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# 6.10 Heat flux in evaporators

A brazed plate heat exchanger is designed as an evaporator in SSP, the SWEP calculation program. The software calculates the film coefficients and the pressure drops from correlations describing the phenomena. An overall heat transfer coefficient is calculated, and the required heat surface is decided. The required area and the pressure drop limitations, together with the economic aspects, determine the heat exchanger model and the number of plates the duty requires. A simple way of evaluating different design calculations is to compare the heat flux of the brazed plate heat exchangers. Heat flux can be regarded as the heat exchanger's density of heat transfer, and is defined as the heat flow per heat transfer surface: This equation is derived from the heat flow equation. The heat flow in a heat exchanger is: In chapter 1.5, the LMTD (logarithmic mean temperature difference) was introduced for single-phase calculations. The reason for using a logarithmic mean value is the logarithmic characteristics of the temperature profiles in a single-phase heat transfer process. In two-phase calculations, a so-called MTD must be used. The calculation of MTD is not shown in this handbook, because it is too difficult to calculate manually.

The k-value depends on the brazed plate heat exchanger characteristics and the flow profile inside the channels. Correlations integrated in SSP calculate the k-value for the temperature program used to design the brazed plate heat exchanger. For a given heat transfer surface, the k-value determines the temperature difference needed. A high k-value results in a closer temperature program, and a lower k-value means a higher temperature difference is needed.

A higher k-value means that a lower temperature difference is required between the refrigerant and secondary fluid. However, the mean temperature difference is often difficult to determine practically. An easier way of showing the difference in operating systems is to use the difference between the leaving secondary fluid temperature and the evaporating temperature (LWT - TEVAP) (see Figure 6.49).

The characteristics of the brazed plate heat exchanger are predicted from the correlations in SSP. The k-value depends on the heat transfer media and the turbulence of the flow. It is easy to see from the heat flux equation that a larger temperature difference (LWT - TEVAP) is required to achieve a higher heat flux in a pre-defined brazed plate heat exchanger. Figure 6.50 shows a typical curve of the heat flux as a function of (LWT - TEVAP).

Figure 6.50 shows the typically sloped performance curve. The temperature difference between the evaporating medium and the secondary fluid increases with increased heat transfer per m2 (heat flux). The slope is unique for each heat exchanger and refrigerant, as discussed below.

## The influence of heat exchanger characteristics

The physical dimensions of the heat exchanger influence the film coefficient and thus the heat flux. The hydraulic diameter is twice the pressing depth, and will affect the flow because a smaller hydraulic diameter increases the k-value and also the pressure drop. The corrugation angle may be in a specific range, approximately 30-80°. The larger the angle, the higher the film coefficient becomes, but a larger angle will also cause a higher pressure drop.

## The influence of evaporating fluid

The physical properties of refrigerant fluids differ between the liquid and vapor phases. Due to the differences in physical properties, the film coefficient and the heat flux will vary. Some important parameters are: The easiest way of comparing the heat flux between different refrigerants is by using the heat flux diagram, similar to Figure 6.50. The different physical properties of R22, R404A and R134a require more or less heat surface area to achieve the same performance. Figure 6.51 shows SSP calculations to reach an evaporation temperature of 2°C (corresponding to LWT - TEVAP = 5).

As Figure 6.51 shows, R404A would need less area than R22 or R134a. For the same evaporation temperature (2°C), the heat flux is higher: 12 kW/m2 compared with 9.5 kW/m2 and 8.8 kW/m2 for R22 and R134a, respectively.