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
lengthT180 °C120 °C85 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 120 °C while the cold fluid heats from 15 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 120 °CTc: 15 → 85 °C
ΔTlm = K
2.Easy
lengthT180 °C95 °C120 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 95 °C while the cold fluid heats from 15 to 120 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 95 °CTc: 15 → 120 °C
ΔTlm = K
3.Medium
lengthT85 °C40 °C60 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 490 kW. The hot fluid cools from 85 to 40 °C and the cold fluid heats from 20 to 60 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 490 kWU = 1500 W/(m²·K)Th: 85 → 40 °CTc: 20 → 60 °C
A = m²
4.Medium
lengthT85 °C55 °C55 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 210 kW. The hot fluid cools from 85 to 55 °C and the cold fluid heats from 15 to 55 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 210 kWU = 1500 W/(m²·K)Th: 85 → 55 °CTc: 15 → 55 °C
A = m²
5.Hard
lengthT140 °C105 °C38.79 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 140 to 105 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 140 → 105 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT120 °C60 °C31.96 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 60 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 60 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 99.92 K
  2. 2. ΔTlm = 69.52 K
  3. 3. A = 14.58 m²
  4. 4. A = 4.028 m²
  5. 5. A = 0.8405 m²
  6. 6. A = 2.463 m²

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