In steady-state heat conduction through a composite wall with three layers in series, if the thermal conductivities are k₁ > k₂ > k₃, which layer will have the maximum temperature drop?
Answer: C
Temperature drop across a layer is inversely proportional to thermal conductivity (ΔT ∝ 1/k). Since k₃ is smallest, layer 3 experiences maximum temperature drop.
Q.122Easy
The Biot number (Bi) is defined as the ratio of which resistances in transient heat conduction?
Answer: B
Bi = hL_c/k, representing the ratio of internal conduction resistance to external convection resistance at the surface.
Q.123Medium
For a circular fin of diameter d and length L attached to a surface at temperature T₀, the fin effectiveness approaches zero when:
Answer: B
When mL → ∞, the temperature along the fin drops rapidly and efficiency decreases, approaching zero as the fin becomes ineffective.
Q.124Medium
In forced convection heat transfer, the Colburn factor (j_H) is related to which dimensionless numbers?
Answer: A
The Colburn analogy relates Stanton number to Nusselt, Reynolds, and Prandtl numbers: j_H = St·Pr^(32) = Nu/(Re·Pr^(31)).
Q.125Easy
The Fourier number (Fo = αt/L²) in unsteady-state conduction represents the ratio of:
Answer: A
Fo represents the relative importance of heat conducted (diffused) into the object compared to heat stored, dimensionless time.
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Q.126Hard
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.127Easy
The Stefan-Boltzmann constant (σ) has SI units of:
Answer: B
From Q = σAT⁴, σ has units W·m⁻²·K⁻⁴ (5.67 × 10⁻⁸ W·m⁻²·K⁻⁴).
Q.128Medium
In laminar flow through a circular tube with constant wall temperature, the Nusselt number is constant at Nu ≈ 3.66. This means:
Answer: C
Constant Nu in fully developed laminar flow indicates entrance effects are negligible and thermal profile is established.
Q.129Hard
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.130Easy
The Rayleigh number (Ra) in natural convection is defined as Ra = Gr·Pr. When Ra < 10⁹ for vertical surfaces, the heat transfer is primarily:
Answer: B
For Ra < 10⁹, natural convection remains laminar; transition to turbulence occurs around Ra ≈ 10⁹.
Q.131Medium
In a recuperative heat exchanger, the effectiveness (ε) is defined as the ratio of actual heat transfer to:
Answer: A
Effectiveness ε = Q_actual/Q_max = Q/(C_min(T_h,in - T_c,in)) for counterflow and parallel flow exchangers.
Q.132Medium
The Peclet number (Pe = Re·Pr) in convective heat transfer indicates that:
Answer: C
Pe represents relative importance of convection to diffusion: Pe >> 1 indicates convection dominance, Pe << 1 indicates diffusion dominance.
Q.133Hard
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.134Medium
The mean free path (λ) in gas kinetic theory at standard conditions is approximately 60 nm. This implies that at atmospheric pressure, heat conduction in gases is primarily through:
Answer: A
Small mean free path (60 nm << device dimension) ensures continuous medium behavior and heat transfer via molecular diffusion.
Q.135Hard
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.136Hard
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.137Medium
The convective heat transfer coefficient 'h' for natural convection from a vertical surface at constant temperature increases with height due to:
Answer: C
While boundary layer grows (reducing h), buoyancy increases velocity and local Gr increases (increasing h). Combined effect shows h varies as x^(-41).
Q.138Medium
In radiation view factor calculations, the reciprocity relation F₁₂·A₁ = F₂₁·A₂ ensures:
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.140Easy
The dimensionless Stanton number (St = h/(ρ·v·c_p)) in heat transfer represents:
Answer: A
St represents the fraction of heat that can be transferred relative to the sensible heat available in flowing fluid per unit area per unit time.
