Two roads to the same duty
There are exactly two ways to say how much heat an exchanger moves, and a rating is honest only when both agree.
The stream road: , read Q-dot equals m-dot c-p delta-T. (m-dot) is the mass flow in kg/s, the specific heat in — take 4.2 for water — and that stream's own temperature change across the unit. This road knows nothing about the metal; it is pure bookkeeping on one fluid.
The surface road: . is the overall coefficient, the heat transfer area in , the counterflow log mean, and is the LMTD correction factor: a bare number, never above 1, that derates true counterflow for a real shell-and-tube or crossflow arrangement in which some of the fluid inevitably flows the wrong way. is true counterflow; below about 0.75 the arrangement is considered thermally unsound and the design is changed rather than fudged.
Sizing runs the two roads in order: the streams tell you the duty, and the surface equation, rearranged to , tells you how much metal that duty costs. Watch the one unit trap in the whole lesson: duties are quoted in kilowatts and in watts, and a thousandfold slip here produces an exchanger the size of a postcard.