1.Easy
In a counter-flow heat exchanger the hot fluid cools from 110 to 80 °C while the cold fluid heats from 15 to 70 °C. Find the log-mean temperature difference ΔTlm.
Th: 110 → 80 °CTc: 15 → 70 °C
ΔTlm = K
Heat exchangers (LMTD) worksheet with answers
2.Easy
A counter-flow heat exchanger has a heat transfer area of 2 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 85 to 55 °C and the cold fluid heats from 15 to 75 °C. Find the heat transfer rate Q̇.
A = 2 m²U = 1000 W/(m²·K)Th: 85 → 55 °CTc: 15 → 75 °C
Q̇ = kW
3.Medium
A parallel-flow heat exchanger transfers 320 kW. Its heat transfer area is 20 m². The hot fluid cools from 140 to 125 °C and the cold fluid heats from 10 to 85 °C. Find the overall heat transfer coefficient U.
Q̇ = 320 kWA = 20 m²Th: 140 → 125 °CTc: 10 → 85 °C
U = W/(m²·K)
4.Medium
A counter-flow heat exchanger transfers 100 kW. The hot fluid cools from 95 to 65 °C and the cold fluid heats from 25 to 70 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.
Q̇ = 100 kWU = 300 W/(m²·K)Th: 95 → 65 °CTc: 25 → 70 °C
A = m²
5.Hard
Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 170 to 65 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.
ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 170 → 65 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 800 W/(m²·K)
A = m²
6.Hard
Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 50 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.
ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 50 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²
Answer key
- 1. ΔTlm = 51.49 K
- 2. Q̇ = 43.28 kW
- 3. U = 209.5 W/(m²·K)
- 4. A = 10.44 m²
- 5. A = 2.033 m²
- 6. A = 4.74 m²
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