What is the Biot number (Bi) used to determine in transient heat conduction?
Answer: A
Biot number = hL_c/k determines whether lumped capacitance method is applicable. Bi << 0.1 indicates uniform internal temperature.
Q.2Medium
For fully developed laminar flow in a circular pipe with constant wall heat flux, which Nusselt number (Nu) is approximately correct?
Answer: B
For constant heat flux boundary condition (H1 type) in circular pipes with fully developed laminar flow, Nu ≈ 4.36. For constant wall temperature (H2), Nu ≈ 3.66.
Q.3Medium
In a counter-current heat exchanger with equal heat capacities, what is the maximum possible effectiveness?
Answer: A
For counter-current arrangement, maximum effectiveness can approach 1.0 (100%) with infinite NTU. For co-current, it's limited to (1-exp(-NTU(1+C_r)))/(1+C_r).
Q.4Medium
The Number of Transfer Units (NTU) is defined as which of the following?
Answer: A
NTU = UA/(ṁC_p)_min is the ratio of overall heat transfer capacity to minimum heat capacity rate, used in ε-NTU method.
Q.5Medium
The log mean temperature difference (LMTD) correction factor F is required primarily for which configuration?
Answer: B
F-correction factor is used for non-counter-current arrangements (cross-flow, 1-2 shell-tube, etc.) where LMTD doesn't directly apply without correction.
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Q.6Medium
For turbulent flow in smooth pipes (Pr > 0.6), which correlation is most commonly used?
Answer: A
Dittus-Boelert correlation is the most widely used for turbulent flow with Pr > 0.6. Valid for Re > 10,000, smooth pipes, and fully developed flow.
Q.7Medium
In a shell-and-tube heat exchanger (1 shell pass, 2 tube passes), the effectiveness is lower than counter-current primarily because:
Answer: A
In 1-2 arrangement, portion of shell-side flows co-currently with tube-side, reducing overall effectiveness compared to true counter-current.
Q.8Medium
For a flat plate solar collector with selective coating, which of the following is most desirable?
Answer: B
Selective coatings should absorb solar radiation (high α_sol) but minimize thermal radiation losses (low ε_IR), maximizing collector efficiency.
Q.9Medium
For natural convection from a vertical isothermal plate in air, which correlation applies best?
Answer: A
For natural convection: Nu = C(Ra)^n where Ra = Gr×Pr. For laminar boundary layer (Ra < 10^9), n ≈ 0.25. For turbulent (Ra > 10^9), n ≈ 0.33.
Q.10Medium
In unsteady-state conduction with Bi << 0.1, what assumption is valid?
Answer: A
When Bi < 0.1, convective resistance is much larger than conductive resistance, allowing assumption of uniform temperature throughout the object.
Q.11Medium
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.12Medium
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.13Medium
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.14Medium
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.15Medium
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.16Medium
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.17Medium
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.18Medium
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.19Medium
In radiation view factor calculations, the reciprocity relation F₁₂·A₁ = F₂₁·A₂ ensures:
A steel rod (k = 50 W/m·K) of diameter 10 mm and length 100 mm is exposed to air at 25°C with h = 20 W/m²·K. The rod is maintained at 100°C at one end. Calculate the fin efficiency if m = √(hP/kA) = 8.37 m⁻¹.
Answer: B
mL = 8.37 × 0.1 = 0.837. Fin efficiency η = tanh(mL)/(mL) = tanh(0.837)/0.837 = 0.0688.837 ≈ 0.72
