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.62Medium
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.63Medium
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.64Medium
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.65Medium
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
Q.67Medium
Which heat exchanger type provides the maximum temperature effectiveness under the same flow conditions?
Answer: A
Counter-flow heat exchangers are most effective because they maintain the maximum temperature gradient throughout the exchanger length, resulting in higher heat transfer rates and effectiveness compared to parallel or cross-flow configurations.
Q.68Medium
A surface at 300 K with emissivity 0.8 radiates heat to surroundings at 250 K. Calculate the net radiative heat transfer per m² (σ = 5.67 × 10⁻⁸ W/m²·K⁴).
In transient heat conduction, the Fourier number (Fo = α·t/L²) represents:
Answer: D
Fourier number represents the dimensionless time or the measure of how far thermal disturbances have penetrated into the material. High Fo indicates significant internal temperature changes, while low Fo indicates the disturbance is confined to the surface.
Q.70Medium
For natural convection over a vertical flat plate, the Nusselt number correlation is typically given by Nu = C·Ra^n. What is the typical value of exponent 'n'?
Answer: B
For laminar natural convection on vertical plates, Nu = 0.59·Ra⁰·²⁵ is used, while for turbulent natural convection (Ra > 10⁹), Nu = 0.1·Ra⁰·³³ is commonly used. The value 0.33 or 31 is standard for turbulent natural convection.
Q.71Medium
In a shell and tube heat exchanger, which configuration reduces the pressure drop while maintaining adequate heat transfer?
Answer: A
Increasing the number of tube passes distributes the flow over more tubes, reducing the velocity in each tube and consequently reducing pressure drop while maintaining heat transfer area. This is a design optimization technique in shell and tube exchangers.
Q.72Medium
A spherical tank of diameter 1 m containing hot liquid at 90°C is placed in ambient air at 15°C. If h = 8 W/m²·K and k_insulation = 0.05 W/m·K with 50 mm insulation thickness, calculate the heat loss rate.
Answer: A
Surface area A = 4πr² = 4π(0.5)² = 3.14 m². Convection resistance R_conv = 1/(h·A) = 1/(8×3.14) = 0.0398 K/W. Conduction resistance (spherical) can be neglected due to small thickness. Q = ΔT/(R_conv) = 075.67 ≈ 112 W
Q.73Medium
In a finned tube heat exchanger, the overall surface effectiveness is 0.75. This means:
Answer: A
Overall surface effectiveness accounts for both fin and base surface contributions. A value of 0.75 indicates that 75% of the theoretical maximum heat transfer (assuming entire surface at base temperature) is actually achieved due to fin efficiency and geometric factors.
Q.74Medium
In a double-pipe heat exchanger with counter-flow arrangement, the LMTD correction factor F = 0.95. What does this indicate?
Answer: C
The LMTD correction factor F accounts for deviations from ideal counter-flow behavior in real heat exchangers. F = 0.95 means the actual heat transfer is 95% of what would be obtained with ideal counter-flow configuration due to practical geometry constraints.
Q.75Medium
A heat pipe is used to transfer heat from an electronic component at 80°C to ambient air at 25°C through evaporation and condensation. What is the primary advantage of a heat pipe over conventional conduction cooling?
Answer: B
Heat pipes achieve very high effective thermal conductivity (often >1000 times that of copper) through the latent heat of evaporation and condensation of working fluid, making them ideal for high-power electronics cooling despite the small cross-sectional area.
Q.76Medium
A condenser operates with steam at 100°C condensing on a tube bank at 20°C. The saturation temperature drop is negligible. Which phase of condensation provides maximum heat transfer rate?
Answer: B
Dropwise condensation provides heat transfer coefficients 5-10 times higher than filmwise condensation because liquid droplets continuously shed, exposing fresh surface to direct contact with steam. However, filmwise condensation is more common industrially due to stability issues with dropwise condensation.
Q.77Medium
Which of the following methods is most suitable for measuring the convective heat transfer coefficient in real-time industrial applications?
Answer: B
Thermographic imaging using infrared cameras is a non-intrusive, real-time method that can measure surface temperature variations across the heat transfer surface without disturbing the flow, making it practical for industrial monitoring.
Q.78Medium
In a cross-flow heat exchanger where both fluids are unmixed, the effectiveness (ε) is lower than in a counter-flow arrangement. What is the main reason for this?
Answer: C
In cross-flow (especially unmixed-unmixed), the temperature gradients are not as favorable as counter-flow because one or both fluids cannot maintain continuous temperature gradient alignment, resulting in lower effectiveness and hence lower LMTD correction factor.
Q.79Medium
The Grashof number (Gr) is used to characterize natural convection. For natural convection heat transfer, which of the following correctly describes the Grashof number?
Answer: A
The Grashof number Gr = (ρ²gβΔT L³)/(μ²) represents the ratio of buoyancy forces to viscous forces in natural convection. It determines the onset of natural convection and its intensity.
Q.80Medium
In heat exchanger design for petrochemical plants, fouling resistance (Rf) is critical. For a crude oil preheater, the typical internal fouling resistance is 0.0005 m²·K/W. If the design duty is 5 MW, what is the maximum temperature difference loss due to fouling on a surface area of 100 m²?
Answer: A
Using Q = UAΔT and considering fouling resistance: ΔT_fouling = Q × Rf / A = 5×10⁶ × 0.1000005 = 25 K. However, for the temperature loss specifically attributed to fouling layer: ΔT = Rf × (Q/A) = 0.0005 × (5×10⁶/100) = 2.5 K.
