Training Convection & Dimensionless Numbers Practice Test — Convection & Dimensionless Numbers
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Practice Test — Convection & Dimensionless Numbers

24 min Convection & Dimensionless Numbers

Practice Test — Convection & Dimensionless Numbers

Practice Test — 20 Questions

1. State Newton’s law of cooling.
2. Air at 25°C blows over a 50°C plate ($A = 2$ m², $h = 30$). $\dot{Q}$?
3. Define the Reynolds number and state the transition value for pipe flow.
4. Water ($\nu = 10^{-6}$) at 3 m/s in a 4 cm pipe. Find $Re$.
5. $Pr$ for air is $\approx$ 0.7. What does this mean physically?
6. Define the Nusselt number. What does $Nu = 1$ mean?
7. Use Dittus–Boelter for $Re = 50{,}000$, $Pr = 3$, $k = 0.65$, $D = 2$ cm (heating).
8. Laminar pipe flow with constant $T_s$. What is $Nu$?
9. Define the Grashof number.
10. What is $\beta$ for an ideal gas at 350 K?
11. $Ra = 5 \times 10^{10}$. Laminar or turbulent natural convection?
12. Why does natural convection have lower $h$ than forced convection?
13. A vertical plate: $Ra = 10^7$, $Pr = 0.71$. Use the simpler Churchill–Chu. $Nu$?
14. Pipe, $Nu = 150$, $D = 5$ cm, $k_f = 0.03$. Find $h$.
15. If $Re$ triples in turbulent pipe flow, $Nu$ changes by factor?
16. $Gr = 10^{11}$, $Re = 10{,}000$. Forced, natural, or mixed?
17. Heat flux from a surface: $h = 500$, $T_s = 80$°C, $T_\infty = 20$°C. $q''$?
18. Why do we evaluate properties at the film temperature?
19. External flat plate, laminar: $Re_x = 2 \times 10^5$, $Pr = 0.71$. Find $Nu_x$.
20. What conditions make the Dittus–Boelter correlation valid?
Show Answer Key

1. $\dot{Q} = hA_s(T_s - T_\infty)$

2. $\dot{Q} = 30 \times 2 \times 25 = 1500$ W

3. $Re = VD/\nu$; transition at $Re \approx 2300$

4. $Re = 3 \times 0.04/10^{-6} = 120{,}000$

5. Momentum and thermal diffusivities are similar; boundary layers have comparable thickness.

6. $Nu = hL_c/k_f$; $Nu = 1$ means convection equals pure conduction.

7. $Nu = 0.023 \times 50{,}000^{0.8} \times 3^{0.4} = 0.023 \times 5792 \times 1.552 = 206.7$. $h = 206.7 \times 0.65/0.02 = 6718$ W/(m²·K)

8. $Nu = 3.66$

9. $Gr = g\beta\Delta T L_c^3/\nu^2$ — ratio of buoyancy to viscous forces.

10. $\beta = 1/350 = 0.00286$ K⁻¹

11. Turbulent ($Ra > 10^9$)

12. Buoyancy-driven velocities are much lower than pump/fan-driven velocities.

13. $\psi = (1+(0.492/0.71)^{9/16})^{4/9} = 1.626^{0.444} = 1.236$. $Nu = 0.68 + 0.670 \times (10^7)^{0.25}/1.236 = 0.68 + 0.670 \times 56.23/1.236 = 0.68 + 30.5 = 31.2$

14. $h = 150 \times 0.03/0.05 = 90$ W/(m²·K)

15. $3^{0.8} = 2.41$

16. $Gr/Re^2 = 10^{11}/10^8 = 1000 \gg 1$ → Natural convection

17. $q'' = 500 \times 60 = 30{,}000$ W/m²

18. $T_f = (T_s + T_\infty)/2$ gives representative average properties across the boundary layer.

19. $Nu = 0.332 \times (2 \times 10^5)^{0.5} \times 0.71^{1/3} = 0.332 \times 447.2 \times 0.893 = 132.6$

20. $Re_D > 10{,}000$, $0.6 \le Pr \le 160$, $L/D > 10$, smooth tube, moderate property variation.

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