Why holding an outlet needs something else to move. Five things go in — two inlet temperatures, two flows, and the surface — and two come out. An inlet is already an input, so holding one is just leaving the slider alone. An outlet is an answer, so pinning it removes a degree of freedom and one input has to give it back. Which input you pick is the whole engineering decision: moving the hot flow is a control valve, moving the plate count is a purchase, moving the hot inlet is a boiler or chiller reset. Hold both outlets and you have specified the duty itself — one flow follows from the energy balance and the plate count follows from the LMTD. That is the datasheet problem, and it is the one a sizing calculator actually solves.

Adding plates stops paying, and here is why. In a single-pass unit the same flow spread over more channels moves slower, so the film coefficient drops roughly as velocity^0.7 while the area climbs linearly. You buy NTU at a worsening exchange rate and you lose the pressure drop that was doing the work. The honest lever for a close approach is a longer plate, a second pass, or a bigger frame — watch the pressure drop when you take the second pass, because it costs about six or seven times the first.

The approach is the number to argue about. A plate unit gets closer than a shell-and-tube because it is true counterflow, but a 2 °F approach and a 10 °F approach are different machines and different money. Both approaches are shown because the tight one moves to whichever end has the smaller capacity rate — unequal flows push the pinch to one end and leave surface idle at the other.

What is modelled and what is not. Rating is ε-NTU for pure counterflow, which is what a single-pass plate unit is. Equal multi-pass — the same pass count on both sides — is treated as overall counterflow, a teaching simplification with F≈1, not a full unequal-pass F correction. Film coefficients use calibrated chevron-family presets (C and K): Nu = C·Re^0.70·Pr^1/3 above Re 400 and blended to laminar slopes below it, with C and K set so a hard plate in water at Re 5000 lands near the published range for chevron plates — roughly 8000 W/m²·K and a few psi over a 36-inch plate. The Re 400 trip is a chevron-channel heuristic, not the pipe-flow transition at Re 2300, and the correlation is continuous there, so film coefficients drop sharply rather than discontinuously. These are not any manufacturer's plate curves. This is a teaching model: a real selection will not match it to better than 20 or 30 percent, and you should expect double-digit percent differences versus OEM software. Real plate data is proprietary and differs by pattern. Water properties are fitted over temperature except c_p, which is held constant. Check ASHRAE for glycol. The propylene-glycol fits are approximate, not for freeze-protection sizing, and ethylene glycol is not modelled. Not modelled: the end-channel effect (the two outer channels only transfer on one face, which costs a little on small packs), flow maldistribution across the ports, unequal-pass F correction, gasket and frame pressure limits, and any two-phase duty.

An explanation tool, not a selection tool. Size real equipment with the manufacturer's software and a licensed engineer's judgment.