The fig.8.11 shows an important parameter, mc_p, the product of mass flow rate (m) and the specific heat, c_p, of the fluids. The product mc_p is called the rate of heat capacity.
The overall energy balance of the heat exchanger gives the total heat transfer between the fluids, q, expressed by eq.8.5,

(8.5)

The fig.8.11 shows the relative variation of the two fluid temperatures through the heat exchanger, which is influenced by whether  is greater or less than .
In particular, for counter flow, examination of the sketches in fig.8.11 shows that limiting condition for maximum heat transfer is determine by whether  is greater or less than . When, > the maximum possible heat transfer is determined by the fact that the hot fluid can be cooled to the temperature of the cold fluid inlet. Thus, for >

Fig.8.11: Temperature profiles of (a) parallel flow, and (b) counter flow, for different   inequalities

For the other case when the limit is determined as the cold fluid is heated to the inlet temperature of the hot fluid:

For,