E5.10 Optimum Water Outlet Temperature

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.