Aerothermodynamics in High-Speed Flight: Mathematical Problems on
Heat Transfer to Aircraft Surfaces
1. An aircraft flying at Mach 2 experiences a temperature rise due to kinetic heating. If the ambient
temperature is -50°C, what is the stagnation temperature, assuming a recovery factor of 1?
a) 89°C
b) 91°C
c) 93°C
d) 95°C
Answer: c) 93°C
2. Calculate the heat flux (in W/m²) to an aircraft surface if the heat transfer coefficient is 50
W/(m²·K) and the temperature difference between the surface and the free stream is 100 K.
a) 4500
b) 5000
c) 5500
d) 6000
Answer: b) 5000
3. The skin temperature of a supersonic aircraft increases by 2°C per second during acceleration. How
long will it take for the temperature to rise from 20°C to 100°C?
a) 35 seconds
b) 40 seconds
c) 45 seconds
d) 50 seconds
Answer: b) 40 seconds
4. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density
of 0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
. What is the Stanton number for a flow with a heat transfer coefficient of 60 W/(m²·K), air density of
0.5 kg/m³, velocity of 600 m/s, and specific heat capacity of 1000 J/(kg·K)?
a) 0.0002
b) 0.0003
c) 0.0004
d) 0.0005
Answer: a) 0.0002
5. An aircraft surface has an emissivity of 0.8 and a temperature of 400 K. What is the radiative heat
flux (in W/m²) emitted by the surface?
a) 1089
b) 1149
c) 1209
d) 1269
Answer: c) 1209
6. Calculate the Reynolds number for a flow over a 5 m long aircraft surface with a velocity of 300
m/s, density of 0.8 kg/m³, and dynamic viscosity of 2 × 10⁻⁵ Pa·s.
a) 5.0 × 10⁷
b) 6.0 × 10⁷
c) 7.0 × 10⁷
d) 8.0 × 10⁷
Answer: b) 6.0 × 10⁷
7. What is the thermal conductivity (in W/(m·K)) of an aircraft skin material if a temperature
difference of 50 K exists across a 5 mm thickness, with a heat flux of 20,000 W/m²?
a) 1.5
b) 2.0
c) 2.5
d) 3.0
Answer: b) 2.0
8. The recovery factor for a turbulent boundary layer over a flat plate is approximately the cube root
of the Prandtl number. What is the recovery factor if the Prandtl number is 0.72?
a) 0.86
b) 0.88
c) 0.90
d) 0.92
Answer: c) 0.90
9. Calculate the Nusselt number for a flow over a flat plate with a Reynolds number of 10⁶ and a
Prandtl number of 0.7, using the Dittus-Boelter correlation (Nu = 0.023 Re⁰·⁸ Pr⁰·⁴).
a) 1754
b) 1954
c) 2154
d) 2354
Answer: b) 1954
10. What is the temperature (in °C) at which an aluminum alloy with a melting point of 660°C will
begin to soften, assuming softening occurs at 50% of the melting point temperature in Kelvin?
a) 193.5°C
b) 203.5°C
c) 213.5°C
d) 223.5°C
Answer: c) 213.5°C
11. An aircraft flying at Mach 3 experiences aerodynamic heating. If the ambient temperature is -
40°C, what is the adiabatic wall temperature, assuming a recovery factor of 0.9?
a) 376°C
b) 386°C
c) 396°C
d) 406°C
Answer: c) 396°C
12. Calculate the heat transfer coefficient (in W/(m²·K)) if the Nusselt number is 1000, the thermal
conductivity of air is 0.03 W/(m·K), and the characteristic length is 2 m.
a) 12
b) 15
c) 18
d) 21
Answer: b) 15
13. The skin friction coefficient for a turbulent boundary layer is given by Cf = 0.026 / Re⁰·²⁵. What is
the skin friction coefficient for a Reynolds number of 10⁸?
a) 0.0021
b) 0.0023
c) 0.0025
d) 0.0027
Answer: c) 0.0025
14. What is the Biot number for a 10 mm thick aircraft skin with a thermal conductivity of 20
W/(m·K) and a convective heat transfer coefficient of 200 W/(m²·K)?
