In a parallel flow heat exchanger, hot fluid enters at 80°C and exits at 50°C while cold fluid enters at 20°C and exits at 40°C. Calculate the Log Mean Temperature Difference (LMTD).
Which of the following dimensionless numbers is used to predict the transition from laminar to turbulent flow in forced convection?
Answer: B
Reynolds number determines the flow regime in forced convection. Re < 2300 indicates laminar flow, Re > 4000 indicates turbulent flow. Grashof and Rayleigh are used for natural convection, while Fourier number is for transient conduction.
Q.43Medium
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.44Easy
In the context of thermal radiation, the Stefan-Boltzmann constant has a value of:
Answer: A
The Stefan-Boltzmann constant σ = 5.67 × 10⁻⁸ W/m²·K⁴ is used in radiation heat transfer calculations (Q = σAε(T⁴)). Other options are physical constants used in different domains.
Q.45Easy
A horizontal cylindrical pipe carries hot water at 80°C through ambient air at 20°C. The convective heat transfer coefficient is 25 W/m²·K and pipe diameter is 50 mm. Calculate heat loss per unit length if the pipe is not insulated.
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.47Medium
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.49Hard
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.
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.51Medium
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.52Medium
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.53Hard
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.54Medium
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.55Medium
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.56Medium
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.57Hard
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.58Easy
Which of the following materials would be most suitable for a heat sink application requiring high thermal conductivity and low cost?
Answer: B
Aluminum alloys offer an excellent balance of thermal conductivity (160 W/m·K, sufficient for most applications), cost-effectiveness, light weight, corrosion resistance, and ease of machining. While copper has higher conductivity, aluminum's cost-benefit ratio is superior for heat sink applications.
Q.59Hard
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.60Medium
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.
