F applied to LMTD.
  • Design with a fouled (not clean) U for realistic long-term sizing.

Frequently Asked Questions

U varies widely by fluid pairing and exchanger type: roughly 800–1500 W/m²K for water-to-water, 300–900 W/m²K for water-to-light-organics, 100–300 W/m²K for gas-to-liquid, and as low as 10–50 W/m²K for gas-to-gas exchangers. Always prefer a value from equipment data or a design correlation over a generic table when accuracy matters.

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