Heat exchanger effectiveness (ε) is defined how, in terms of actual heat transfer relative to the thermodynamic maximum possible?

Introduction / Context:
Effectiveness–NTU analysis allows heat exchanger performance evaluation independent of outlet temperatures. The definition of effectiveness anchors all derived relations across flow arrangements and capacity-rate ratios.

Given Data / Assumptions:

• Two-stream heat exchanger with capacity rates C_hot and C_cold.
• Maximum possible heat transfer is limited by Cmin and the inlet temperature difference.

Concept / Approach:
Effectiveness ε quantifies how closely an exchanger approaches its theoretical limit: ε = q_actual / q_max, where q_max = Cmin * (T_h,in − T_c,in). This definition is universal across LMTD and NTU methods; specific formulas like ε(NTU, C_r) depend on flow arrangement (parallel, counter, cross-flow) and are derived from this definition.

Step-by-Step Solution:

Verification / Alternative check:
For a given NTU = UA / Cmin and capacity ratio C_r = Cmin / Cmax, tables provide ε as a function ε(NTU, C_r), consistently rooted in ε = q_actual / q_max.

Why Other Options Are Wrong:

• (b) Inverts the definition.
• (c) UA/Cmax is NTU only for a specific normalization; not ε.
• (d) Is one special-case formula, not the general definition.
• (e) Cmin/Cmax is capacity ratio, not effectiveness.

Common Pitfalls:
Mixing up NTU and ε or assuming a single ε equation applies to all configurations.

Final Answer:
ε = actual heat transfer / maximum possible heat transfer