a) 0.05
b) 0.10
c) 0.15
d) 0.20
Answer: b) 0.10
15. Calculate the Eckert number for a flow with a velocity of 800 m/s, specific heat capacity of 1000
J/(kg·K), and temperature difference of 200 K.
a) 2.8
b) 3.2
c) 3.6
d) 4.0
Answer: b) 3.2
16. What is the Prandtl number for air with a specific heat capacity of 1005 J/(kg·K), thermal
conductivity of 0.026 W/(m·K), and dynamic viscosity of 1.8 × 10⁻⁵ Pa·s?
a) 0.65
b) 0.70
c) 0.75
d) 0.80
Answer: b) 0.70
17. Calculate the thermal diffusivity (in m²/s) of an aircraft skin material with a thermal conductivity
of 15 W/(m·K), density of 2700 kg/m³, and specific heat capacity of 900 J/(kg·K).
a) 5.56 × 10⁻⁶
b) 6.17 × 10⁻⁶
c) 6.78 × 10⁻⁶
d) 7.39 × 10⁻⁶
Answer: b) 6.17 × 10⁻⁶
18. An aircraft surface experiences a heat flux of 50,000 W/m². If the surface area is 100 m², what is
the total heat transfer rate (in kW)?
a) 4000
b) 4500
c) 5000
d) 5500
Answer: c) 5000
19. What is the Mach number at which the stagnation temperature is twice the ambient
temperature, assuming a specific heat ratio of 1.4?
a) 1.73
b) 1.83
c) 1.93
d) 2.03
Answer: b) 1.83
20. Calculate the Knudsen number for a flow with a mean free path of 1 × 10⁻⁷ m and a characteristic
length of 1 m.
a) 1 × 10⁻⁷
b) 1 × 10⁻⁶
c) 1 × 10⁻⁵
d) 1 × 10⁻⁴
Answer: a) 1 × 10⁻⁷
21. What is the temperature (in K) at which the viscosity of air doubles, given that the viscosity at
273 K is 1.71 × 10⁻⁵ Pa·s and using Sutherland's law with C = 110 K?
a) 515 K
b) 525 K
c) 535 K
d) 545 K
Answer: c) 535 K
22. Calculate the Grashof number for air at 300 K with a temperature difference of 50 K,
characteristic length of 1 m, kinematic viscosity of 1.5 × 10⁻⁵ m²/s, and coefficient of thermal
expansion of 1/300 K⁻¹.
a) 6.67 × 10⁸
b) 7.41 × 10⁸
c) 8.15 × 10⁸
d) 8.89 × 10⁸
Answer: b) 7.41 × 10⁸
23. An aircraft skin has a thermal resistance of 0.05 m²·K/W. What is the heat flux (in W/m²) if the
temperature difference across the skin is 100 K?
a) 1500
b) 1750
c) 2000
d) 2250
Answer: c) 2000
24. What is the Rayleigh number for a flow with a Grashof number of 10⁹ and a Prandtl number of
0.7?
a) 6.0 × 10⁸
b) 7.0 × 10⁸
c) 8.0 × 10⁸
d) 9.0 × 10⁸
Answer: b) 7.0 × 10⁸
25. Calculate the Fourier number for a thermal process lasting 10 seconds in an aircraft skin with a
thermal diffusivity of 5 × 10⁻⁶ m²/s and a thickness of 5 mm.
a) 0.2
b) 0.4
c) 0.6
d) 0.8
Answer: a) 0.2
26. What is the convective heat transfer coefficient (in W/(m²·K)) if the Stanton number is 0.001, the
air density is 1 kg/m³, the velocity is 300 m/s, and the specific heat capacity is 1000 J/(kg·K)?
a) 250
b) 300
c) 350
d) 400
Answer: b) 300
27. Calculate the temperature rise (in K) of an aircraft skin with a specific heat capacity of 900
J/(kg·K) and a density of 2700 kg/m³, if it absorbs a heat flux of 50,000 W/m² for 5 seconds.
