Sizing a heat exchanger is not guesswork. It is a sequence of calculations that starts with the duty and ends with a surface area. Get the steps right, and the unit performs. Skip a step, and you oversize, undersize, or miss the fouling that kills performance.
This guide walks through the core calculations: heat duty, flow rate, temperature difference (LMTD), overall heat transfer coefficient (U), and area. It also covers the practical checks that decide whether the design works in the real plant.
The Core Equation
Every heat exchanger sizing calculation comes back to one equation:
Q = U × A × LMTD
Where:
Q = heat duty (W or BTU/hr)
U = overall heat transfer coefficient (W/m²·K or BTU/hr·ft²·°F)
A = heat transfer area (m² or ft²)
LMTD = log mean temperature difference (K or °F)
You need Q, U, and LMTD to find A. Each one requires its own calculation.
Step 1: Calculate the Heat Duty (Q)
The duty is the amount of heat added or removed. It comes from the process stream.
Q = m × Cp × ΔT
Where:
m = mass flow rate (kg/s or lb/hr)
Cp = specific heat (J/kg·K or BTU/lb·°F)
ΔT = temperature change of the stream (°C, K, or °F)
Example: Cool 10 kg/s of oil from 120°C to 60°C. Cp = 2.0 kJ/kg·K.
Q = 10 × 2.0 × (120 − 60) = 1,200 kW
If you know the flow in volume instead of mass, multiply by density:
m = ρ × V
Where ρ is density (kg/m³) and V is volumetric flow (m³/s).
Step 2: Determine Flow Rates and Temperature Changes
The duty must balance on both sides. The hot side loses heat. The cold side gains it.
Q_hot = Q_cold
So:
m_hot × Cp_hot × ΔT_hot = m_cold × Cp_cold × ΔT_cold
Use this to find the unknown flow or temperature change.
Example: The oil duty is 1,200 kW. Cooling water enters at 25°C and leaves at 45°C. Cp_water = 4.18 kJ/kg·K.
m_water = Q / (Cp × ΔT) = 1,200 / (4.18 × 20) = 14.35 kg/s
If you know the water flow but not the outlet temperature, rearrange the equation.
Key point: You need at least three of the four terminal temperatures and one flow rate to start. If you have less, assume or measure.
Step 3: Calculate the Temperature Difference (LMTD)
The driving force for heat transfer is not the arithmetic average of the temperature differences. It is the log mean temperature difference.
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂)
Where ΔT₁ and ΔT₂ are the temperature differences at each end of the exchanger.
For counter-current flow:
ΔT₁ = T_hot_in − T_cold_out
ΔT₂ = T_hot_out − T_cold_in
Example: Hot oil 120°C → 60°C. Cold water 25°C → 45°C.
ΔT₁ = 120 − 45 = 75°C
ΔT₂ = 60 − 25 = 35°C
LMTD = (75 − 35) / ln(75/35) = 40 / ln(2.143) = 40 / 0.762 = 52.5°C
If the flow is not pure counter-current, multiply LMTD by a correction factor F. F is typically 0.8–0.95 for shell and tube, and close to 1.0 for plate heat exchangers. Always check the F factor for your configuration. If F is below 0.75, the design is inefficient. Consider more passes or a different type.
Never use arithmetic average ΔT for sizing. It overestimates performance and leads to undersized units.
Step 4: Estimate the Overall Heat Transfer Coefficient (U)
U is the hardest number to pin down. It depends on both fluids, the materials, and the fouling.
1/U = 1/h_hot + 1/h_cold + R_fouling + R_wall
Where:
h = individual film coefficient (W/m²·K)
R_fouling = fouling resistance (m²·K/W)
R_wall = wall resistance (usually small for thin metal)
Film coefficients depend on velocity, viscosity, density, and thermal conductivity. They are calculated from correlations like Dittus-Boelter for turbulent flow.
For practical sizing, use typical U-values from experience or supplier data:
| Service | Typical U (W/m²·K) |
|---|---|
| Water-to-water | 800–1,500 |
| Oil-to-water | 200–600 |
| Oil-to-oil | 100–300 |
| Steam-to-water | 1,000–2,000 |
| Gas-to-gas | 20–100 |
| Plate heat exchanger, water | 3,000–7,000 |
Always add fouling resistance. TEMA gives typical fouling factors:
Clean water: 0.0001–0.0002 m²·K/W
Cooling tower water: 0.0003–0.0006
Hydrocarbons: 0.0002–0.0005
Steam: 0.0001
If you ignore fouling, the unit will be undersized from day one.
