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The effectiveness-NTU method

NTU methodheat exchanger effectivenessepsilon-NTU

Sizing or rating a heat exchanger without knowing the outlet temperatures — capacity rates, NTU, effectiveness and the maximum possible duty.

Capacity Rate Ratio (Cr)

Cr=m˙mincminm˙maxcmaxC_r = \frac{\dot{m}_{min} c_{min}}{\dot{m}_{max} c_{max}}

Ratio of the smaller to the larger stream heat capacity rate ṁcₚ, the second dimensionless group the effectiveness-NTU method needs.

Number of Transfer Units (NTU)

NTU=UAm˙ cp\mathrm{NTU} = \frac{U A}{\dot{m} \, c_p}

Dimensionless size of an exchanger: its conductance UA divided by the heat capacity rate of the minimum stream, ṁ times its specific heat.

Effectiveness from NTU (Counterflow)

ε=1−e−NTU(1−Cr)1−Cr e−NTU(1−Cr)\varepsilon = \frac{1 - e^{-\mathrm{NTU}(1 - C_r)}}{1 - C_r \, e^{-\mathrm{NTU}(1 - C_r)}}

Counterflow effectiveness from the two dimensionless groups NTU and Cr, valid for any Cr from 0 to 1 with the balanced case handled as a limit.

Maximum Possible Heat Transfer (Qmax)

Q˙max=m˙mincmin(Th,in−Tc,in)\dot{Q}_{max} = \dot{m}_{min} c_{min} (T_{h,in} - T_{c,in})

The thermodynamic ceiling on exchanger duty: the minimum capacity rate multiplied by the full inlet-to-inlet temperature difference.

Heat Exchanger Effectiveness (ε = Q/Qmax)

ε=Q˙Q˙max\varepsilon = \frac{\dot{Q}}{\dot{Q}_{max}}

Effectiveness as the ratio of actual duty to the thermodynamic maximum, the performance figure that needs no outlet temperatures to interpret.

How they fit together

The LMTD method needs all four terminal temperatures, which is fine for rating an exchanger you already have and useless for sizing one you do not. Effectiveness-NTU sidesteps that: it asks what the maximum conceivable heat transfer would be — the minimum capacity rate times the full inlet temperature difference — and then what fraction of it this exchanger actually achieves.

NTU is the exchanger's size expressed as UA divided by that minimum capacity rate, and effectiveness rises with it but flattens hard. Going from NTU 1 to 2 buys a lot; going from 4 to 5 buys almost nothing, which is why enormous exchangers are rarely worth their surface area.