Training Heat Exchangers — LMTD Method Practice Test — Heat Exchangers (LMTD)
5 / 5

Practice Test — Heat Exchangers (LMTD)

24 min Heat Exchangers — LMTD Method

Practice Test — Heat Exchangers (LMTD)

Practice Test — 20 Questions

1. Write the heat exchanger design equation.
2. Counter-flow: $T_h$ 200→120, $T_c$ 40→100. Find $\Delta T_{\text{lm}}$.
3. Same temps, parallel-flow. $\Delta T_{\text{lm}}$?
4. Which arrangement always gives a higher $\Delta T_{\text{lm}}$?
5. $U = 1000$, $A = 5$ m², $\Delta T_{\text{lm}} = 30$. $\dot{Q}$?
6. $\dot{Q} = 400$ kW, $U = 800$, $\Delta T_{\text{lm}} = 50$. $A$?
7. Hot water ($\dot{m} = 3$ kg/s, $c_p = 4180$) cools from 80°C to 50°C. $\dot{Q}$?
8. In Problem 7, cold water enters at 10°C, $\dot{m} = 5$ kg/s. $T_{c,\text{out}}$?
9. Define the overall heat transfer coefficient $U$.
10. $h_i = 2000$, $h_o = 400$, fouling $R''_f = 0.0005$ (total). Find $U$.
11. What is $F$ and when is it used?
12. 1-shell 2-tube-pass: $P = 0.5$, $R = 0.8$. Estimate $F$.
13. If $F = 0.60$, what does this tell you about the design?
14. $U_{\text{clean}} = 1200$. Fouling: $R''_{f,i} = 0.0002$, $R''_{f,o} = 0.0003$. $U_{\text{dirty}}$?
15. Overdesign: clean $A = 6$ m², specify 8 m². What’s the overdesign percentage?
16. A condenser has $T_{h,\text{in}} = T_{h,\text{out}} = 100$°C. Why?
17. For a condenser, the LMTD simplifies to what?
18. Name 3 types of heat exchangers.
19. $C_{\min} = 2000$ W/K, $C_{\max} = 5000$ W/K. $C_r$?
20. Why is counter-flow preferred over parallel-flow?
Show Answer Key

1. $\dot{Q} = UA\Delta T_{\text{lm}}$ (or $\dot{Q} = UAF\Delta T_{\text{lm,CF}}$ for multi-pass)

2. $\Delta T_1 = 200-100 = 100$, $\Delta T_2 = 120-40 = 80$. $\Delta T_{\text{lm}} = 20/\ln(100/80) = 20/0.2231 = 89.6$°C

3. $\Delta T_1 = 200-40 = 160$, $\Delta T_2 = 120-100 = 20$. $\Delta T_{\text{lm}} = 140/\ln 8 = 140/2.079 = 67.3$°C

4. Counter-flow

5. $\dot{Q} = 1000 \times 5 \times 30 = 150{,}000$ W = 150 kW

6. $A = 400{,}000/(800 \times 50) = 10$ m²

7. $\dot{Q} = 3 \times 4180 \times 30 = 376{,}200$ W

8. $T_{c,o} = 10 + 376{,}200/(5 \times 4180) = 10 + 18 = 28$°C

9. $U$ accounts for all resistances in series: inner convection + fouling + wall conduction + fouling + outer convection.

10. $1/U = 1/2000 + 0.0005 + 1/400 = 0.0005 + 0.0005 + 0.0025 = 0.0035$. $U = 286$ W/(m²·K)

11. Correction factor for multi-pass/cross-flow HX. Multiply by counter-flow LMTD.

12. $F \approx 0.87$ (from standard charts)

13. Poor design — temperature cross or near-cross. Redesign needed ($F < 0.75$).

14. $1/U = 1/1200 + 0.0005 = 0.000833 + 0.0005 = 0.001333$. $U = 750$ W/(m²·K)

15. $(8-6)/6 = 33\%$

16. Phase change (condensation) occurs at constant temperature.

17. $\Delta T_{\text{lm}} = \frac{(T_{\text{sat}}-T_{c,\text{in}}) - (T_{\text{sat}}-T_{c,\text{out}})}{\ln\frac{T_{\text{sat}}-T_{c,\text{in}}}{T_{\text{sat}}-T_{c,\text{out}}}}$

18. Double-pipe, shell-and-tube, plate, cross-flow (any three).

19. $C_r = C_{\min}/C_{\max} = 2000/5000 = 0.4$

20. Higher LMTD → less area needed; outlet cold temp can approach inlet hot temp (thermodynamically impossible in parallel-flow).

Fouling and Design Considerations Back to Module