Solution Heat Exchanger
The solution heat exchanger (SHX) sits between the generator and the absorber, on the solution circuit only. The weak solution — the stream leaving the generator, high in LiBr and poor in refrigerant (sgp on the generator page) — runs hot from generator to absorber. The rich solution — the stream leaving the absorber, low in LiBr and rich in refrigerant (sgr on the generator page) — runs cold from absorber to generator. The two streams exchange heat in countercurrent flow: the rich solution is preheated before entering the generator, the weak solution precooled before entering the absorber. Both inlet states are fixed by the neighbouring components — generator outlet on the weak side, absorber outlet on the rich side — so this component has no inlet freedom of its own.
Trial calculation: the duty from a given minimum temperature difference
Given the minimum temperature difference ΔTmin, each stream is booked on its own side. On the rich side, the outlet temperature is set against the weak inlet: Trich,out = Tweak,in − ΔTmin; on the weak side, the outlet is set against the rich inlet: Tweak,out = Trich,in + ΔTmin. Each side's enthalpy difference is multiplied by its own flow, giving two duties; the smaller of the two is the heat this exchanger transfers, Qshx. All enthalpies are computed server-side by the site's LiBr–water library (Patterson hsol).
| Outlet T (°C) | hin (kJ/kg) | hout (kJ/kg) | Δh (kJ/kg) | Duty (kW) | |
|---|---|---|---|---|---|
| Rich side | 78.00 | 88.67 | 174.58 | 85.91 | 15.66 |
| Weak side | 37.76 | 185.28 | 101.97 | 83.31 | 14.56 |
Qshx = 14.56 kW — the smaller duty, on the weak side
Difference between the two duties = 1.10 kW (shown as computed; not reconciled, not averaged)
Rich side: Δhrich = h(Trich,out, ξrich) − h(Trich,in, ξrich), Qrich = ṁrich·Δhrich. Weak side: Δhweak = h(Tweak,in, ξweak) − h(Tweak,out, ξweak), Qweak = ṁweak·Δhweak. Qshx = min(Qrich, Qweak), decided by the numbers. Solution enthalpy: Patterson hsol of this site's library, on the same reference as the generator page (saturated liquid water at 0 °C has h = 0). Inputs outside the fitted range of hsol return the range and no number — nothing is extrapolated.
1. The booking principle
Given the minimum temperature difference, each stream's enthalpy difference at that difference is computed on its own side, multiplied by its own flow — two duties come out, and the smaller one is the heat this solution heat exchanger transfers:
- Fix each outlet from the other stream's inlet: Trich,out = Tweak,in − ΔTmin and Tweak,out = Trich,in + ΔTmin.
- Look up both enthalpies of each stream with hsol at its own concentration.
- Form each side's enthalpy difference: Δhrich across the rich stream, Δhweak across the weak stream.
- Multiply by the stream's own flow: Qrich = ṁrich·Δhrich, Qweak = ṁweak·Δhweak.
Qshx = min(Qrich, Qweak)
With the minimum temperature difference given, the duty is therefore not an independent unknown of the model: both inlet states are fixed by the generator and the absorber, ΔTmin pins both outlets, and the two enthalpy balances follow. The two duties generally differ — here by 1.10 kW on duties of 14.56 and 15.66 kW — because each outlet is pinned on its own side and the two streams have different flows and different enthalpy–temperature slopes; the difference is printed as computed, not reconciled away.
2. Formulas and basis
Trich,out = Tweak,in − ΔTmin ; Qrich = ṁrich [ h(Trich,out, ξrich) − h(Trich,in, ξrich) ]
Tweak,out = Trich,in + ΔTmin ; Qweak = ṁweak [ h(Tweak,in, ξweak) − h(Tweak,out, ξweak) ]
- Solution enthalpy h: the Patterson & Perez-Blanco (1988) polynomial set of this site's LiBr–water library (hsol), reference state saturated liquid water at 0 °C, h = 0 — the same basis as the generator page.
- ξ is the LiBr mass percent (58.07 means 58.07 wt%), temperatures in °C, flows in kg/s, duties in kW.
- The ΔTmin = 5 K defaults in the literature sit on the rich side's definition used here — between the entering weak solution and the leaving rich solution: Wang & Infante Ferreira (2016) assume a 5 K minimum temperature difference; Abumandour (2015) likewise places 5 K between the hot-stream inlet and the cold-stream outlet.
3. Other bookings, in one line
An effectiveness-given booking pins the duty just as completely, by another handle; only a UA-given or ε-NTU booking leaves the duty to float with the operating point, because there the hardware — area and coefficient — is what is given.