Thermodynamics & Heat Transfer · Rating the exchanger
Two roads to the same duty
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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: Q˙=m˙cpΔT\dot{Q} = \dot{m} \, c_p \, \Delta T, read Q-dot equals m-dot c-p delta-T. m˙\dot{m} (m-dot) is the mass flow in kg/s, cpc_p the specific heat in kJ/(kgK)\mathrm{kJ/(kg \cdot K)} — take 4.2 for water — and ΔT\Delta T 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: Q˙=UAFΔTlm\dot{Q} = U A F \, \Delta T_{lm}. UU is the overall coefficient, AA the heat transfer area in m2\mathrm{m^2}, ΔTlm\Delta T_{lm} the counterflow log mean, and FF 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. F=1.0F = 1.0 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 A=Q˙UFΔTlmA = \dfrac{\dot{Q}}{U F \, \Delta T_{lm}}, tells you how much metal that duty costs. Watch the one unit trap in the whole lesson: duties are quoted in kilowatts and UU in watts, and a thousandfold slip here produces an exchanger the size of a postcard.