The thermal entrance length for laminar flow in a pipe is given by x_th/D ≈ 0.05·Re·Pr. For water flowing in a 25 mm diameter pipe with Reynolds number of 1000 and Prandtl number of 7, what is the thermal entrance length?
Answer: A
x_th = 0.05 × Re × Pr × D = 0.05 × 1000 × 7 × 0.025 = 8.75 m. This is the distance from the entrance where thermal development is completed (approximately 99% developed).
Q.82Medium
In a parallel-flow heat exchanger with hot inlet temperature Th,in = 100°C, cold inlet temperature Tc,in = 30°C, and hot outlet temperature Th,out = 60°C, what is the hot fluid capacity rate ratio if the cold outlet temperature is 50°C?
Answer: A
For energy balance: Ch(Th,in - Th,out) = Cc(Tc,out - Tc,in). So Ch(100-60) = Cc(50-30), which gives Ch/Cc = 4020 = 0.5. This is the capacity rate ratio.
Q.83Medium
The Colburn factor (j) for heat transfer is related to the Nusselt number. For turbulent flow over a flat plate, the typical correlation is j ≈ 0.037·Re^(-0.2). What does the Colburn factor represent?
Answer: B
The Colburn factor (j) is a dimensionless group that relates heat transfer characteristics to flow properties. It connects the Stanton number to the Prandtl number: St = j/Pr^(32), allowing transfer of empirical heat transfer data to different systems.
Q.84Medium
In the design of a heat recovery steam generator (HRSG) for a combined cycle power plant, the approach temperature is 5°C. If the exhaust gas inlet temperature is 450°C and the approach temperature represents the difference between exhaust gas exit and steam outlet temperatures, what is the steam outlet temperature?
Answer: B
The approach temperature is defined as: Approach = T_gas,out - T_steam,out. Given that typical exhaust exit from HRSG is around 450°C and approach is 5°C, T_steam,out = 450 - 5 = 445°C.
Q.85Medium
The effectiveness-NTU (Number of Transfer Units) method is preferred over LMTD method when designing heat exchangers because:
Answer: B
In heat exchanger design, outlet temperatures are unknown, making the LMTD method iterative and cumbersome. The NTU method (ε-NTU) directly uses inlet temperatures and known parameters to find the outlet temperatures without iteration, making it ideal for design problems.
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Q.86Medium
For turbulent flow in a rough pipe, the friction factor is determined by both Reynolds number and relative roughness (ε/D). According to the Moody chart, in the complete turbulence zone, the friction factor becomes independent of:
Answer: A
In the complete turbulence zone (very high Reynolds numbers), the friction factor depends only on the relative roughness (ε/D) and becomes independent of Reynolds number. This is because inertial forces completely dominate over viscous forces.
Q.87Medium
The Peclet number (Pe = Re·Pr) is used to determine the relative importance of convection to conduction. For Pe << 1, which heat transfer mechanism is dominant?
Answer: B
The Peclet number Pe = Re·Pr = (velocity × characteristic length × ρ·cp)/k represents the ratio of convection to conduction. When Pe << 1, conduction dominates over convection because advective transport is very slow compared to thermal diffusion.
Q.88Medium
A shell-and-tube heat exchanger with one shell pass and two tube passes (1-2 STHE) has a correction factor F. What is the typical range of F values?
Answer: A
The correction factor F (applied to LMTD) for 1-2 STHE typically ranges from 0.5 to 0.9 depending on temperature ratios and heat capacity ratios. F is always ≤ 1.
Q.89Medium
In convective heat transfer, which dimensionless number represents the ratio of buoyant to viscous forces?
Answer: D
Grashof number (Gr = gβΔT L³/ν²) directly represents buoyancy to viscous force ratio. Rayleigh number (Ra = Gr·Pr) combines Grashof and Prandtl numbers for natural convection.
Q.90Medium
For radiation heat transfer between two surfaces, increasing the absolute temperature of the hot surface by 10% will increase radiative heat transfer by approximately what percentage?
Answer: D
Radiative heat transfer follows Stefan-Boltzmann law: Q ∝ T⁴. If T increases by 10%, new flux = (1.1T)⁴ = 1.464T⁴ ≈ 46.4% increase.
Q.91Medium
The overall heat transfer coefficient U in a composite system (series resistances) is determined by which method?
Answer: A
Overall heat transfer coefficient is the reciprocal of total thermal resistance: 1/U = 1/(h₁A) + L/(kA) + 1/(h₂A). This accounts for series arrangement of convection and conduction resistances.
Q.92Medium
In pool boiling, the critical heat flux (CHF) occurs at which point on the boiling curve?
Answer: B
Critical heat flux (CHF) is the maximum heat flux in nucleate boiling. Beyond this point, further heat input causes transition to film boiling with lower heat transfer coefficient, leading to surface temperature rise (burnout).
Q.93Medium
The Prandtl number (Pr = Cp·μ/k) represents the ratio of which two transport properties?
Answer: A
Prandtl number = ν/α where ν = μ/ρ (momentum diffusivity) and α = k/(ρCp) (thermal diffusivity). Pr << 1 means heat diffuses faster than momentum; Pr >> 1 means momentum diffuses faster.
Q.94Medium
In a multipass heat exchanger design, increasing the number of shell passes from 1 to 2 will predominantly affect which parameter?
Answer: B
Adding shell passes (1-2 or 2-4 configuration) brings the temperature distribution closer to counterflow arrangement, increasing the correction factor F (reducing mismatch with LMTD). This increases effective heat transfer driving force without changing h significantly.
Q.95Medium
For turbulent flow in rough pipes at high Reynolds numbers, which friction factor equation is most applicable?
Answer: B
Colebrook-White equation is implicit but accurate for all turbulent regimes including rough pipes. For very rough pipes at high Re, relative roughness dominates.
Q.96Medium
Water flows through a venturimeter with inlet diameter 0.1 m and throat diameter 0.05 m. The pressure difference is 5 kPa. Assuming ideal flow, calculate the velocity at the inlet (ρ = 1000 kg/m³).
Answer: B
Using continuity and Bernoulli: V₁ = √[2ΔP/(ρ(A₁²/A₂² - 1))]. With area ratio 4, V₁ = √[2×5000/(1000×15)] = 2.88 m/s.
Q.97Medium
Which type of pump is most suitable for high-head, low-flow applications?
Answer: B
Reciprocating pumps (piston/plunger) are positive displacement pumps ideal for high-head, low-flow conditions. Centrifugal pumps suit high-flow, low-head applications.
Q.98Medium
What is the relationship between Fanning friction factor (f) and Darcy friction factor (fD)?
Answer: A
Fanning factor is ¼ of Darcy factor: f = fD/4. Both relate pressure drop to flow, but through different equations.
Q.99Medium
In a packed bed, if particle diameter increases while maintaining constant bed porosity and superficial velocity, the pressure drop will:
Answer: B
Ergun equation: ΔP ∝ (1-ε)²V/(ε³dp²). Pressure drop is inversely proportional to dp². Larger particles = lower pressure drop.
Q.100Medium
The drag coefficient for a sphere in creeping flow (Re < 0.1) is given by:
Answer: A
For creeping flow (Stokes law), CD = 24/Re. This is valid for Re < 0.1. For higher Re, additional terms and constant drag apply.
