A plate and frame heat exchanger is a stack of thin corrugated plates squeezed between two frame plates. Gaskets around each plate close off alternating channels, so hot fluid runs through every other gap and cold fluid runs through the ones in between, in opposite directions. Every plate is a wall with fluid on both sides, and the corrugations do two jobs at once: they hold the plates apart at a fixed gap, and they trip the flow into turbulence at Reynolds numbers where a plain tube would still be laminar. That is the whole trick. It is why a plate unit reaches a 2 °F approach in a fraction of the volume a shell-and-tube would need.
Sizing one is a bookkeeping problem before it is a heat transfer problem. Five things go in — the two inlet temperatures, the two flows, and the surface — and two come out: the two outlet temperatures. If you want to hold an outlet at a number, you have taken away a degree of freedom, and one of the five inputs has to give it back. Which one you pick is the engineering decision, and it is rarely arbitrary. Moving the hot-side flow is a control valve and a sequence of operation. Moving the plate count is a purchase order. Moving the hot inlet is a boiler or chiller reset schedule. Pin both outlets and you have specified the duty itself, at which point one flow follows from the energy balance and the surface follows from the LMTD — that is the problem a selection program solves, and the answer comes back as a plate count and two pressure drops.
The figure below does all of that, but the reason to move the sliders is what happens to the numbers you did not ask about. Adding plates to a single-pass unit spreads the same flow over more channels, so the fluid slows down, the film coefficient falls off roughly as velocity to the 0.7, and the surface you bought is working against you. The pressure drop that vanishes along with it was not waste — it was the turbulence doing the heat transfer. Watch the resistance bar to see which side is actually the bottleneck, and watch what a second pass costs before you reach for it.
Two temperatures deserve more attention than they usually get. The approach at each end tells you where the surface is idle: when the capacity rates are unequal, the pinch moves to one end and the other end runs with plenty of driving force and nothing to do about it. And the Reynolds number in each channel tells you whether the unit is still in the regime the whole technology depends on. Below roughly Re 400 — a chevron-channel heuristic, not the pipe-flow trip at Re 2300 — the corrugations stop tripping the flow, the film coefficients drop sharply, and the channels stop scouring themselves — which is the same turndown condition that shows up later as a fouling complaint.
The figure is a teaching model, not a selection tool. Propylene-glycol properties in the sliders are approximate fits: check ASHRAE before they carry any weight, they are not for freeze-protection sizing, and ethylene glycol is not modelled.