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 ε = 1 − e^(−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_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.