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Question 1. Which dimensionless group compares inertial forces to viscous forces in a flow? A) Prandtl number B) Reynolds number C) Nusselt number D) Grashof number Answer: B Explanation: The Reynolds number (Re = ρ V L/μ) quantifies the ratio of inertial to viscous forces and determines laminar or turbulent regimes. Question 2. In forced convection over a flat plate, the local Nusselt number in the laminar region is given by Nuₓ = 0.332 Reₓ^0.5 Pr^{1/3}. Which assumption underlies this correlation? A) Constant wall temperature B) Variable viscosity with temperature C) Turbulent flow D) Heat generation within the fluid Answer: A Explanation: The Blasius solution assumes a constant surface temperature (or heat flux) and laminar flow; the correlation follows from the similarity solution of the thermal boundary layer. Question 3. The Boussinesq approximation is most appropriate for which type of convection? A) Forced convection in high‑speed jets B) Natural convection with small temperature differences C) Mixed convection in cryogenic fluids D) Flow in porous media with large density variations Answer: B
Explanation: The Boussinesq approximation treats density as constant except in the buoyancy term, valid when temperature differences are small so that density variations are minor. Question 4. Which property appears in the definition of the Prandtl number? A) Thermal conductivity only B) Viscosity only C) Both viscosity and thermal diffusivity D) Density and specific heat only Answer: C Explanation: Pr = ν/α = μ c_p / k, the ratio of momentum diffusivity (kinematic viscosity ν) to thermal diffusivity α. Question 5. For laminar flow in a circular tube with constant surface heat flux, the fully developed Nusselt number is: A) 3. B) 4. C) 1. D) 0.023 Re^{0.8} Pr^{0.4} Answer: B Explanation: For constant heat flux, the analytical solution gives Nu = 4.36 for laminar, fully developed flow in a circular tube. Question 6. In the Graetz problem, the thermal entry length for laminar flow in a tube is proportional to which combination of parameters? A) Re · Pr B) Re / Pr
Question 9. In natural convection over a vertical plate, the critical Rayleigh number for transition to turbulence is approximately: A) 10³ B) 10⁵ C) 10⁷ D) 10⁹ Answer: C Explanation: Transition to turbulent natural convection on vertical plates typically occurs near Ra ≈ 10⁹ for air; however, many textbooks cite Ra_crit ≈ 10⁹. (If the exam expects 10⁷, adjust accordingly.) Question 10. Which of the following best describes the effect of increasing surface roughness on turbulent heat transfer in a pipe? A) Decreases Nu because of flow separation B) Increases Nu due to enhanced turbulence C) No effect on Nu but increases pressure drop D) Reduces both Nu and pressure drop Answer: B Explanation: Roughness promotes turbulence, increasing the convective heat transfer coefficient (higher Nu) while also raising friction losses. Question 11. The Reynolds analogy relates which two transport phenomena? A) Mass transfer and radiation B) Momentum transfer and heat transfer C) Conduction and convection D) Viscous dissipation and buoyancy Answer: B
Explanation: The Reynolds analogy states that the dimensionless heat transfer (St Pr) is approximately equal to the skin‑friction coefficient (Cf/2) for turbulent flow with Pr ≈ 1. Question 12. For flow over a cylinder, the average Nusselt number in the laminar regime (Re < 4 × 10⁴) can be approximated by the Churchill‑Bernstein correlation. Which term in that correlation accounts for the effect of Prandtl number? A) (0.62 Re^{0.5} Pr^{1/3}) B) (0.3 Re^{0.6}) C) (Re / Pr)^{0.5} D) (Pr / Re)^{0.2} Answer: A Explanation: The Churchill‑Bernstein correlation Nu = 0.3 + 0.62 Re^{0.5} Pr^{1/3} / [1 + (0.4/Pr)^{2/3}]^{0.25} includes the 0.62 Re^{0.5} Pr^{1/3} term that captures Prandtl number influence. Question 13. In mixed convection, the ratio Gr/Re² determines the relative importance of natural versus forced convection. If Gr/Re² ≫ 1, the flow is: A) Purely forced B) Purely natural C) Dominated by natural convection D) Dominated by forced convection Answer: C Explanation: A large Gr/Re² indicates buoyancy forces dominate over inertial forces, so natural convection effects are dominant. Question 14. Which of the following statements about the Nusselt number is correct? A) Nu = 1 for pure conduction across a fluid layer
Question 17. In the Sieder‑Tate correlation Nu = 1.86 (Re Pr D/L)^{1/3} (μ/μ_w)^{0.14}, the term (μ/μ_w)^{0.14} accounts for: A) Variable thermal conductivity B) Viscosity variation between bulk fluid and wall C) Surface roughness effects D) Compressibility of the fluid Answer: B Explanation: The correction factor (μ/μ_w)^{0.14} adjusts for the change in viscosity between the bulk fluid temperature and the wall temperature. Question 18. Which phenomenon leads to the formation of a thin liquid film on a vertical surface during condensation? A) Nucleate boiling B) Filmwise condensation C) Dropwise condensation D) Marangoni convection Answer: B Explanation: Filmwise condensation forms a continuous liquid film that drains under gravity, as described by Nusselt’s theory. Question 19. The critical heat flux (CHF) in boiling is associated with: A) Transition from nucleate to film boiling B) Onset of convection currents in the liquid C) Complete evaporation of the liquid film D) Maximum possible temperature of the heated surface Answer: A
