Presets
Playback
Fan, pump and load
Fan speed sets the air capacity rate and the air-side conductance, the pump sets the coolant capacity rate. The smaller capacity rate limits the heat that can be moved, and fouled fins cut the conductance.
Model checks
The science
What is modelled
A cross-flow radiator with both streams unmixed moves heat from the hot coolant to the air. Its effectiveness depends on the number of transfer units NTU = UA / Cmin and on the capacity-rate ratio Cr = Cmin / Cmax. The loop has a lumped thermal mass, so the coolant temperature rises exponentially to the level where the radiator rejects exactly the heat load.
Equations
- Capacity rates
C = ṁ cp;ε = 1 - exp[(NTU0.22/Cr)(exp(-Cr NTU0.78) - 1)]. - Heat rejected
Q = ε Cmin (Thot - Tamb), steadyThot = Tamb + Q/(ε Cmin). - Warm-up
Cth dT/dt = Q - ε Cmin (T - Tamb), time constantCth/(ε Cmin). - Conductance
UA ∝ (ṁair)0.65 (ṁcoolant)0.2 (1 - fouling).
Checks run in the page
- Steady-state energy balance on both streams.
- The correlation against a 40 x 40-cell numerical cross-flow solution.
- The Cr = 0 limit.
- The warm-up transient against its exponential solution.
Honest simplifications
Constant fluid properties, a single lumped coolant thermal mass, a plausible but illustrative conductance law, a fixed cold-plate resistance, no pressure-drop matching of the pump and fan curves (the fan power shown follows the cube law) and no condensation. The loop is not a validated design of any real cooling assembly.
What to try
- Press Fan failure and watch the source climb past the 85 C limit while the time constant stretches.
- Press Pump failure: the coolant capacity rate becomes the limit instead.
- Press Hot day, fouled fins to see the margin disappear.