In heat-exchanger analysis using the NTU–effectiveness method, the number of transfer units (NTU) is defined in terms of overall heat transfer coefficient U, heat transfer area A, and the minimum heat capacity rate Cmin. Which expression is correct?

Introduction / Context:
The NTU–effectiveness method is a standard framework for analyzing heat exchangers without detailed temperature profiles. The definition of NTU is central to selecting charts/correlations for effectiveness based on flow arrangement and capacity-rate ratio.

Given Data / Assumptions:

• U is the overall heat transfer coefficient (W/m^2·K).
• A is the effective heat transfer area (m^2).
• Cmin is the smaller of the two capacity rates (W/K).

Concept / Approach:
NTU is a nondimensional parameter quantifying the size/conductance of a heat exchanger relative to the minimum capacity rate. By definition, NTU = (U * A) / Cmin. This links exchanger size and thermal conductance to the stream that most limits the temperature change.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional check: (W/m^2·K * m^2) / (W/K) → (W/K) / (W/K) = dimensionless, as required for NTU.

Why Other Options Are Wrong:

• Using Cmax in the denominator gives a smaller NTU than correct and is not the standard definition.
• Reciprocal forms invert the dimensionless group and are inconsistent with standard charts.
• U/(ACmin) or A/(UCmin) are dimensionally incorrect for NTU.

Common Pitfalls:
Mixing up Cmin and Cmax; forgetting that NTU must be dimensionless; confusing NTU with effectiveness (ε), which depends on NTU and capacity-rate ratio (Cmin/Cmax).

Final Answer:
NTU = U * A / Cmin