Textile Dye-Bath Heat Recovery Simulator (2D)

Dye-Bath Discharge

Hot wastewater in T_h,in 70 °C

Fresh mains water in T_c,in 15 °C

Heat Exchanger

Flow rate (both streams) 20 L/min

Exchanger size (UA) 2000 W/K

Flow Arrangement

Live Readouts

Heat recovered Q

0.0 kW

Effectiveness ε

0 %

Preheated out T_c,out

0.0 °C

Discharge out T_h,out

0.0 °C

Dye-bath heating energy saved

0 %

Probe (drag the diagram)

—

■ hot wastewater (draining out) ■ fresh water (preheating in)
Drag across the pipe diagram or the temperature graph to probe the local temperature at any point along the exchanger.

How it works

A counter-flow heat exchanger routes hot dye-bath wastewater one way and incoming fresh mains water the other way through a shared thermal core, so the fresh water leaves already warm — cutting the energy the next dye bath needs from its heater. This uses the effectiveness–NTU method with balanced flow (equal mass flow, equal specific heat c_p on both sides, so capacity ratio C_r = 1):

C = ṁ·c_p                 (thermal capacity rate, W/K)
NTU = UA / C               (number of transfer units, same for either arrangement)
Counter-flow:  ε = NTU / (1 + NTU)
Parallel-flow: ε = (1 − e^(−2·NTU)) / 2      (Cr=1 special case; caps at 50%)
Q = ε·C·(T_h,in − T_c,in)
T_c,out = T_c,in + Q/C
T_h,out = T_h,in − Q/C

In the balanced (C_r=1) counter-flow case, the temperature gap between the two streams stays constant along the whole exchanger, so both profiles are straight lines running in opposite directions. Switch to parallel-flow (both streams entering the same end) and the gap instead decays exponentially, e^−2·NTU·x, along the length — the "Compare overlay" toggle draws both on the temperature graph so you can see why counter-flow always recovers more heat for the same hardware.

T_h,in — how hot the dye-bath discharge is (higher-temperature dye processes recover more).
T_c,in — incoming mains water temperature (colder mains → bigger possible gain).
Flow rate — raising it raises C, which lowers NTU and effectiveness ε, but each liter still carries more heat — a real design trade-off (see the small Q-vs-flow curve at the bottom of the diagram).
Exchanger size (UA) — a bigger/better plate exchanger raises UA, raising NTU and effectiveness, at higher capital cost.

Real mills routinely recover 40–60% of dye-bath heating energy this way with counter-flow exchangers, since dyeing and rinsing baths are drained hot (60–90 °C) and immediately refilled with cold mains water for the next batch. Parallel-flow hardware is simpler to plumb but is mathematically capped at 50% effectiveness for balanced streams, however large UA gets — that ceiling is a direct consequence of the exponential decay above, not a hardware limitation.

Hot wastewater Fresh preheated water

Drag anywhere in the diagram or graph to probe a cross-section