For a long thin fin with adiabatic tip condition, the fin efficiency is given by:
Answer: A
For adiabatic tip condition: η_fin = tanh(mL)/(mL), where m = √(hP/kA_c). This represents the efficiency of heat transfer through the fin.
Q.2Hard
In a parallel plate channel with constant heat flux q'' on both walls, what is the thermal entrance length relationship with hydrodynamic entrance length?
Answer: A
Thermal entrance length L_th ≈ L_h/Pr for laminar flow, where Pr < 1 for metals means thermal entrance is shorter than hydrodynamic entrance.
Q.3Hard
The Graetz number in laminar heat transfer represents:
Answer: A
Graetz number Gz = (D_h/L) × Re × Pr indicates relative importance of entrance effects. Gz > 100 means entrance region dominates.
Q.4Hard
Which statement best describes radiation heat transfer in participating media?
Answer: B
In participating media (like CO₂, H₂O vapor), radiation is absorbed and re-emitted by gas molecules, affecting net radiative heat transfer significantly.
Q.5Hard
For a microfin tube (enhanced surface), the heat transfer improvement comes primarily from:
Answer: C
Microfins provide dual benefits: (1) increased surface area A, and (2) enhanced convection coefficient h by disrupting boundary layer development, thus improving overall heat transfer coefficient.
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Q.6Hard
In a counter-flow double pipe heat exchanger, the outlet temperature of hot fluid becomes lower than the outlet temperature of cold fluid. This is:
Answer: C
In counter-flow, the temperature profiles allow hot outlet to be lower than cold outlet with sufficient heat transfer area, limited by second law of thermodynamics.
Q.7Hard
For radiation heat exchange between two parallel plates at temperatures T₁ and T₂ with emissivities ε₁ and ε₂, the radiation heat transfer is reduced by factor:
Answer: B
For two parallel plates, Q = σA·F(T₁⁴ - T₂⁴) where F = ε₁ε₂/(ε₁ + ε₂ - ε₁ε₂), derived from network resistance analogy.
Q.8Hard
For boiling heat transfer, the critical heat flux (CHF) depends on which property most strongly?
Answer: C
CHF correlations (Zuber equation) strongly depend on surface tension (σ) and (ρ_l - ρ_v) density difference.
Q.9Hard
In turbulent flow heat transfer for gases (Pr ≈ 0.7), the viscous sublayer thickness δ_v relates to thermal boundary layer thickness δ_t as:
Answer: B
For turbulent flow, thermal boundary layer is thicker than viscous sublayer by factor 1/Pr^(31) when Pr < 1.
Q.10Hard
In a once-through steam generator (OTSG) for heat recovery, the effectiveness-NTU relation for counterflow is ε = 1 - exp(-NTU(1-C_r))/(1-C_r·exp(-NTU(1-C_r))) where C_r = C_min/C_max. When C_r = 1, this simplifies to:
Answer: A
For C_r = 1 (equal capacity rates), counterflow relation simplifies to ε = NTU/(1 + NTU), same as parallel flow.
Q.11Hard
For condensation of saturated steam on a vertical cold surface, the local heat transfer coefficient h_x at height x is given by Nusselt equation: h_x = 0.943[ρ_l(ρ_l-ρ_v)gk_l³h_fg/(μ_l·ΔT·x)]^(41). When condensate film thickness increases:
Answer: B
Nusselt condensation correlation shows h_x ∝ x^(-41), meaning heat transfer coefficient decreases as film thickness grows from top to bottom.
Q.12Hard
A copper plate (k = 400 W/m·K) of thickness 5 mm experiences thermal shock due to sudden temperature change from 20°C to 500°C. Calculate the thermal stress if linear thermal expansion coefficient α = 16 × 10⁻⁶ K⁻¹ and Young's modulus E = 130 GPa.
Which of the following statements about the thermal boundary layer in forced convection is incorrect?
Answer: D
Thermal boundary layer thickness δₜ depends on thermal conductivity through the thermal diffusivity (α = k/ρ·Cₚ). Statement D is incorrect as k directly affects the temperature profile and boundary layer development in the thermal region.
Q.14Hard
In a gas turbine blade cooling system, film cooling effectiveness is defined as η = (T_g - T_surface)/(T_g - T_coolant). If T_g = 1200 K, T_coolant = 600 K, and measured T_surface = 900 K, calculate the cooling effectiveness.
Answer: B
η = (1200 - 900)/(1200 - 600) = 600300 = 0.50 or 50%. This indicates moderate cooling effectiveness, typical for turbine blade film cooling systems.
Q.15Hard
In turbulent forced convection over a flat plate, the local Nusselt number varies as Nu_x ∝ x^n. What is the typical exponent 'n'?
Answer: A
For turbulent flow over a flat plate, the local Nusselt number Nu_x decreases along the flow direction due to development of the thermal boundary layer. The relationship follows Nu_x ∝ x⁻⁰·² or Re_x⁰·⁸, indicating decreasing local heat transfer coefficient with distance from leading edge.
Q.16Hard
In the design of a steam generator, the pinch point is the minimum temperature approach between steam and feedwater. What is its practical significance?
Answer: C
The pinch point represents the location where the minimum temperature difference exists between hot and cold fluids. A smaller pinch point requires larger heat transfer area (higher capital cost) but improves thermal effectiveness. The pinch point design directly impacts equipment sizing and economic optimization.
Q.17Hard
A cryogenic heat exchanger operates with liquid nitrogen at 77 K on one side. The convective heat transfer coefficient on the nitrogen side is 800 W/(m²·K). The copper tubing has an inner diameter of 12 mm and outer diameter of 14 mm. Assuming the thermal conductivity of copper is 400 W/(m·K), what is the approximate overall heat transfer coefficient (considering only internal convection and conduction through copper wall)?
Answer: C
For a thin tube with copper wall, the thermal resistance is minimal. Using 1/U = 1/h_i + (r_o ln(r_o/r_i))/(k). With h_i = 800, thin wall effect: 1/U ≈ 8001 + very small value ≈ 0.00125, so U ≈ 780 W/(m²·K), closest to 775.
Q.18Hard
In the analysis of thermal stability of a convective system, the Richardson number (Ri) is used to compare natural and forced convection. Ri = Gr/Re². When Ri >> 1, what flow regime dominates?
Answer: B
The Richardson number Ri = Gr/Re² compares buoyancy effects (Grashof) to external flow effects (Reynolds). When Ri >> 1, the Grashof number is much larger, meaning buoyancy forces dominate and natural convection is the primary mechanism.
Q.19Hard
For a finned surface used in air-cooled heat exchangers, the fin efficiency is given by η_f = tanh(mL)/(mL), where m = √(hP/(kA_c)). As the fin length L increases, what happens to the fin efficiency?
Answer: B
As fin length increases, the parameter mL increases, making tanh(mL)/(mL) decrease. This is because heat must travel a longer distance through the fin material, causing temperature gradients and reducing effectiveness of the fin tip area.
Q.20Hard
In a regenerative heat exchanger (rotary wheel type), the effectiveness depends on the capacity rate ratio and heat capacity of the wheel material. If the wheel rotates slowly (high residence time), what effect does this have on effectiveness?
Answer: A
In rotary regenerators, slower rotation provides longer residence time for each sector in contact with hot and cold fluids, increasing heat transfer duration and thereby increasing the overall effectiveness of heat recovery.
