Calculators
Shell-and-Tube HX LMTD Rating
Counter-current LMTD with Bowman Ft correction for TEMA E (1-shell / 2N-tube pass) shell-and-tube exchangers. Solves duty Q from the hot side, the cold outlet by energy balance, the corrected effective LMTD, and required UA / surface area at the design overall coefficient.
Method: Energy balance Q = mh·cp,h·(T1−T2); cold outlet t2 = t1 + Q/(mc·cp,c). Counter-current LMTD = (ΔT1−ΔT2) / ln(ΔT1/ΔT2) with ΔT1=T1−t2, ΔT2=T2−t1. Temperature efficiency P = (t2−t1)/(T1−t1); heat-capacity ratio R = (T1−T2)/(t2−t1). Bowman Ft for 1-shell / 2N-tube TEMA E: Ft = √(R²+1)·ln[(1−P)/(1−P·R)] / [(R−1)·ln{(2−P·(R+1−√(R²+1))) / (2−P·(R+1+√(R²+1)))}]. UA = Q / (Ft·LMTD); Areq = UA / U. TEMA practice: Ft < 0.75 indicates a temperature cross — add shells in series. References: Kern, Process Heat Transfer (1950); Bowman, Mueller & Nagle (1940); TEMA 10th Ed. RCB-4.32; Perry's 8th Ed. Sec. 11.
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