LMTD Calculator

Log Mean Temperature Difference — the effective driving force for heat transfer in a heat exchanger. Used in Q = U × A × F × LMTD to size or rate heat exchangers.

Heat Transfer · HX Design

Inputs

Flow configuration:

Counterflow: hot and cold fluids flow in opposite directions — highest possible LMTD for given terminal temperatures.

Temperature units:

Hot-side inlet temperature Th,in (°C)

Hot-side outlet temperature Th,out (°C)

Cold-side inlet temperature Tc,in (°C)

Cold-side outlet temperature Tc,out (°C)

Apply F-factor correction (multi-pass shell-and-tube or crossflow HX)

Also compute heat duty Q = U × A × F × LMTD

Theory

Formula and end-temperature definitions:

LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁ / ΔT₂)

Counterflow:

ΔT₁ = T_h,in − T_c,out ΔT₂ = T_h,out − T_c,in

Parallel flow:

ΔT₁ = T_h,in − T_c,in ΔT₂ = T_h,out − T_c,out

Design equation:

Q = U × A × F × LMTD

F = 1.0 for pure counterflow · F < 1 for multi-pass or crossflow

F-factor correction (non-counterflow configurations):

HX type	Typical F	Note
Double-pipe counterflow	1.00	Reference — no correction needed
Double-pipe parallel flow	< 1.00	Calculated from LMTD ratio
1-2 shell-and-tube	0.80–0.97	Read from TEMA chart vs R, P
2-4 shell-and-tube	0.90–0.99	Higher F than 1-2 for same R, P
Crossflow (both unmixed)	0.90–0.97	Plate-fin type
Crossflow (one fluid mixed)	0.85–0.95	Shell-and-tube crossflow

Temperature parameters R and P:

R = (T_h,in − T_h,out) / (T_c,out − T_c,in) [heat capacity ratio]

P = (T_c,out − T_c,in) / (T_h,in − T_c,in) [cold-side effectiveness]

R and P are used to read the F-factor from TEMA charts. F is only defined for P < 1 (cold outlet cannot exceed hot inlet). When RP = 1 the LMTD method breaks down and the NTU-effectiveness method should be used.

When ΔT₁ = ΔT₂ (uniform temperature difference):

LMTD → ΔT (L'Hôpital's rule: 0/0 limit)

This occurs in a counterflow HX where R = 1 (equal heat capacity rates). The LMTD is simply the constant temperature difference along the exchanger.