Heat Transfer is 7-11 questions on the FE Mechanical exam. It leans on thermodynamics for energy balances and on fluid mechanics for the flow behaviour that sets convection coefficients, so it is best studied after both rather than in isolation.
The single most useful habit in this area is drawing the thermal resistance network. A composite wall, a pipe with insulation and a heat exchanger all become one-line problems once the resistances are laid out in series and parallel.
Exam weight: NCEES lists Heat Transfer at 7-11 questions of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Heat Transfer
The specification covers conduction, convection, radiation, and transient processes as well as masses, heat exchangers and thermal resistance. Expect a composite wall or cylinder with a driving temperature difference, a convection coefficient supplied or derived from a Nusselt correlation, a fin efficiency, and a radiation exchange between surfaces.
Heat exchanger items ask for the log mean temperature difference or an effectiveness-NTU result. Transient problems typically use the lumped capacitance method, which is valid only when the Biot number is small enough, and the exam does test whether you check that.
5 Free Heat Transfer Practice Problems
Each heat transfer problem below comes from the FEExamClick FE Mechanical question bank, with worked solutions, and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — B. Convection
Hot air at 200°C flows across a surface at 50°C. If the convection heat-transfer coefficient is 72 W/(m\(^{2}\)·°C), the heat-transfer rate (W) over 2 m\(^{2}\) of the surface is most nearly:
Answer: D) 21,600
Refer to the Convection section in the Heat Transfer chapter of the FE Reference Handbook.
Newton’s law of cooling:
\(Q = hA(T_\infty - T_s)\)
Substitute:
\(Q = 72 \times 2 \times (200 - 50)\)
\(\boxed{Q = 144 \times 150 = 21,600 W}\)
Problem 2 — C. Radiation
A gray surface with emissivity ε = 0.7 is at 600 K. The total emissive power (W/m\(^{2}\)) of the surface is most nearly:
Answer: C) 5,143
Refer to the Radiation section in the Heat Transfer chapter of the FE Reference Handbook.
Emissive power of a gray surface:
\(E = \epsilon\sigma T^4\)
First compute blackbody emissive power:
\(E_b = \sigma T^4 = 5.67 \times 10^{-8} \times (600)^4\)
\((600)^4 = 1.296 \times 10^{11}\)
\(E_b = 5.67 \times 10^{-8} \times 1.296 \times 10^{11} = 7,348 W/m^2\)
$$E = 0.7 \times 7,348 = 5,144 W/m^2 \approx 5,143 W/m^2$$
Problem 3 — E. Heat exchangers
Hot oil (\(c_p\) = 2100 J/(kg·K)) enters a counterflow heat exchanger at 150°C and exits at 90°C with a mass flow rate of 3 kg/s. Cold water (\(c_p\) = 4180 J/(kg·K)) enters at 20°C and exits at 60°C. The mass flow rate of the water (kg/s) is most nearly:
Answer: A) 2.26
Refer to the Heat Exchangers section in the Heat Transfer chapter of the FE Reference Handbook.
Energy balance (heat lost by hot = heat gained by cold):
\(m_h\) c_{p,h} (T_{h,in} − T_{h,out}) = \(m_c\) c_{p,c} (T_{c,out} − T_{c,in})
Substitute:
\(3 \times 2100 \times (150 - 90) = m_c \times 4180 \times (60 - 20)\)
\(3 \times 2100 \times 60 = m_c \times 4180 \times 40\)
\(378,000 = m_c \times 167,200\)
\(m_c = 378,000 / 167,200 = 2.261 kg/s \approx 2.26 kg/s\)
Problem 4 — A. Conduction
A plane wall (k = 20 W/(m·K), L = 0.3 m) has uniform internal heat generation of 5 \(\times\) 10\(^{5}\) W/m\(^{3}\). Both surfaces are maintained at 50°C. For a plane wall of thickness \( L \) with uniform volumetric generation \( \dot{q} \) and both surfaces at \( T_s \), the maximum temperature is \( T_{\mathrm{max}} = T_s + \dot{q}L^{2}/(8k) \). The maximum temperature (°C) in the wall is most nearly:
Answer: D) 331
Refer to the Conduction section in the Heat Transfer chapter of the FE Reference Handbook.
