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Calcimator

Heat Exchanger Duty Calculator

Calculate heat exchanger duty using the Log Mean Temperature Difference (LMTD) method: Q = U × A × ΔTlm for counter-current or parallel flow.

About this calculator

Computes heat exchanger duty using the classic Q = U × A × ΔTlm relationship, where the log mean temperature difference (LMTD) captures how the temperature gap between hot and cold streams changes as they move through the exchanger. The calculator handles both counter-current flow (hot and cold streams moving in opposite directions, where ΔT1 is the hot-inlet/cold-outlet gap and ΔT2 is the hot-outlet/cold-inlet gap) and parallel/co-current flow (both streams entering the same end), which changes which temperature pairs define the two end-approach differences. LMTD itself is (ΔT1 − ΔT2)/ln(ΔT1/ΔT2); when the two approach temperatures are nearly equal the formula is numerically unstable (dividing by a near-zero log), so the calculator falls back to using ΔT1 directly, which is the correct limiting value from L'Hôpital's rule.

Duty is reported in kW, W, and BTU/hr for convenience. The overall heat transfer coefficient U is the single biggest source of uncertainty in any real exchanger duty estimate — it depends heavily on fluid properties, fouling, and exchanger geometry, so the helpText ranges given (800-1500 W/m²K for water-water, much lower for gas-gas service) are only starting points, not substitutes for vendor data or a fouled-condition design margin. Note that counter-current arrangements always achieve a higher LMTD than parallel flow for the same four terminal temperatures, which is why counter-current is preferred whenever the process allows it — this calculator will show that difference if you toggle the flow arrangement with the same four temperatures.

Inputs

Results

LMTD (°C)

72.24

Heat duty (kW)

361.2

Heat duty (BTU/hr)1,232,476
ΔT₁ (°C)80
ΔT₂ (°C)65
Heat duty (W)361,203
Effectiveness NTU1
How to Use This Calculator
  1. Enter Hot fluid inlet temperature (°C), Hot fluid outlet temperature (°C), and Cold fluid inlet temperature (°C).
  2. Set Cold fluid outlet temperature (°C), Overall heat transfer coefficient U (W/m²·K), and Heat transfer area (m²).
  3. Select the Flow arrangement (counter-current or parallel) as needed.
  4. Review LMTD (°C) and Heat duty (kW).
  5. Use Heat duty (BTU/hr) and ΔT₁ (°C) to inform your decision.

How the result changes with Hot fluid inlet temperature (°C)

Hot fluid inlet temperature (°C)LMTD (°C)Heat duty (kW)
7523.39116.96
11353.24266.22
225103.56517.81
375155.25776.23

What each input means

Hot fluid inlet temperature (°C)
Temperature of the hot stream entering the exchanger.
Hot fluid outlet temperature (°C)
Temperature of the hot stream leaving the exchanger.
Cold fluid inlet temperature (°C)
Temperature of the cold stream entering the exchanger.
Cold fluid outlet temperature (°C)
Temperature of the cold stream leaving the exchanger.
Overall heat transfer coefficient U (W/m²·K)
Typical values: water-water 800-1500, steam-water 1000-6000, gas-gas 10-50 W/(m²·K).
Heat transfer area (m²)
Total effective heat transfer surface area.
Flow arrangement
The relative direction of hot and cold fluid flow through the exchanger.

What each result means

LMTD (°C)
Log Mean Temperature Difference driving the heat exchange.
Heat duty (kW)
Total heat transfer rate Q = U × A × LMTD.
Heat duty (BTU/hr)
Duty converted to imperial units.
ΔT₁ (°C)
Temperature approach at one end of the exchanger.
ΔT₂ (°C)
Temperature approach at the other end.
Heat duty (W)
Duty in Watts.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Hot fluid inlet temperature (°C) = 150, Hot fluid outlet temperature (°C) = 90, Cold fluid inlet temperature (°C) = 25, Cold fluid outlet temperature (°C) = 70 = 7 input(s) provided
  2. Calculate LMTD
    LMTD
    72.24 = 72.24
  3. Calculate Heat duty
    Heat duty = dutyW / 1000
    361.2 = 361.2
  4. Calculate Heat duty
    Heat duty = dutyW * 3.41214
    1232476 = 1232476
  5. Calculate ΔT₁
    ΔT₁
    80 = 80

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does switching from counter-current to parallel flow change the result with the same four temperatures?

The flow arrangement changes which temperature pairs define the two end-approach differences: counter-current pairs the hot inlet with the cold outlet and the hot outlet with the cold inlet, while parallel flow pairs both inlets together and both outlets together. Because LMTD is a nonlinear function of those two approach differences, counter-current always produces a higher LMTD (and therefore a higher duty for the same U and A) than parallel flow given identical terminal temperatures.

What happens when the hot and cold approach temperatures are nearly equal?

The LMTD formula (ΔT1 − ΔT2)/ln(ΔT1/ΔT2) becomes a 0/0 division as ΔT1 approaches ΔT2, which would produce a numerically unstable result. The calculator detects when the two are within 0.01°C of each other and falls back to using ΔT1 directly, which is the mathematically correct limiting value per L'Hôpital's rule, not an approximation.

Why is the overall heat transfer coefficient U the biggest source of uncertainty here?

U depends on the fluid properties on both sides, the exchanger's exact geometry, and fouling buildup over time — none of which this calculator can know from four temperatures and an area alone. The helpText ranges (roughly 800–1500 W/m²K for water-water, far lower for gas-gas service) are only rough starting points; a real design should use vendor or fouled-condition data rather than these defaults.

Can this calculator size the exchanger instead of just checking duty?

Not directly — it takes U and area as inputs and solves for duty (Q = U·A·LMTD), so to back out a required area for a target duty you'd rearrange the same formula (A = Q/(U·LMTD)) using the LMTD this tool computes for your chosen flow arrangement and temperatures. It doesn't perform that reverse calculation automatically.

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