Capacity Rate Ratio (Cr)

Heat capacity rate, C = ṁcₚ in watts per kelvin, is how much heat a stream absorbs for each degree it warms. Divide the smaller by the larger and you get Cr, which by construction runs from 0 to 1 and controls how effectiveness responds to size. Example: 1.2 kg/s of air (cₚ ≈ 1005) is 1206 W/K; 0.8 kg/s of water (cₚ ≈ 4186) is 3349 W/K; Cr = 0.36, and the air, despite the higher flow, is the limiting stream, because water carries four times the heat per kilogram per degree.

The two ends of the range are the interesting ones. Cr = 0 means one stream's capacity rate is effectively infinite, which is exactly what happens when a fluid boils or condenses: it absorbs heat at constant temperature, and every exchanger arrangement (counterflow, parallel, crossflow) collapses to the same $\varepsilon = 1 - e^{-\mathrm{NTU}}$. Cr = 1 is the balanced exchanger, hardest to make effective, and the case where counterflow's advantage over parallel flow is largest. The trap is bookkeeping: identify $C_{\mathrm{min}}$ from ṁcₚ, not from flow rate alone. Steam-to-water and refrigerant-to-air units are Cr = 0 problems no matter what the flow meters read.