For a plane wall with uniform heat generation and equal surface temperatures, the maximum temperature occurs at the center:
$$T_{max} = T_s + (q_{gen} \times L^2)/(8k)$$
Substitute:
\(T_{max} = 50 + (5 \times 10^5 \times (0.3)^2)/(8 \times 20)\)
\(T_{max} = 50 + (500,000 \times 0.09)/160\)
\(T_{max} = 50 + 45,000/160\)
\(\boxed{T_{max} = 50 + 281.25 = 331^{\circ}C}\)
Problem 5 — D. Transient processes
A large aluminum slab (α = 97.1 \(\times\) 10\(^{-6}\) m\(^{2}\)/s) has a half-thickness of 5 cm. After 60 seconds, the Fourier number (Fo) is most nearly:
Answer: A) 2.33
Refer to the Approximate Solution for Solid with Sudden Convection section (p. 212) in the Heat Transfer chapter of the FE Reference Handbook.
Fourier number:
\(Fo = \alpha t/L^2\)
Substitute (L = half-thickness = 0.05 m):
\(Fo = (97.1 \times 10^{-6} \times 60) / (0.05)^2\)
\(Fo = 5.826 \times 10^{-3} / 2.5 \times 10^{-3}\)
\(Fo = 2.33\)
Using the FE Reference Handbook for Heat Transfer
The Heat Transfer section holds the conduction shape factors, the thermal resistance expressions for plane and cylindrical geometries, fin efficiency charts and the Nusselt correlations. The cylindrical resistance expression with its natural logarithm of the radius ratio is the one worth locating before exam day, because writing it from memory is where sign and ratio errors creep in.
Four Mistakes That Cost Points
- Adding parallel thermal resistances in series. Layers stacked through the heat flow path add directly; parallel paths combine as reciprocals. Mis-wiring the network is the dominant error in composite-wall problems, and both totals are on the answer list.
- Using Celsius in a radiation calculation. The Stefan-Boltzmann law requires absolute temperature raised to the fourth power. A Celsius substitution does not give a slightly wrong answer, it gives a wildly wrong one, which at least makes it easy to catch if you sanity-check magnitude.
- Applying lumped capacitance without checking the Biot number. Lumped capacitance assumes negligible internal temperature gradient, valid for a small Biot number. Applying it to a thick, low-conductivity body is precisely the trap a transient question is built around.
- Using the wrong area for a cylinder. Conduction through a cylindrical wall uses the log mean area, not the inner or outer surface area. Convection at the surface uses that surface's actual area. Using one where the other belongs is a designed distractor.
Frequently Asked Questions
How many heat transfer questions are on the FE Mechanical exam?
NCEES specifies 7-11 questions out of 110. That is the same weight as Material Properties and Processing, and slightly less than Thermodynamics at 10-15.
Do I need to memorise Nusselt number correlations?
No. The handbook provides correlations for the standard geometries and flow regimes. What you must do is identify the regime first, since a correlation for laminar internal flow gives a wrong answer when applied to turbulent flow, and the exam supplies the numbers needed to tell them apart.
How are heat exchangers tested?
Usually through the log mean temperature difference method for a straightforward duty calculation, or through effectiveness-NTU when outlet temperatures are unknown. Know which method each situation calls for; that decision is often the whole question.
Should I study heat transfer before or after thermodynamics?
After. Heat transfer questions frequently open with an energy balance that assumes thermodynamic fluency, and convection depends on flow behaviour from fluid mechanics. Studying it first means learning three subjects at once.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Thermodynamics practice problems — 10-15 questions on the exam
- FE Mechanical Fluid Mechanics practice problems — 10-15 questions on the exam
- FE Mechanical Material Properties and Processing practice problems — 7-11 questions on the exam
Done with heat transfer? Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline. Or test yourself against the clock with the free FE Mechanical practice exam: 20 timed questions in the CBT format.