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The mean temperature difference of a plate heat exchanger can be calculated by several different methods, depending on the type of heat exchanger and the specific conditions. A common method is the Logarithmic Mean Temperature Difference. Here's how you can calculate it:

Formula for Logarithmic Mean Temperature Difference

LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)

Variables

• LMTD: logarithmic mean temperature difference
• ΔT1: temperature difference at one end of the heat exchanger
• ΔT2: temperature difference at the other end of the heat exchanger

Example

• Temperature of hot liquid at inlet (Th): 150 °C
• Temperature of cold liquid at inlet (Tc): 30 °C
• Temperature of hot liquid at outlet (Th'): 80 °C
• Temperature of cold liquid at outlet (Tc'): 60 °C

1. Calculation of ΔT1 & ΔT2

ΔT1 = Th - Tc = 150 °C - 30 °C = 120 °C

ΔT2 = Th' - Tc' = 80 °C - 60 °C = 20 °C

2. Calculation of the mean temperature difference

LMTD = (120 °C - 20 °C) / ln(120 °C / 20 °C)

LMTD ≈ 55.8 °C

Q = U * A * LMTD

• Q: heat flow (W)
• U: total heat transfer coefficient (W/m²·K)
• A: heat transfer area (m²)
• LMTD: logarithmic mean temperature difference (K)

or

Q = ṁ * cp * LMTD

• Q: heat flow (W)
• ṁ: mass flow rate (kg/s)
• cp: specific heat capacity (J/kg·K)
• LMTD: logarithmic mean temperature difference (K)

Cocurrent and countercurrent principles
The heat energy that can be transferred in a plate heat exchanger is not only determined by the size of the exchange surface and the heat transfer coefficient (k), but is also significantly influenced by the flow directions of the media involved. If both media flow in the plate heat exchanger in the same direction, this is referred to as the cocurrent principle. If, however, they flow in opposite directions, this is the countercurrent principle.The direction of flow has a significant influence on the average temperature difference between the media, which in turn determines the efficiency of the heat transfer.

Temperature curve with the cocurrent principle | Temperature curve with the countercurrent principle

Theoretical consideration of the connection options for a plate heat exchanger:

In this example, we are assuming two media with the same heat capacity and the same mass flow.

• Medium 1: 80 °C
• Medium 2: 20 °C

With the cocurrent principle, the maximum temperature that can be reached for both media would be 50 °C, which corresponds to the mixing temperature. With the countercurrent principle, however, medium 2 could reach a temperature of up to 80 °C, while medium 1 can be cooled to 20 °C.

This means that with the countercurrent principle, a larger amount of heat can be transferred with the same exchange surface.

Finding the right plate heat exchanger doesn't have to be complicated. If you have any questions or need support, don't hesitate to contact us. We'll be happy to help you choose the right model for your needs.