Heat exchanger calculation

The formulas behind a heat exchanger calculation

If you want to check the numbers yourself, four formulas are all you need. They belong together: the capacity follows from the flow rate and the temperature difference, and that capacity, together with the temperature difference across the exchanger, determines how much plate surface area you need. Below they are listed in the order you use them in practice. For readability, water is used as the medium.

Calculating heat exchanger capacity

The capacity of a heat exchanger is the heat flow it transfers, expressed in kW. The formula is Q = m × cp × ΔT: the mass flow rate times the specific heat times the temperature difference. For water you can work with the volume flow rate, which is quicker:

Q (kW) = flow rate (m³/h) × 1.163 × ΔT (K)

The factor 1.163 comes from the specific heat of water (4.186 kJ/kg·K) times the density (1,000 kg/m³), divided by 3,600 seconds per hour. If you work with a glycol mixture, the specific heat and density are different and that factor changes; in that case pass on the mixing percentage and we will calculate with the correct values.

Calculating heat exchanger duty

The duty of a heat exchanger is the same quantity as the capacity, only approached from your installation: how many kW need to be removed or added? If you already know the duty, you turn the formula around and work back to the required flow rate or temperature difference.

Flow rate (m³/h) = Q (kW) ÷ (1.163 × ΔT) and ΔT (K) = Q (kW) ÷ (1.163 × flow rate)

An example. For 120 kW at a difference of 10 K you need 120 ÷ (1.163 × 10) ≈ 10.3 m³/h. The same method applies when calculating the duty of a plate heat exchanger — the type of exchanger does not change the energy balance, only the required surface area.

Calculating heat exchanger efficiency

The efficiency of a heat exchanger, also called the effectiveness, is the ratio between the temperature change you actually achieve and the maximum possible change. That maximum change is the difference between the two inlet temperatures.

ε = (T hot in − T hot out) ÷ (T hot in − T cold in)

An exchanger that brings water from 80 °C down to 50 °C while the cold side enters at 20 °C achieves (80 − 50) ÷ (80 − 20) = 0.50. The closer you want to get to 1, the more plate surface area it costs — efficiency is therefore mainly a design choice, not a property of the device.

Calculating heat exchanger surface area

The required plate surface area follows from the duty, the heat transfer coefficient and the mean temperature difference across the exchanger:

A (m²) = Q ÷ (U × ΔT log)

Here A is the surface area, U the heat transfer coefficient in kW/m²·K and ΔT log the logarithmic mean temperature difference (see below). The U-value is the tricky one: it depends on the medium, the flow velocity, the plate geometry and the degree of fouling, and cannot simply be taken from a table. The selection software contains that value per plate type; that is why the final step of a heat transfer calculation runs through the sizing tool or through us in practice.

Counter-flow heat exchanger calculation

In a plate heat exchanger the two media run in counter-flow: they move towards each other instead of alongside each other. That keeps the temperature difference roughly constant along the entire length and yields a higher mean difference than parallel flow, so you need less surface area. You calculate the mean difference like this:

ΔT log = (ΔT1 − ΔT2) ÷ ln(ΔT1 ÷ ΔT2)

ΔT1 and ΔT2 are the temperature differences at the two ends of the exchanger. In counter-flow, ΔT1 is the difference between the hot inlet and the cold outlet, and ΔT2 the difference between the cold inlet and the hot outlet. If both differences are equal, ΔT log equals that difference and you do not need the logarithm.

Calculate a heat exchanger without an Excel file

Those who calculate regularly usually reach for a spreadsheet. That is not necessary here: you do not need an Excel file to calculate a heat exchanger, because the calculation aid on this page does the same work. You enter the temperatures, the flow rate and the required capacity and immediately see the temperature difference, the logarithmic mean and the required surface area.

So if you are looking for a heat exchanger calculation in Excel, you can skip that step and calculate right here. The result gives a good first indication for sizing. For the final selection of a type we are happy to look at it with you, because the heat transfer coefficient differs per plate type.

Calculating a plate heat exchanger: where the type makes the difference

The energy balance above applies to every heat exchanger. The difference lies in the final step: how many plates do you need, and which model. Calculating a plate heat exchanger in practice means translating the required surface area into a number of plates of a particular type — while staying within the permitted pressure drop. More plates means more surface area, but also a different flow velocity and therefore a different pressure drop.

With a gasketed model you can add plates later if the capacity falls short; with a brazed model the number of plates is fixed. That makes the upfront calculation more important for a brazed exchanger.

From calculation to quotation

Once your calculation is complete, the rest is short: pass on the calculated capacity and the connection size, and we will send a quotation within one working day with the model and its availability. If you have doubts about the outcome or the model, our specialists will take a look with you — call +31 (0)162 429 068 or request heat exchanger advice.