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
lengthT130 °C70 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 130 to 70 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 130 → 70 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
2.Easy
lengthT175 °C75 °C35 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 75 °C while the cold fluid heats from 20 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 75 °CTc: 20 → 35 °C
ΔTlm = K
3.Medium
lengthT115 °C45 °C105 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 410 kW. The hot fluid cools from 115 to 45 °C and the cold fluid heats from 20 to 105 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 300 W/(m²·K)Th: 115 → 45 °CTc: 20 → 105 °C
A = m²
4.Medium
lengthT135 °C65 °C50 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 40 kW. The hot fluid cools from 135 to 65 °C and the cold fluid heats from 30 to 50 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 40 kWU = 800 W/(m²·K)Th: 135 → 65 °CTc: 30 → 50 °C
A = m²
5.Hard
lengthT175 °C145 °C47.94 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 175 to 145 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 175 → 145 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT115 °C85 °C30.1 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 85 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 85 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 45.89 °C
  2. 2. ΔTlm = 90.98 K
  3. 3. A = 83.48 m²
  4. 4. A = 0.8873 m²
  5. 5. A = 1.24 m²
  6. 6. A = 1.972 m²

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