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
lengthT145 °C120 °C65 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 120 °C while the cold fluid heats from 30 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 120 °CTc: 30 → 65 °C
ΔTlm = K
2.Easy

In a heat exchanger 0.5 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is heated from 20 to 60 °C. Find the heat transfer rate Q̇.

ṁ = 0.5 kg/scp = 2.44 kJ/(kg·K)T: 20 → 60 °C
Q̇ = kW
3.Medium
lengthT145 °C85 °C110 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 320 kW. The hot fluid cools from 145 to 85 °C and the cold fluid heats from 30 to 110 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 320 kWU = 800 W/(m²·K)Th: 145 → 85 °CTc: 30 → 110 °C
A = m²
4.Medium
lengthT155 °C50 °C95 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 170 kW. Its heat transfer area is 8 m². The hot fluid cools from 155 to 50 °C and the cold fluid heats from 30 to 95 °C. Find the overall heat transfer coefficient U.

Q̇ = 170 kWA = 8 m²Th: 155 → 50 °CTc: 30 → 95 °C
U = W/(m²·K)
5.Hard
lengthT155 °C90 °C41.92 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 155 to 90 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 155 → 90 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT120 °C80 °C41.51 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 120 to 80 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 120 → 80 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 84.9 K
  2. 2. Q̇ = 48.8 kW
  3. 3. A = 9.04 m²
  4. 4. U = 583.6 W/(m²·K)
  5. 5. A = 2.975 m²
  6. 6. A = 6.964 m²

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