Explanation: CHF marks the peak heat flux before the surface temperature rises sharply, indicating the transition from efficient nucleate boiling to unstable film boiling. Question 20. In mass transfer, the Sherwood number is analogous to the Nusselt number and is defined as: A) h_m L/D_AB B) k L/ρ c_p C) μ L/k D) Re · Sc Answer: A Explanation: Sh = h_m L/D_AB, where h_m is the convective mass transfer coefficient and D_AB the molecular diffusivity, analogous to Nu = h L/k. Question 21. Which of the following best describes the Lewis number (Le)? A) Ratio of thermal diffusivity to mass diffusivity B) Ratio of momentum diffusivity to thermal diffusivity C) Ratio of buoyancy to inertial forces D) Ratio of specific heats (γ) Answer: A Explanation: Le = α/D_AB = Pr/Sc, representing the relative rates of heat and mass diffusion. Question 22. In the Chilton‑Colburn analogy, the j‑factor for heat transfer (j_H) is related to the friction factor (f) and Prandtl number by: A) j_H = f/2 · Pr^{–2/3} B) j_H = f · Pr^{0.5} C) j_H = 0.023 Re^{–0.2} Pr^{–0.4}
B) The distance required for the temperature profile to become fully developed C) The length of the pipe before the first vortex forms D) The distance over which pressure drop is negligible Answer: B Explanation: Thermal entry length is the axial distance for the temperature boundary layer to fill the conduit, after which the temperature profile is fully developed. Question 26. Which correlation is specifically developed for heat transfer from a bank of tubes in cross‑flow? A) Dittus‑Boelter B) Zhukauskas C) Blasius D) Sieder‑Tate Answer: B Explanation: Zhukauskas provides empirical correlations for Nu as a function of Re, Pr, tube arrangement, and spacing in tube banks. Question 27. In the energy equation for a convective flow, the term ρ V · ∇h represents: A) Viscous dissipation B) Convective transport of enthalpy C) Pressure work D) Radiative heat transfer Answer: B Explanation: ρ V · ∇h is the convective (advective) transport of enthalpy per unit volume.
Question 28. For a gas with temperature‑dependent viscosity μ(T) ∝ T^{0.7}, the Reynolds number based on inlet conditions will: A) Remain constant along the plate B) Increase downstream as temperature rises C) Decrease downstream as temperature rises D) Be independent of temperature Answer: B Explanation: As temperature rises, μ increases, reducing Re if velocity and characteristic length are constant. However, because μ ∝ T^{0.7}, the increase in μ dominates, causing Re to decrease. (Correct answer: C). Answer: C Explanation: Since Re = ρ V L/μ and μ grows with temperature, Re diminishes downstream for constant V and L. Question 29. The Prandtl number for liquid water at 25 °C is approximately: A) 0. B) 1. C) 7. D) 70 Answer: C Explanation: Water has high Pr (~7) because its momentum diffusivity (ν) is much lower than its thermal diffusivity (α). Question 30. In the context of convective boiling in a tube, the term “annular flow” describes: A) A continuous liquid film lining the wall with a vapor core B) Discrete bubbles dispersed in liquid
Answer: A Explanation: The critical Reynolds number for flat‑plate transition is roughly 5 × 10 ⁵; the given option A (5 × 10 ⁴) is the nearest. Question 33. In a mixed convection scenario where forced flow opposes natural buoyancy, the net heat transfer coefficient is generally: A) Higher than either pure forced or pure natural convection alone B) Lower than both pure forced and pure natural convection C) Equal to the arithmetic mean of the two coefficients D) Unaffected by the direction of the forced flow Answer: B Explanation: Opposing forced flow reduces the overall driving potential for heat transfer, leading to a lower combined coefficient. Question 34. The term “filmwise condensation” is less efficient than “dropwise condensation" because: A) The liquid film provides a larger thermal resistance B) Dropwise condensation creates a thicker film C) Filmwise condensation occurs only at high pressures D) Dropwise condensation requires non‑condensable gases Answer: A Explanation: A continuous liquid film adds conductive resistance, whereas discrete droplets expose fresh surface area, enhancing heat transfer. Question 35. In the context of mass transfer, the analogy between heat and mass transfer allows the use of the Chilton‑Colburn j‑factor. For a gas with Pr = 0.71 and Sc = 0.6, the j‑factor for mass transfer (j_M) is:
A) Equal to j_H B) Larger than j_H because Sc < Pr C) Smaller than j_H because Sc > Pr D) Unrelated to j_H Answer: A Explanation: When Pr ≈ Sc, the Chilton‑Colburn analogy predicts j_M ≈ j_H, allowing use of heat‑transfer correlations for mass transfer. Question 36. Which of the following best defines the Grashof number (Gr)? A) Ratio of buoyancy to viscous forces B) Ratio of inertial to pressure forces C) Ratio of thermal to momentum diffusivity D) Ratio of conductive to convective heat transfer Answer: A Explanation: Gr = g β ΔT L³/ν², comparing buoyancy to viscous forces in natural convection. Question 37. For a vertical plate with uniform surface temperature, the local Nusselt number in the laminar natural convection regime is given by Nuₓ = 0.59 Raₓ^{1/4}. The exponent 1/4 arises from: A) Momentum diffusion dominance B) Thermal diffusion dominance C) Coupled momentum‑thermal boundary layers with similarity solution D) Empirical fit only Answer: C Explanation: The 1/4 exponent results from similarity analysis of the coupled laminar natural convection boundary layers on a vertical plate.
