In a parallel-flow heat exchanger, the hot and cold fluids enter at the same end and flow in the same direction. Which statement about the cold fluid's outlet temperature is correct?

It can't exceed the hot fluid's outlet temperature, no matter how long the exchanger is

It can exceed the hot fluid's outlet temperature if the exchanger is made long enough

It approaches the hot fluid's inlet temperature as the exchanger length becomes very large

It can exceed the hot fluid's inlet temperature when the cold-fluid flow rate is very low

For radiation between two surfaces, the reciprocity relation states that:

\(A_1 = A_2\) for any enclosure

A plate (k = 200 W/m·K) is 0.02 m thick with a 10°C temperature difference across it. The conduction heat flux is:

40 W/m², multiplying by thickness

2 kW/m², omitting the thickness

FE · 7% of the exam

Heat Transfer practice questions

10 free Heat Transfer questions for the FE Mechanical Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questions Free 10-question FE quiz

What this domain covers

How heat moves by conduction, convection and radiation, including transient cases and heat exchangers.

Exam weight: 7%
On a real exam: ≈ 8 questions
In our bank: 42 questions

Topics that come up most

Conduction and thermal resistance networks
Forced and natural convection correlations
Radiation and view factors
Lumped capacitance and transient conduction
Heat exchangers by LMTD and effectiveness-NTU

How to study it

Treat walls, pipes and films as resistances in series; drawing the network first makes composite problems routine.

Sample Heat Transfer questions

Try each one before opening the answer. Original questions written to the official exam objectives.

Question 1
In a parallel-flow heat exchanger, the hot and cold fluids enter at the same end and flow in the same direction. Which statement about the cold fluid's outlet temperature is correct?
- AIt can exceed the hot fluid's outlet temperature if the exchanger is made long enough
- BIt can't exceed the hot fluid's outlet temperature, no matter how long the exchanger is
- CIt approaches the hot fluid's inlet temperature as the exchanger length becomes very large
- DIt can exceed the hot fluid's inlet temperature when the cold-fluid flow rate is very low
Show answer and explanation
Answer: B) It can't exceed the hot fluid's outlet temperature, no matter how long the exchanger is
In parallel flow, both fluids exit at the same end and approach a common temperature, so the cold outlet temperature always stays below the hot outlet temperature. Only counterflow lets the cold outlet exceed the hot outlet.
- AIncorrect. This is possible in counterflow, where the cold stream leaves next to the hot inlet. In parallel flow, both streams leave at the same end, so the temperatures can't cross.
- BCorrect. In parallel flow, the temperature difference shrinks along the length. Both streams approach a common exit temperature, so the cold outlet can only approach the hot outlet from below.
- CIncorrect. In a very long parallel-flow unit, both streams approach a common temperature that lies between the two inlet temperatures, not the hot inlet temperature.
- DIncorrect. Heat flows only from hot to cold. The cold fluid can never be heated above the hottest temperature in the exchanger, in any flow arrangement.
Question 2
For radiation between two surfaces, the reciprocity relation states that:
- A\(F_{12} = F_{21}\) always
- B\(A_1F_{12} = A_2F_{21}\)
- C\(F_{12} + F_{21} = 1\)
- D\(A_1 = A_2\) for any enclosure
Show answer and explanation
Answer: B) \(A_1F_{12} = A_2F_{21}\)
- AIncorrect. Only when areas are equal.
- BCorrect. View factors relate through areas.
- CIncorrect. That isn't the relation.
- DIncorrect. Areas can differ.
Question 3
For an enclosure, the view factors from one surface to all surfaces must sum to:
- AThe surface emissivity
- B0
- C1
- Dπ
Show answer and explanation
Answer: C) 1
- AIncorrect. View factors are geometric.
- BIncorrect. All radiation goes somewhere.
- CCorrect. The summation rule.
- DIncorrect. They sum to 1.
Question 4
Lumped-capacitance analysis of a cooling object is generally valid when the Biot number is:
- ALess than about 0.1
- BGreater than 10
- CExactly 1
- DNegative
Show answer and explanation
Answer: A) Less than about 0.1
- ACorrect. Internal temperature gradients are negligible.
- BIncorrect. Then internal gradients matter.
- CIncorrect. It must be small.
- DIncorrect. Biot number is positive.
Question 5
Using σ = 5.67 × 10⁻⁸ W/m²·K⁴, a blackbody surface at 500 K emits radiation at a rate per unit area of about:
- A354 W/m²
- B7.1 W/m²
- C14,175 W/m²
- D3,544 W/m²
Show answer and explanation
Answer: D) 3,544 W/m²
The Stefan-Boltzmann law gives blackbody emissive power E_b = σT⁴ with T in kelvin. At 500 K that is about 3,544 W/m².
- AIncorrect. This is one-tenth of the right value, a power-of-ten slip when working out σT⁴.
- BIncorrect. This is σT³ = 5.67×10⁻⁸ × 1.25×10⁸. The Stefan-Boltzmann law raises absolute temperature to the fourth power, not the third.
- CIncorrect. This is 4σT⁴, which multiplies the correct emissive power by 4 for no reason. The blackbody emissive power is just σT⁴.
- DCorrect. E_b = σT⁴ = 5.67×10⁻⁸ × (500)⁴ = 5.67×10⁻⁸ × 6.25×10¹⁰ ≈ 3,544 W/m².
Question 6
A heat exchanger has end temperature differences of 60 K and 20 K. The log-mean temperature difference is about:
- A36.4 K
- B40.0 K
- C13.3 K
- D26.7 K
Show answer and explanation
Answer: A) 36.4 K
- ACorrect. \((60 - 20)/\ln(60/20)\).
- BIncorrect. That's the arithmetic mean.
- CIncorrect. Recheck the formula.
- DIncorrect. Recheck the logarithm.
Question 7
The Grashof number is used mainly in correlations for:
- AConduction in solids
- BForced convection in pipes
- CRadiation between surfaces
- DNatural (free) convection
Show answer and explanation
Answer: D) Natural (free) convection
- AIncorrect. That uses Fourier's law.
- BIncorrect. That uses the Reynolds number.
- CIncorrect. That uses view factors.
- DCorrect. It compares buoyancy with viscous forces.
Question 8
Using Wien's law \(\lambda_{max}T = 2{,}898\ \mu\text{m·K}\), a 5,800-K surface emits most strongly near:
- A5.0 μm
- B2.0 μm
- C0.5 μm
- D0.05 μm
Show answer and explanation
Answer: C) 0.5 μm
- AIncorrect. Recheck the division.
- BIncorrect. Recheck the division.
- CCorrect. 2,898/5,800.
- DIncorrect. Recheck the division.
Question 9
A plate (k = 200 W/m·K) is 0.02 m thick with a 10°C temperature difference across it. The conduction heat flux is:
- A100 kW/m²
- B40 W/m², multiplying by thickness
- C10 kW/m²
- D2 kW/m², omitting the thickness
Show answer and explanation
Answer: A) 100 kW/m²
- ACorrect. \(q'' = k\Delta T/L\).
- BIncorrect. Divide by thickness.
- CIncorrect. That's off by a factor of 10.
- DIncorrect. Divide by thickness.
Question 10
For the same inlet and outlet temperatures, a counterflow heat exchanger compared with a parallel-flow one:
- ANeeds less area
- BNeeds more area
- CNeeds the same area
- DCan't be built
Show answer and explanation
Answer: A) Needs less area
- ACorrect. It has a larger LMTD.
- BIncorrect. Counterflow is more effective.
- CIncorrect. Counterflow has a larger LMTD.
- DIncorrect. Counterflow is common.

