Training Conduction & Thermal Resistance Practice Test — Conduction & Thermal Resistance
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Practice Test — Conduction & Thermal Resistance

24 min Conduction & Thermal Resistance

Practice Test — Conduction & Thermal Resistance

Practice Test — 20 Questions

1. State Fourier’s law for 1-D planar steady-state conduction.
2. $\dot{Q}$ through 8 cm of steel ($k = 50$), $A = 1$ m², $\Delta T = 60$°C.
3. What is the thermal resistance of a 25 cm brick wall ($k = 0.7$), $A = 10$ m²?
4. Three resistances in series: 0.2, 1.5, 0.1 K/W. $R_{\text{total}}$?
5. Two resistances in parallel: 4 and 6 K/W. $R_{\text{eq}}$?
6. Find $R_{\text{conv}}$ for $h = 100$ W/(m²·K), $A = 2$ m².
7. Composite wall: 5 cm wood ($k = 0.15$) + 10 cm insulation ($k = 0.04$). $A = 1$ m². $R_{\text{total}}$?
8. Pipe: $r_1 = 3$ cm, $r_2 = 5$ cm, $k = 60$, $L = 2$ m. Find $R_{\text{cyl}}$.
9. Critical radius: $k_{\text{ins}} = 0.1$, $h = 5$. Find $r_{\text{cr}}$.
10. Wire radius = 1 mm, $r_{\text{cr}} = 3$ mm. Does adding insulation help or hurt cooling?
11. Hollow sphere: $r_1 = 20$ cm, $r_2 = 30$ cm, $k = 10$, $\Delta T = 100$°C. $\dot{Q}$?
12. Contact resistance $R''_c = 10^{-3}$ m²·K/W, $A = 0.02$ m². $R_{\text{contact}}$?
13. Doubling $k$ does what to conduction resistance?
14. Is thermal resistance additive in series or parallel?
15. A furnace wall: 20 cm fire brick ($k = 1.0$) + 15 cm insulation ($k = 0.05$) + 1 cm steel ($k = 50$). $A = 1$ m². $R_{\text{total}}$?
16. In Problem 15, which layer has the highest resistance?
17. Heat flux through a window: $k = 0.8$, $L = 6$ mm, $\Delta T = 15$°C. Find $q$.
18. Why is the critical radius concept not relevant for flat walls?
19. A pipe with $r_1 = 4$ cm gains insulation ($k = 0.03$) to $r_2 = 8$ cm, $h = 8$, $L = 1$ m. Find $R_{\text{ins}} + R_{\text{conv}}$.
20. Thermal resistance analogy: $\Delta T \leftrightarrow$ ?, $\dot{Q} \leftrightarrow$ ?, $R_{\text{th}} \leftrightarrow$ ?
Show Answer Key

1. $\dot{Q} = kA\Delta T / L$

2. $50 \times 1 \times 60 / 0.08 = 37{,}500$ W

3. $R = 0.25/(0.7 \times 10) = 0.0357$ K/W

4. 1.8 K/W

5. $R_{\text{eq}} = 24/10 = 2.4$ K/W

6. $R = 1/(100 \times 2) = 0.005$ K/W

7. $R = 0.05/0.15 + 0.10/0.04 = 0.333 + 2.5 = 2.833$ K/W

8. $R = \ln(5/3)/(2\pi \times 60 \times 2) = 0.5108/753.98 = 6.77 \times 10^{-4}$ K/W

9. $r_{\text{cr}} = 0.1/5 = 0.02$ m = 2 cm

10. Helps cooling (increases $\dot{Q}$) because $r < r_{\text{cr}}$

11. $\dot{Q} = 4\pi(10)(0.20)(0.30)(100)/0.10 = 75{,}398$ W

12. $R = 10^{-3}/0.02 = 0.05$ K/W

13. Halves it ($R \propto 1/k$)

14. Series (add directly); parallel uses reciprocal sum

15. $0.20/1.0 + 0.15/0.05 + 0.01/50 = 0.20 + 3.0 + 0.0002 = 3.2$ K/W

16. Insulation (3.0 K/W)

17. $q = 0.8 \times 15/0.006 = 2000$ W/m²

18. Flat walls have constant area regardless of thickness, so there’s no competing area effect.

19. $R_{\text{ins}} = \ln(0.08/0.04)/(2\pi \times 0.03 \times 1) = 0.693/0.1885 = 3.676$ K/W. $R_{\text{conv}} = 1/(8 \times 2\pi \times 0.08 \times 1) = 1/4.021 = 0.2487$ K/W. Total = 3.925 K/W

20. $\Delta T \leftrightarrow \Delta V$ (voltage), $\dot{Q} \leftrightarrow I$ (current), $R_{\text{th}} \leftrightarrow R$ (electrical resistance)

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