The heat exchanger effectiveness is defined as:

Explanation:

The heat exchanger effectiveness is defined as the ratio of actual heat transfer to the maximum possible heat transfer.

\(\epsilon = \frac{{{\rm{Actual\;heat\;transfer}}}}{{{\rm{Maximum\;possible\;heat\;transfer}}}} = \frac{Q}{{{Q_{max}}}}\)

\(NTU = \frac{{UA}}{{{C_{min}}}}\)

NTU is a measure of the effectiveness of the heat exchanger.

The NTU is a measure of the heat transfer size of the exchanger; larger the value of NTU the closer the heat exchanger approaches its thermodynamic limit.

Capacity Ratio:

\(R = \frac{{{C_{min}}}}{{{C_{max}}}}\)

Effectiveness of a parallel flow heat exchanger:

\({\epsilon_{parallel}} = \frac{{1 - \exp \left[ { - NTU\left( {1 + R} \right)} \right]}}{{1 + R}}\)

Effectiveness of a counterflow heat exchanger:

\({\epsilon_{counter}} = \frac{{1 - \exp \left[ { - NTU\left( {1 - R} \right)} \right]}}{{1 - R\exp \left[ { - NTU\left( {1 - R} \right)} \right]}}\)

Therefore effectiveness is the function of both NTU and Capacity Ratio

Important Point:

For condensor and evaporator (R = 0)

In condenser and evaporators in which one fluid remains at constant temperature throughout the exchanger. Here Cmax = ∞ and thus \(R = \frac{{{C_{min}}}}{{{C_{max}}}} = 0\)

By using the above case we arrive at the following common expression for parallel flow as well as counter – flow heat exchangers.

\(\epsilon = 1 - {\rm{exp}}\left( { - NTU} \right)\)