Heat exchangers (LMTD) worksheet with answers

Free printable Heat exchangers (LMTD) worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

In a heat exchanger 3 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is heated from 25 to 55 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 2.1 kJ/(kg·K)T: 25 → 55 °C
Q̇ = kW
2.Easy
lengthT115 °C65 °C85 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 65 °C while the cold fluid heats from 10 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 65 °CTc: 10 → 85 °C
ΔTlm = K
3.Medium
lengthT120 °C90 °C105 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 90 kW. Its heat transfer area is 8 m². The hot fluid cools from 120 to 90 °C and the cold fluid heats from 30 to 105 °C. Find the overall heat transfer coefficient U.

Q̇ = 90 kWA = 8 m²Th: 120 → 90 °CTc: 30 → 105 °C
U = W/(m²·K)
4.Medium
lengthT170 °C105 °C115 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 220 kW. The hot fluid cools from 170 to 105 °C and the cold fluid heats from 10 to 115 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 220 kWU = 1000 W/(m²·K)Th: 170 → 105 °CTc: 10 → 115 °C
A = m²
5.Hard
lengthT105 °C50 °C52.89 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 105 to 50 °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 = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 105 → 50 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT140 °C45 °C49.85 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 140 to 45 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 140 → 45 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 189 kW
  2. 2. ΔTlm = 41.24 K
  3. 3. U = 346.6 W/(m²·K)
  4. 4. A = 3.006 m²
  5. 5. A = 8.585 m²
  6. 6. A = 9.992 m²

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