Driving Force for Heat Transfer, ΔT: Heat transfer is a strong function of the temperature driving force. This depends on the type and arrangement of heat exchangers. These equations are provided in Table 5.8.

Example 5.9: A hot fluid enters a concentric pipe at a temperature of 300 °F and is cooled by a fluid that enters the heat exchanger at 70 °F and leaves at 190 °F. Calculate the mean temperature difference for the following cases:

(1) Counter-current flow, (2) co-current (parallel) flow, (3) 1-2 Multipass, (4) 2-4 Multipass,

(5) 1-1 Cross-flow, (6) 1-2 Cross Flow heat exchangers.

Solution:

Inlet temperature of hot fluid, T₁ = 300 °F,

Outlet temperature of hot fluid, T₂ = 200 °F,

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

Outlet temperature of cold fluid, t₂ = 190 °F.

(1) Countercurrent Flow:

ΔT at the hot end, Δt_h = T₁ - t₂ = 110 °F,

ΔT at the cold end, Δt_c = T₂ - t₁ = 130 °F

(2) Co-current Flow:

ΔT at the hot end, Δt_h = T₁ - t₁ = 230 °F

ΔT at the cold end, Δt_c = T₂ - t₂ = 10 °F

For other arrangements, a temperature correction factor, F_T, is needed that is based upon two additional parameters R, and S.

$ Temperature correction factor, F_T, (Figure 5.1)

$

$

(3) 1-2 Multipass: F_T = 0.86, ΔT = (0.86)(119.7) = 102.9 °F

(4) 2-4 Multipass: F_T = 0.98, ΔT = (0.98)(119.7) = 117.3 °F

(5) 1-1 Cross-flow: F_T = 0.9, ΔT = (0.9)(119.7) = 107.7 °F

(6) 1-2 Cross-flow: F_T = 0.98, ΔT = (0.98)(119.7) = 117.3 °F