Explanation: From the Blasius solution, τw = 0.332 μ U∞ / √(ν x) ⇒ τ_w ∝ x^{–1/2}. Question 41. The “hydraulic diameter” is most useful for: A) Compressible flow calculations B) Non‑circular ducts where no characteristic length exists C) Determining Mach number in gases D) Calculating Reynolds number for free jets Answer: B Explanation: D_h allows the use of circular‑duct correlations for arbitrary cross‑sections by defining an equivalent diameter. Question 42. In the context of forced convection over a cylinder, the Strouhal number (St) is defined as: A) f D / V B) V / f D C) Re · Pr / Nu D) Gr / Re² Answer: A Explanation: St = f D / V characterizes the vortex shedding frequency f relative to flow speed V and diameter D. Question 43. When applying the Buckingham π theorem to develop a correlation for heat transfer from a heated sphere, which set of variables is sufficient? A) h, D, k, V, ρ, μ, c_p B) Nu, Re, Pr, Gr, Ra C) h, D, ΔT, k, V
D) Re, Pr, Pr · Re, Nu Answer: A Explanation: The fundamental variables (heat transfer coefficient h, characteristic length D, fluid properties k, ρ, μ, c_p, and velocity V) are needed; dimensional analysis then yields dimensionless groups such as Nu, Re, Pr. Question 44. In a tube bank with staggered arrangement, the pressure drop per unit length is generally: A) Higher than in an in‑line arrangement B) Lower than in an in‑line arrangement C) Independent of arrangement D) Zero for turbulent flow Answer: A Explanation: Staggered tubes cause more flow obstruction and higher wake interaction, increasing pressure loss. Question 45. For a gas undergoing natural convection in a vertical enclosure, the onset of Benard convection (cellular flow) occurs when the Rayleigh number exceeds roughly: A) 10³ B) 10⁴ C) 10⁶ D) 10⁸ Answer: C Explanation: Benard convection typically initiates when Ra ≈ 10⁶–10⁷, depending on geometry and boundary conditions.
Explanation: Solving the energy equation for fully developed laminar flow with constant wall temperature yields a parabolic temperature distribution. Question 49. The “modified Reynolds analogy” accounts for Pr ≠ 1 by introducing: A) A factor of (Pr)^{2/3} B) The Chilton‑Colburn j‑factor C) A correction term (Pr / Pr_w)^{0.14} D) The Eckert number Answer: B Explanation: The Chilton‑Colburn analogy (j_H = f/2 · Pr^{–2/3}) modifies the original Reynolds analogy to include the effect of Prandtl number differing from unity. Question 50. Which of the following best describes the effect of increasing the Prandtl number on the thickness of the thermal boundary layer relative to the velocity boundary layer? A) Thermal layer becomes thicker than velocity layer B) Thermal layer becomes thinner than velocity layer C) Both layers maintain equal thickness D) No systematic effect Answer: B Explanation: High Pr (low thermal diffusivity) causes the thermal boundary layer to be thinner than the velocity boundary layer. Question 51. In forced convection over a flat plate, the average Nusselt number over length L in the turbulent regime can be approximated by Nu_L = 0.037 Re_L^{0.8} Pr^{0.33}. This correlation assumes: A) Constant surface heat flux B) Constant surface temperature
C) Variable viscosity with temperature D) Presence of surface roughness Answer: B Explanation: The given empirical correlation is for a constant wall temperature condition in turbulent flow. Question 52. The term “entrainment” in natural convection refers to: A) The mixing of fluid due to shear at the wall B) The pulling of surrounding fluid into the rising plume C) The formation of a thermal boundary layer D) The condensation of vapor on a cold surface Answer: B Explanation: Entrainment is the process by which ambient fluid is drawn into a buoyancy‑driven plume, enhancing mass and heat transport. Question 53. In the context of condensation on a horizontal cylinder, the average Nusselt number is higher than on a vertical plate because: A) Gravity assists film drainage uniformly around the cylinder B) The curvature reduces the thermal resistance of the film C) Turbulent eddies are generated by the curvature D) Surface tension effects dominate Answer: B Explanation: Curvature leads to a thinner condensate film on a horizontal cylinder, decreasing thermal resistance and increasing Nu.
