AixLib.Fluid.MassExchangers.MembraneBasedEnthalpyExchangers.BaseClasses.Functions.CoefficientCrossToCounterFlow

# .AixLib.Fluid.MassExchangers.MembraneBasedEnthalpyExchangers.BaseClasses.Functions.CoefficientCrossToCounterFlow

Calculates coefficient of efficiency of cross flow exchanger to counter flow exchanger based on NTU-method

## Information

This function calculates an coefficient to derive the heat/mass transfer of a cross-flow enthalpy exchanger out of the heat/mass transfer of a counter-flow enthalpy exchanger.

The coefficient calculation is based on the effectiveness correlations for the NTU-Method[1].

The effectiveness of a counter-flow heat exchanger can be expressed as:

ε = (1 - exp[- NTU (1 - Cr )]) ⁄ (1 - Cr exp[- NTU (1 - Cr )])

for (Cr < 1)

ε = NTU ⁄ (1 + NTU)

for (Cr = 1)

With

Cr = (ṁ cp )min ⁄ (ṁ cp )max

The effectiveness of a cross-flow heat exchanger can be expressed as:

ε = 1 - exp[(exp(- NTU 0.78 Cr ) - 1 ) ⁄ (NTU -0.22 Cr )]

By dividing the correlation for the cross-flow heat exchanger through the correlation for the counter-flow heat exchanger it is possible to derive the efficiency of a cross-flow heat exhcanger from the efficiency of a counter-flow heat exchanger.

C = εcross ⁄ εcounter = f(NTU,Cr)

The coefficient C was evaluated for different NTU and Cr . It has shown, that for Cr near to 1 the coefficient can be approximated through a polynom of third degree:

C = -9 · 10 -5 NTU 3 + 0.0023 NTU 2 - 0.0207 NTU + 0.956

[1]: Incropera, F.P.; De Witt, D.P.; Bergman, T. L.; Lavine, A. S. : Fundamentals of Heat and Mass Transfer ; 6th Edition; 2007; John Wiley & Sons, Inc.

#### Interface

>     function CoefficientCrossToCounterFlow
>       input Real NTU "number of transfer units";
>       output Real coeCroCou "coefficient for reduced efficiency in quasi-counter flow";
>     end CoefficientCrossToCounterFlow;

## Revisions

- August 21, 2018, by Martin Kremer:
  First implementation.

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