Heat Transfer: FAQs

How much of the FE exam is Heat Transfer?

Heat Transfer is 7% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 8 questions. The real exam's exact split varies by form.

What does the Heat Transfer domain cover?

How heat moves by conduction, convection and radiation, including transient cases and heat exchangers.

How should I study Heat Transfer for FE?

Treat walls, pipes and films as resistances in series; drawing the network first makes composite problems routine.

Where can I practise more Heat Transfer questions?

This page has 10 free Heat Transfer questions with answers. The ExamWize FE question bank has 42 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Get Heat Transfer exam-ready

The full FE bank has 42 Heat Transfer questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

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Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.

Heat Transfer practice questions

What this domain covers

Topics that come up most

How to study it

Sample Heat Transfer questions

In a parallel-flow heat exchanger, the hot and cold fluids enter at the same end and flow in the same direction. Which statement about the cold fluid's outlet temperature is correct?

For radiation between two surfaces, the reciprocity relation states that:

For an enclosure, the view factors from one surface to all surfaces must sum to:

Lumped-capacitance analysis of a cooling object is generally valid when the Biot number is:

Using σ = 5.67 × 10⁻⁸ W/m²·K⁴, a blackbody surface at 500 K emits radiation at a rate per unit area of about:

A heat exchanger has end temperature differences of 60 K and 20 K. The log-mean temperature difference is about:

The Grashof number is used mainly in correlations for:

Using Wien's law \(\lambda_{max}T = 2{,}898\ \mu\text{m·K}\), a 5,800-K surface emits most strongly near: