General design equations. Dimensionless groups

The first law of thermodynamics is applied to for both fluids. The heat transferred causes an enthalpy increase in the cold fluid 2 and a decrease in the warm fluid 1. This gives 

The two fluids flow through the heat exchanger without undergoing a phase change, i.e. they do not boil or condense. The small change in specific enthalpy with pressure is neglected. Therefore only the temperature dependence is important, and with 

As an abbreviation the heat capacity flow rate is introduced by 

The temperature changes in both fluids are linked to each other due to the first law of thermodynamics. They are related inversely to the ratio of the heat capacity flow rates. 

These belong to only two types of quantity either temperature (unit K) or heat capacity flow rate (units W/K). According to section 1.1.4, that leaves four (= 6 — 2) characteristic quantities to be defined. These are the dimensionless temperature changes in both fluids 

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This general equation involves the use of four dimensionless groups, although it may frequently be simplified for design purposes. In equation 9.56 ... 

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