a) 9.3
b) 10.3
c) 11.3
d) 12.3
Answer: b) 10.3
28. What is the Lewis number for a flow with a thermal diffusivity of 2 × 10⁻⁵ m²/s and a mass
diffusivity of 1.5 × 10⁻⁵ m²/s?
a) 1.20
b) 1.25
c) 1.30
d) 1.33
Answer: d) 1.33
29. Calculate the Damköhler number for a chemical reaction with a rate constant of 1000 s⁻¹ and a
flow with a characteristic time of 0.01 s.
a) 8
b) 9
c) 10
d) 11
Answer: c) 10
30. What is the thermal penetration depth (in mm) after 1 second for a material with a thermal
diffusivity of 1 × 10⁻⁶ m²/s?
a) 1.0
b) 1.5
c) 2.0
d) 2.5
Answer: a) 1.0
31. Calculate the Nusselt number for natural convection over a vertical flat plate using the correlation
Nu = 0.1(Gr·Pr)¹/³, given Gr = 10⁹ and Pr = 0.7.
a) 90
b) 100
c) 110
d) 120
Answer: b) 100
32. What is the Stefan-Boltzmann constant (in W/(m²·K⁴)) to three significant figures?
a) 5.67 × 10⁻⁸
b) 5.77 × 10⁻⁸
c) 5.87 × 10⁻⁸
d) 5.97 × 10⁻⁸
Answer: a) 5.67 × 10⁻⁸
33. Calculate the critical Reynolds number for the onset of turbulence in a boundary layer over a flat
plate.
a) 3 × 10⁵
b) 4 × 10⁵
c) 5 × 10⁵
d) 6 × 10⁵
Answer: c) 5 × 10⁵
34. What is the Mach angle (in degrees) for a flow at Mach 2?
a) 25.0°
b) 27.5°
c) 30.0°
d) 32.5°
Answer: c) 30.0°
35. Calculate the speed of sound (in m/s) in air at 20°C, given that the specific heat ratio is 1.4 and
the gas constant for air is 287 J/(kg·K).
a) 333
b) 343
c) 353
d) 363
Answer: b) 343
36. What is the temperature (in K) behind a normal shock wave in air (γ = 1.4) at Mach 3, if the
freestream temperature is 250 K?
a) 525
b) 550
c) 575
d) 600
Answer: c) 575
37. Calculate the Stanton number for a flow with a Nusselt number of 1000, Reynolds number of 10⁶,
and Prandtl number of 0.7.
a) 0.00143
b) 0.00153
c) 0.00163
d) 0.00173
Answer: a) 0.00143
38. What is the thickness (in mm) of a thermal boundary layer at a distance of 1 m from the leading
edge, given a Reynolds number of 10⁶ and a Prandtl number of 0.7?
a) 2.65
b) 2.75
c) 2.85
d) 2.95
Answer: c) 2.85
39. Calculate the Nusselt number for forced convection over a flat plate using the correlation Nu =
0.664 Re½ Pr⅓, given Re = 10⁵ and Pr = 0.7.
a) 170
b) 180
c) 190
d) 200
Answer: c) 190
40. What is the ratio of convective to radiative heat transfer for an aircraft surface at 500 K with a
convective heat transfer coefficient of 50 W/(m²·K) and an emissivity of 0.8, if the surrounding
temperature is 300 K?
a) 0.8
b) 1.0
c) 1.2
d) 1.4
Answer: c) 1.2
41. Calculate the Mach number at which the static temperature is 80% of the stagnation
temperature, assuming γ = 1.4.
a) 0.60
b) 0.65
c) 0.70
d) 0.75
Answer: c) 0.70
42. What is the thermal conductivity (in W/(m·K)) of a material if a 10 mm thick slab has a
temperature difference of 100 K across it and a heat flux of 5000 W/m²?
a) 0.4
b) 0.5
c) 0.6
d) 0.7
Answer: b) 0.5
43. Calculate the Péclet number for a flow with a Reynolds number of 10⁵ and a Prandtl number of
0.7.
a) 6.5 × 10⁴
b) 7.0 × 10⁴
c) 7.5 × 10⁴
d) 8.0 × 10⁴
Answer: b