Step 5: Calculate the Heat Transfer Area (A)
Rearrange the core equation:
A = Q / (U × LMTD)
Using the example: Q = 1,200,000 W, U = 400 W/m²·K, LMTD = 52.5 K.
A = 1,200,000 / (400 × 52.5) = 57.1 m²
Add a margin for uncertainty. A typical design margin is 10–20% on area. But do not over-margin. Too much area lowers velocity and promotes fouling.
A = 57.1 × 1.15 = 65.7 m²
Now you have the required surface area. The next step is selecting a heat exchanger that provides that area within the pressure drop, velocity, and space limits.
Step 6: Check Velocity, Pressure Drop, and Fouling
Area alone does not make a good design. You must check the hydraulics.
Velocity:
Too low causes fouling. Too high causes erosion and high pressure drop.
Typical tube-side velocities:
Water-like fluids: 1.5–2.5 m/s
Oils: 0.9–1.8 m/s
Gases: 10–30 m/s
Pressure drop:
Calculate or estimate. If ΔP is too high, you may need more parallel passes, larger tubes, or a different type.
Fouling:
Check that the fouling factor you used matches the actual service. If fouling is severe, consider a design with cleaning access or higher velocity.
Flow distribution:
In plate heat exchangers, ensure even flow across plates. In shell and tube, check baffle spacing and nozzle sizes.
Example Calculation Summary
| Step | Value |
|---|---|
| Heat duty Q | 1,200 kW |
| Hot side | Oil, 120°C → 60°C |
| Cold side | Water, 25°C → 45°C |
| LMTD | 52.5 K |
| U (assumed) | 400 W/m²·K |
| Area required | 57.1 m² |
| Area with 15% margin | 65.7 m² |
| Water flow | 14.35 kg/s |
This is a starting point. A real design would refine U with actual film coefficients, check pressure drop, and select a standard model.
Common Mistakes in Heat Exchanger Sizing
Using arithmetic ΔT instead of LMTD
This overestimates performance and undersizes the unit.
Ignoring fouling
The unit works when clean and fails when fouled. Always include fouling resistance.
Using a single U-value for all conditions
U changes with flow, temperature, and fouling. Use a realistic range and verify.
Forgetting the correction factor F
For multi-pass shell and tube, LMTD must be multiplied by F. If F is low, the design is poor.
Oversizing
Extra area lowers velocity, which increases fouling. It also costs more. Size for the duty plus a reasonable margin.
Not checking pressure drop
A unit that meets the thermal duty but has excessive ΔP is not a good design.
Neglecting viscosity changes
Viscosity changes with temperature. Cold startup can have much higher pressure drop and lower U.
Assuming constant Cp
Cp varies with temperature. For wide ranges or phase change, use average or integrated values.
FAQ
What is LMTD and why is it used?
LMTD is the log mean temperature difference. It represents the average driving force for heat transfer in a heat exchanger. It is used because the temperature difference changes along the flow path.
How do I calculate the heat transfer area?
Area = Q / (U × LMTD). You need the duty, overall heat transfer coefficient, and LMTD.
What is a typical U-value for a heat exchanger?
It depends on the fluids. Water-to-water: 800–1,500 W/m²·K. Oil-to-water: 200–600. Plate heat exchangers: 3,000–7,000. Always confirm with actual fluid properties.
How do I calculate flow rate?
From the heat duty: m = Q / (Cp × ΔT). If you know the flow, use it to find the temperature change.
What is the correction factor F?
F accounts for non-counter-current flow in multi-pass or cross-flow heat exchangers. LMTD is multiplied by F. If F < 0.75, the design is inefficient.
How much fouling factor should I use?
Use TEMA or plant data. Clean water: 0.0001–0.0002 m²·K/W. Cooling tower water: 0.0003–0.0006. Hydrocarbons: 0.0002–0.0005.
Can I size a heat exchanger without a computer?
Yes, for simple cases. Use the formulas here. For complex designs, phase change, or multi-pass, use software or supplier support.
Bottom Line
Heat exchanger sizing comes down to four numbers: duty, flow, temperature difference, and U-value. Get those right, and the area calculation is straightforward.
Calculate Q. Determine flows and temperatures. Find LMTD. Estimate U with fouling. Calculate area. Check velocity and pressure drop. Then select the type that fits the service.
If you are sizing a heat exchanger and want a second check, send your flow rates, temperatures, fluid properties, and duty. We will help you verify the area, U-value, and pressure drop—and recommend a design that performs in the real plant, not just on paper.