Training Heat Exchangers — ε-NTU Method Practice Test — Heat Exchangers (ε-NTU)
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Practice Test — Heat Exchangers (ε-NTU)

24 min Heat Exchangers — ε-NTU Method

Practice Test — Heat Exchangers (ε-NTU)

Practice Test — 20 Questions

1. Define heat exchanger effectiveness $\varepsilon$.
2. $C_h = 5000$, $C_c = 3000$, $T_h = 120$, $T_c = 30$. Find $\dot{Q}_{\max}$.
3. What is NTU? Write the formula.
4. $U = 400$, $A = 15$ m², $C_{\min} = 2400$. NTU?
5. Counter-flow: $NTU = 1.0$, $C_r = 0.5$. $\varepsilon$?
6. Parallel-flow: $NTU = 1.0$, $C_r = 0.5$. $\varepsilon$?
7. Condenser: $NTU = 2.5$. $\varepsilon$?
8. Balanced counter-flow ($C_r = 1$): $NTU = 4$. $\varepsilon$?
9. $\varepsilon = 0.85$, $C_{\min} = 1500$, $\Delta T_{\max} = 100$. $\dot{Q}$?
10. Use $\dot{Q}$ from #9 with $C_h = 1500$ to find $T_{h,\text{out}}$ if $T_{h,\text{in}} = 130$°C.
11. When should you use ε-NTU instead of LMTD?
12. Can $\varepsilon$ exceed 1?
13. As $NTU \to \infty$ for a parallel-flow HX with $C_r = 0.4$, $\varepsilon \to$ ?
14. Why is counter-flow superior to parallel-flow?
15. 1-shell 2-tube: $NTU = 3$, $C_r = 0.5$. $\varepsilon \approx$ ? (use formula or estimate)
16. A cross-flow HX (both unmixed) has $NTU = 1$, $C_r = 1$. $\varepsilon \approx$ ?
17. How does fouling affect NTU?
18. $C_r = 0$ occurs in what type of HX?
19. Find NTU for counter-flow: $\varepsilon = 0.70$, $C_r = 0.6$.
20. $NTU = 2$, $C_{\min} = 5000$, $U = 500$. Required $A$?
Show Answer Key

1. $\varepsilon = \dot{Q}/\dot{Q}_{\max}$ = actual / maximum possible heat transfer

2. $C_{\min} = 3000$. $\dot{Q}_{\max} = 3000 \times 90 = 270{,}000$ W = 270 kW

3. Number of Transfer Units: $NTU = UA/C_{\min}$

4. $NTU = 400 \times 15/2400 = 2.5$

5. $\varepsilon = (1-e^{-0.5})/(1-0.5e^{-0.5}) = 0.3935/0.6967 = 0.565$

6. $\varepsilon = (1-e^{-1.5})/1.5 = 0.7769/1.5 = 0.518$

7. $\varepsilon = 1 - e^{-2.5} = 1 - 0.0821 = 0.918$

8. $\varepsilon = 4/(1+4) = 0.80$

9. $\dot{Q} = 0.85 \times 1500 \times 100 = 127{,}500$ W

10. $T_{h,o} = 130 - 127{,}500/1500 = 45$°C

11. When outlet temperatures are unknown (rating problem).

12. No — cannot exceed thermodynamic maximum.

13. $\varepsilon_{\max} = 1/(1+0.4) = 0.714$

14. Higher $\varepsilon$ for same NTU; can achieve $\varepsilon \to 1$; outlet cold temp can exceed outlet hot temp.

15. $\sqrt{1.25} = 1.118$; $e^{-3 \times 1.118} = e^{-3.354} = 0.035$; $(1.035/0.965) = 1.073$; $\varepsilon = 2/(1.5+1.118 \times 1.073) = 2/2.700 = 0.741$

16. Using approximation: $NTU^{0.22} = 1$, $NTU^{0.78} = 1$. $\exp((1/1)(e^{-1}-1)) = \exp(-0.632) = 0.531$. $\varepsilon = 1-0.531 = 0.469$

17. Fouling reduces $U$, which reduces NTU (since $NTU = UA/C_{\min}$), reducing $\varepsilon$.

18. Condensers and evaporators (one fluid undergoes phase change, $C \to \infty$).

19. $NTU = (1/(0.6-1))\ln((0.7-1)/(0.7 \times 0.6-1)) = (-2.5)\ln(0.3/0.58) = (-2.5)(-0.658) = 1.646$

20. $A = NTU \cdot C_{\min}/U = 2 \times 5000/500 = 20$ m²

LMTD vs. ε-NTU — When to Use Which Back to Module