NCEES Heat Transfer 2 — Questions and Answers
Question 1: Thermal diffusivity α is defined as which of the following combinations of material properties?
- k/(ρcp) (Correct answer)
- ρcp/k
- k·ρ·cp
- cp/(ρk)
Correct answer: k/(ρcp)
Thermal diffusivity α = k/(ρcp) represents how quickly a material conducts heat relative to its ability to store it.
Question 2: For a hollow cylinder with inner radius r₁, outer radius r₂, length L, and thermal conductivity k, the conductive thermal resistance is:
- ln(r₂/r₁) / (2πkL) (Correct answer)
- (r₂ − r₁) / (2πkL)
- ln(r₂/r₁) / (πkL)
- 2πkL / ln(r₂/r₁)
Correct answer: ln(r₂/r₁) / (2πkL)
Integrating Fourier's Law in cylindrical coordinates gives R_cyl = ln(r₂/r₁)/(2πkL).
Question 3: The Log Mean Temperature Difference (LMTD) method is primarily used to analyze:
- Transient heat conduction in solids
- Heat exchanger performance (Correct answer)
- Radiation heat transfer between surfaces
- Natural convection from vertical plates
Correct answer: Heat exchanger performance
LMTD provides the effective mean driving temperature difference for heat exchangers where temperatures vary along the length.
Question 4: In a counterflow heat exchanger compared to a parallel-flow arrangement with the same inlet conditions and UA product, which statement is correct?
- Counterflow always has lower effectiveness
- Counterflow achieves higher LMTD and greater heat transfer (Correct answer)
- Both configurations yield identical heat transfer rates
- Parallel flow allows the cold fluid to exceed the hot fluid outlet temperature
Correct answer: Counterflow achieves higher LMTD and greater heat transfer
Counterflow maintains a more uniform temperature difference along its length, yielding a higher LMTD and therefore greater heat transfer capacity.
Question 5: Fin efficiency (η_f) is defined as:
- Actual fin heat transfer divided by maximum heat transfer if entire fin were at base temperature (Correct answer)
- Ratio of fin surface area to fin base area
- Fin heat transfer divided by total bare-wall heat transfer
- Ratio of fin length to fin thickness
Correct answer: Actual fin heat transfer divided by maximum heat transfer if entire fin were at base temperature
Fin efficiency η_f = q_actual / q_max, where q_max = hA_f(T_b − T∞) assumes the entire fin surface is at the base temperature.
Question 6: For radiation exchange between two large parallel plates with emissivities ε₁ and ε₂, the net heat flux is given by:
- q" = σ(T₁⁴ − T₂⁴)·ε₁·ε₂
- q" = σ(T₁⁴ − T₂⁴) / (1/ε₁ + 1/ε₂ − 1) (Correct answer)
- q" = σ(T₁² − T₂²)·(ε₁ + ε₂)
- q" = ε₁·ε₂·σ(T₁ − T₂)⁴
Correct answer: q" = σ(T₁⁴ − T₂⁴) / (1/ε₁ + 1/ε₂ − 1)
The radiation network for two large parallel plates gives q" = σ(T₁⁴−T₂⁴)/(1/ε₁ + 1/ε₂ − 1), accounting for surface resistances.
Question 7: The Prandtl number (Pr) for a fluid is defined as the ratio of:
- Momentum diffusivity to thermal diffusivity (ν/α) (Correct answer)
- Thermal diffusivity to momentum diffusivity (α/ν)
- Buoyancy force to viscous force
- Convective to conductive heat transfer
Correct answer: Momentum diffusivity to thermal diffusivity (ν/α)
Pr = ν/α = μcp/k; it characterizes the relative thickness of the velocity and thermal boundary layers.
NCEES Heat Transfer 2
Thermal diffusivity α is defined as which of the following combinations of material properties?