Sizing and calculating a plate heat exchanger: formula, k value and practice

Sizing a plate heat exchanger means determining the right plate area and the right plate profile for a specific thermal task. This guide shows the governing equation, puts realistic k values into context and names the most common mistakes in the calculation.

What does sizing mean?

Sizing means meeting three requirements at the same time: transferring the required heat duty, staying within the permissible pressure drop, and remaining inside the allowable pressure and temperature limits. The first step is always the required heat duty. It follows from the mass flow rate, the specific heat capacity and the temperature spread of a medium:

Q = m_dot * cp * dt

Here Q is the heat duty in watts, m_dot the mass flow rate in kg/s, cp the specific heat capacity in J/(kg*K), and dt the temperature spread in kelvin. This duty is the target the unit must deliver.

How does the governing equation Q = k * A * dt_log work?

How much area is needed for it is described by the central sizing equation:

Q = k * A * dt_log

The individual quantities mean:

• Q - heat duty to be transferred, in W
• k - overall heat transfer coefficient (k) in W/(m^2*K)
• A - heat transfer area in m^2
• dt_log - logarithmic mean temperature difference in K

The logarithmic mean temperature difference dt_log is the correct averaging of the driving temperature difference between the hot and cold medium across the entire area. It is formed from the temperature differences at both ends of the unit:

dt_log = (dt1 - dt2) / ln(dt1 / dt2)

dt1 and dt2 are the temperature differences between the media at each end. Important: in counterflow dt_log turns out larger than in parallel flow. A larger dt_log means less required area for the same duty - so counterflow is the standard. Solved for A, the required area is A = Q / (k * dt_log).

Which k-values are realistic?

The k value is the most uncertain quantity in the equation, because it depends on the medium, the flow, fouling and the plate profile. The following ranges serve as a rough orientation for plate heat exchangers:

Media pairing	k value in W/(m^2*K)
Water / water	3000 - 7000
Water / oil	500 - 1500
Steam / water	4000 - 8000
Gas / gas (low pressure)	50 - 200

These are guideline values. Fouling, low flow velocities and high viscosities can lower the k value considerably. For a binding sizing the k value must be calculated from fluid data and plate geometry.

Worked example: 250 kW substation

A heating circuit requires 250 kW at 60/40 degrees Celsius, supplied from a district heating network with 80 degrees supply and 50 degrees return. The sizing in four steps:

Step 1 - mass flows. From Q = m_dot * cp * dt the secondary side gives m_dot = 250000 / (4190 * 20) = 3.0 kg/s (around 11 m^3/h), the primary side with a 30 K spread m_dot = 250000 / (4190 * 30) = 2.0 kg/s (a good 7 m^3/h). Different flow rates on the two sides are unproblematic for plate units.

Step 2 - logarithmic mean temperature difference. In counter-current flow the hot supply meets the warm outlet: at the hot end dt1 = 80 - 60 = 20 K, at the cold end dt2 = 50 - 40 = 10 K. This gives:

dt_log = (20 - 10) / ln(20 / 10) = 14.4 K

The arithmetic mean would be 15 K - the logarithmic mean is lower and is the correct basis.

Step 3 - area. For water/water with a fouling margin, a conservative k = 3500 W/(m^2*K) is assumed:

A = 250000 / (3500 * 14.4) = 5.0 m^2

Step 4 - plate count. With an effective area of about 0.25 m^2 per plate, this yields around 20 heat-transferring plates. In practice the next larger pack is chosen and the pressure drop is then cross-checked - the guide Determining pressure drop and plate count shows how.

How are temperature spread and flow rate related?

Temperature spread and flow rate are linked directly through the duty equation. If the spread is increased for the same duty, the required mass flow drops - and with it the flow rate. A smaller flow rate reduces the pressure drop, which saves pump energy.

A very small spread, by contrast, forces high flow rates, drives the pressure drop up and can demand large units. At the same time the flow velocity must not become too low, or turbulence collapses and the k value falls. Sizing is therefore always a trade-off between spread, flow rate, pressure drop and area - within the limit set by the unit’s nominal pressure.

Which mistakes are most common in sizing?

In practice the same mistakes repeatedly lead to wrongly dimensioned units:

• Arithmetic instead of logarithmic mean: anyone calculating with the simple average of the temperature differences instead of dt_log overestimates the driving difference and sizes the unit too small.
• k value too optimistic: table values without a fouling and flow reserve regularly lead to undersizing.
• Parallel flow assumed: assuming counterflow but connecting in parallel flow loses driving temperature difference and capacity.
• Pressure drop ignored: a thermally correct sizing is useless if the pressure drop overwhelms the pump.
• Fluid data at the wrong temperature: cp and viscosity change with temperature; outdated or blanket values distort the calculation.

Avoiding these points and calculating with realistic k values and the correct dt_log leads to a robust sizing.

How do you get your own sizing quickly?

Instead of solving the equations by hand, you can enter your key data directly online and have a suitable plate heat exchanger sized for you.