Choosing a Working Fluid for a Solar Water Heater Loop
A workshop is retrofitting a flat-plate solar collector loop that must deliver heat to a 200 L tank. The pump can supply a pressure head of 12 kPa and the loop has an estimated hydraulic resistance of 3.5 kPa per (L/s)^2. Two candidate fluids are available: water (density 1000 kg/m^3, specific heat 4.18 kJ/kg·K, viscosity 0.001 Pa·s) and a 50% ethylene-glycol mixture (density 1060 kg/m^3, specific heat 3.4 kJ/kg·K, viscosity 0.004 Pa·s). The collector absorbs 1.8 kW. The installer argues the glycol is better because it prevents freezing and is denser, so 'it carries more heat per litre'. A second concern is that the loop must stay turbulent; the tube bore is 10 mm.
1. Determine the achievable volume flow rate with each fluid and decide whether the installer's 'more heat per litre' claim holds for the delivered thermal power.
Read the worked answer
Flow rate from the pump curve. The pump head equals loop resistance at the operating point: 12 = 3.5 Q^2, so Q = sqrt(12/3.5) ≈ 1.85 L/s for both fluids if resistance is taken as identical. Strictly, resistance scales with viscosity for laminar flow, but the dominant losses here are fittings and bends, so treat Q ≈ 1.85 L/s as a first estimate for both.
Heat carried per litre. Volumetric heat capacity is ρc:
- Water: 1000 × 4.18 = 4180 kJ/m^3·K
- Glycol mix: 1060 × 3.4 = 3604 kJ/m^3·K
So per litre the glycol carries less heat, about 14% less, despite being denser. The installer confused density with heat capacity; the specific heat drop outweighs the density gain.
Delivered power. For a fixed ΔT, P = ρcQΔT. With Q fixed by the pump, water delivers 4180/3604 ≈ 1.16 times the power of glycol at the same temperature rise, or reaches the same 1.8 kW with a smaller ΔT. The glycol's real advantage is freeze protection, not thermal transport.
2. Check the Reynolds number for each fluid at the estimated flow and judge whether the turbulence requirement is met.
Read the worked answer
Reynolds number. Re = ρvD/μ, with v = Q/A and A = π(0.005)^2 = 7.85×10^-5 m^2.
At Q = 1.85×10^-3 m^3/s, v = 1.85×10^-3 / 7.85×10^-5 ≈ 23.6 m/s. This is implausibly high for a 10 mm tube and signals the assumed pump head is generous; still, use it to compare fluids.
- Water: Re = 1000 × 23.6 × 0.010 / 0.001 ≈ 2.4×10^5
- Glycol: Re = 1060 × 23.6 × 0.010 / 0.004 ≈ 6.3×10^4
Both exceed the ~4000 transition threshold by a wide margin, so turbulence is satisfied either way. The glycol's fourfold viscosity cuts Re by roughly a factor of four but does not push it into the transitional regime at this flow.
Judgement. The turbulence argument does not decide the choice. If the real flow were much lower (say 0.2 L/s), glycol would approach Re ≈ 7000 and water ≈ 27,000 - still both turbulent, but glycol closer to the margin. The decision should rest on freeze risk versus thermal performance, not on turbulence.