Optimum Outlet Temperature:  This is the temperature of an exchanger at its highest efficiency of operation.  It can be found as follows:

 

Example 5.10:  What is the water outlet temperature that could reasonably be obtained, and the heat that could reasonably be recovered from a co-current exchanger, counter-current exchanger, and 1-2 heat exchanger?  Use the following information.

 

Inlet temperature of hot fluid, T1 = 350 °F,

Inlet temperature of cold fluid, t1 = 70 °F,

Specific heat of hot fluid, C = 1 Btu/(lb·°F),

Specific heat of cold fluid, c = 1 Btu/(lb·°F),

Mass flow rate of hot fluid, W = 10000 lb/hr,

Mass flow rate of cold fluid, w = 20000 lb/hr

 

Solution:   For the given situation, R, can be found as

 

 

(1)    Co-current arrangement: A practical approach at the outlet of the exchanger cannot be less than 5 degrees or Δt = T2 - t2 = 5 °F.

 

$                 t2:

 

 

$                 Outlet temperature of hot fluid, T2 = t2 + Δt = 166.7 °F.

$                  

$                 Heat transfer rate, Q1:

 

 

 

(2) Counter-current arrangement: In this arrangement practical approach cannot be less than 10 degrees or T2 - t1 = 10 °F. 

 

$                 Outlet temperature of hot fluid, T2 = 70 + 10 = 80 °F.  

$                 Outlet temperature of cold fluid, t2:

 

 

$                 Heat transfer rate, Q2 (5.31 or 5.32) = 2.7´106 Btu/hr

 

(3) 1-2 heat exchanger, given R = 2, Use Figure 5.21 to obtain P

$                 P = 0.375 (Fig 5.21)

$                 Outlet temperature of cold fluid, t2:

 

 

$                 Outlet temperature of hot fluid, T2:

 

 

$                 Heat transfer rate, Q3 = (5.31 or 5.32) = 2.1´106 Btu/hr

 

The value of Q is the highest for a counter-current arrangement, Q1.