HEAT EXCHANGERS (LMTD & NTU)

Heat exchanger duty Q = U·A·ΔT_LM where ΔT_LM is the log-mean temperature difference. Counter-flow yields the highest ΔT_LM, parallel-flow the lowest, cross-flow intermediate (apply F-factor correction). When outlet temperatures are unknown but UA and inlet conditions are, use the NTU-effectiveness method: NTU = UA/Cmin, capacity ratio Cr = Cmin/Cmax, then look up effectiveness ε from the appropriate flow-arrangement chart and compute outlets.

• Q = U·A·ΔT_LM
• ΔT_LM = (ΔT₁ - ΔT₂) / ln(ΔT₁/ΔT₂)
• NTU = UA / Cmin
• Cr = Cmin / Cmax
• ε = Q / Q_max = Q / (Cmin·ΔT_max)

References & StandardsTEMA Standards, Kakac "Heat Exchangers", Incropera Ch. 11

Use for sizing and rating shell-and-tube, plate, double-pipe, and air-cooled exchangers. LMTD method when all four inlet/outlet temperatures are known (sizing). NTU method when only inlet temperatures are known (rating). Account for fouling resistance R_f on both sides; fouling can dominate U after a few months of service. Counter-flow over parallel-flow whenever possible.