Heat exchanger effectiveness (ε) is defined how, in terms of actual heat transfer relative to the thermodynamic maximum possible?
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Aε = actual heat transfer / maximum possible heat transfer
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Bε = maximum possible heat transfer / actual heat transfer
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Cε = UA / Cmax
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Dε = 1 − exp(−NTU)
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Eε = Cmin / Cmax only
Answer
Correct Answer: ε = actual heat transfer / maximum possible heat transfer
Explanation
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:
1) Identify Cmin = min(C_hot, C_cold).2) Compute q_max = Cmin * (T_h,in − T_c,in).3) Actual transfer q_actual depends on UA and flow configuration.4) Define ε = q_actual / q_max (dimensionless, 0 to 1).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