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
lengthT165 °C75 °C30 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 165 to 75 °C while the cold fluid heats from 15 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 165 → 75 °CTc: 15 → 30 °C
ΔTlm = K
2.Easy

In a heat exchanger 1.2 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 40 to 70 °C. Find the heat transfer rate Q̇.

ṁ = 1.2 kg/scp = 4.18 kJ/(kg·K)T: 40 → 70 °C
Q̇ = kW
3.Medium
lengthT180 °C40 °C100 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 160 kW. The hot fluid cools from 180 to 40 °C and the cold fluid heats from 15 to 100 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 160 kWU = 1500 W/(m²·K)Th: 180 → 40 °CTc: 15 → 100 °C
A = m²
4.Medium
lengthT130 °C80 °C50 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 250 kW. The hot fluid cools from 130 to 80 °C and the cold fluid heats from 20 to 50 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 250 kWU = 200 W/(m²·K)Th: 130 → 80 °CTc: 20 → 50 °C
A = m²
5.Hard
lengthT165 °C135 °C35.02 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 165 to 135 °C in a counter-flow exchanger. It heats 3 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 = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 165 → 135 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT115 °C70 °C49.76 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 115 to 70 °C in a counter-flow exchanger. It heats 1 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 = 2.3 kJ/(kg·K)Th: 115 → 70 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 92.49 K
  2. 2. Q̇ = 150.5 kW
  3. 3. A = 2.256 m²
  4. 4. A = 17.98 m²
  5. 5. A = 1.077 m²
  6. 6. A = 2.374 m²

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