Questions: Heat Exchanger Effectiveness and NTU Analysis
5 questions to test your understanding
Score: 0 / 5
Question 1 Multiple Choice
A heat exchanger has a hot stream with Ċ_hot = 2000 W/K and a cold stream with Ċ_cold = 800 W/K. If the hot stream enters at 200°C and the cold stream enters at 20°C, what is Q̇_max, the maximum possible heat transfer rate?
A2000 × (200 − 20) = 360,000 W, using the larger heat capacity rate
B800 × (200 − 20) = 144,000 W, using the smaller heat capacity rate
CThe average of both streams: 1400 × (200 − 20) = 252,000 W
DIt depends on the exchanger configuration (counterflow vs. parallelflow)
Q̇_max = Ċ_min × (T_hot,in − T_cold,in). The maximum occurs when the stream with the smaller heat capacity rate undergoes the largest possible temperature change — from its inlet temperature all the way to the other stream's inlet temperature. Here Ċ_min = 800 W/K (the cold stream), so Q̇_max = 800 × (200 − 20) = 144,000 W. The larger heat capacity rate stream (hot) cannot drive the cold stream past its own inlet temperature; the thermodynamic limit is set by Ċ_min. This is independent of configuration.
Question 2 Multiple Choice
Two heat exchangers have identical UA and identical Ċ_min/Ċ_max ratios, but one is counterflow and one is parallelflow. What key difference does configuration introduce?
AConfiguration affects UA but not NTU, so effectiveness is unchanged
BCounterflow achieves higher effectiveness than parallelflow at the same NTU; parallelflow effectiveness is capped below 1 even with infinite area
CParallelflow is always more efficient because the temperature difference driving force is greatest at the inlet
DBoth configurations achieve the same effectiveness; configuration only matters for pressure drop
Configuration fundamentally affects achievable effectiveness. In counterflow, the cold outlet can approach the hot inlet temperature, allowing ε → 1 with sufficient area. In parallelflow, both streams leave at the same intermediate temperature, capping effectiveness at 1/(1 + Ċ_min/Ċ_max) — roughly 50% for equal capacity rates — regardless of how large the exchanger is. The shape of the ε-NTU curve differs by configuration, which is why counterflow is the preferred design for high-effectiveness applications.
Question 3 True / False
The maximum possible heat transfer in a heat exchanger is determined by the stream with the larger heat capacity rate, since it carries more thermal energy.
TTrue
FFalse
Answer: False
This is the most common conceptual error in effectiveness analysis. Q̇_max = Ċ_min × (T_hot,in − T_cold,in). The limiting stream is the one with the *smaller* heat capacity rate, because it is the stream that would reach the extreme temperature first (it changes temperature faster per unit of energy transferred). The stream with the larger Ċ undergoes a smaller temperature change and never becomes the bottleneck. If you used Ċ_max, you'd be predicting a temperature change the Ċ_min stream physically cannot provide.
Question 4 True / False
A counterflow heat exchanger with Ċ_min = Ċ_max can theoretically achieve 100% effectiveness if the heat transfer area is made sufficiently large.
TTrue
FFalse
Answer: True
For a counterflow exchanger with equal heat capacity rates (Ċ_min/Ċ_max = 1), the ε-NTU relation is ε = NTU/(1 + NTU), which approaches 1 as NTU → ∞. This is not true for parallelflow, where the same case gives ε_max = 0.5 regardless of area. Counterflow is uniquely efficient because the temperature driving force is more uniformly distributed along the exchanger length, allowing both streams to approach each other's inlet temperatures at the ends.
Question 5 Short Answer
Why is Ċ_min (the smaller heat capacity rate) used as the reference in both the Q̇_max formula and the NTU definition, rather than Ċ_max or an average?
Think about your answer, then reveal below.
Model answer: Ċ_min sets the thermodynamic limit on heat transfer: the stream with the smaller heat capacity rate changes temperature fastest per unit of energy transferred, so it reaches the extreme temperature (the other stream's inlet) first. Q̇_max represents this limiting case. Using Ċ_min in NTU = UA/Ċ_min normalizes exchanger conductance (UA) against the controlling stream, so that NTU directly reflects how many 'transfer units' the limiting stream experiences. This makes the ε-NTU relationship configuration-dependent but stream-property-independent in a dimensionless sense.
The logic is asymmetric by design: in any exchanger, one stream will hit the thermodynamic limit before the other. Ċ_min identifies which stream that is. Normalizing against it ensures that ε = 1 corresponds to the true thermodynamic maximum regardless of how disparate the two stream capacities are.