Effectiveness-NTU Calculator

ε-NTU method for heat exchanger rating and sizing — useful when outlet temperatures are unknown. Supports counterflow, parallel, and crossflow configurations with forward (NTU → ε) and inverse (ε → NTU) calculation.

Heat Transfer · HX Design

Inputs

Solve for:

Flow configuration:

Hot and cold streams flow in opposite directions — highest possible ε for given NTU and C*.

Number of Transfer Units NTU (dimensionless)

NTU = U × A / C_min

Capacity ratio C* (0 – 1)

C* = C_min / C_max · C* = 0 for condenser / evaporator

Also compute Q = ε × C_min × (T_h,in − T_c,in)

Theory

Definitions:

NTU = U × A / C_min [Number of Transfer Units]

C* = C_min / C_max [Capacity ratio, 0 ≤ C* ≤ 1]

C = ṁ × c_p [Heat capacity rate, W/K]

ε = Q_actual / Q_max [Effectiveness, 0 to 1]

Q_max = C_min × (T_h,in − T_c,in)

ε-NTU correlations by configuration:

Configuration	Formula (C* < 1)
Counterflow	ε = (1 − exp(−NTU(1−C))) / (1 − C exp(−NTU(1−C*)))
Counterflow (C* = 1)	ε = NTU / (1 + NTU)
Parallel flow	ε = (1 − exp(−NTU(1+C))) / (1+C)
Crossflow (both unmixed)	ε = 1 − exp((1/C)(exp(−C·NTU) − 1))
All configs, C* = 0 (condenser/evaporator)	ε = 1 − exp(−NTU)

NTU from ε (inverse formulas):

Counterflow (C* < 1): NTU = ln((1 − C*ε) / (1 − ε)) / (1 − C*)

Counterflow (C* = 1): NTU = ε / (1 − ε)

Parallel flow: NTU = −ln(1 − ε(1+C*)) / (1+C*)

Crossflow: Numerical inversion (bisection)

ε-NTU vs LMTD — when to use each:

Method	Use when…	Knowns
LMTD	All four temperatures known	Th,in Th,out Tc,in Tc,out
ε-NTU	Outlet temperatures unknown (rating)	NTU (= UA/Cmin), C*, inlet temps
ε-NTU	Sizing — find UA from duty	ε (or Q), C*, inlet temps