อัปเดต 2026-09-07

Heat Exchanger (Shell & Tube Sizing)

LMTD sizing method — Kern / Bowman & TEMA

Sizes shell-and-tube exchanger surface area from the stream energy balance (Q = ṁ·Cp·ΔT) and the log-mean temperature difference, corrected for multi-pass (1-2 / 2-4 TEMA E-shell) geometry via the analytic Bowman F-factor.

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Closes the hot/cold stream duty via the energy balance, forms the counterflow/parallel end-temperature differences (ΔT1, ΔT2) and their log-mean (with the ΔT1=ΔT2 removable-singularity limit handled explicitly), applies the closed-form Bowman F-correction for 1-2/2-4 E-shells (splitting the R=1 analytic limiting branch), then solves A = Q/(U·F·ΔT_lm). A temperature cross or F below the 0.75 TEMA floor is flagged rather than thrown.

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Log-Mean Temperature Difference

Δ T_{l m} = \frac{Δ T _{1} - Δ T _{2}}{ln ( \frac{Δ T _{1}}{Δ T _{2}} )}

Counterflow end differences ΔT1 = Th,in−Tc,out, ΔT2 = Th,out−Tc,in (Kern 1950; Incropera & DeWitt).

TEMA 1-2 Shell F-Correction (Bowman, R≠1)

F = \frac{R ^{2} + 1 ln [ \frac{1 - P}{1 - P R} ]}{( R - 1 ) ln [ \frac{2 - P ( R + 1 - R ^{2} + 1 )}{2 - P ( R + 1 + R ^{2} + 1 )} ]}

P=(t2−t1)/(T1−t1), R=(T1−T2)/(t2−t1); Bowman, Mueller & Nagle, Trans. ASME 62 (1940). TEMA design floor F≥0.75.

Required Surface Area

A = \frac{Q}{U \cdot F \cdot Δ T _{l m}}

Q=ṁ·Cp·ΔT sensible duty; U from Kern (1950) Table 8 low/typical/high presets.

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