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
lengthT125 °C110 °C55 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 110 °C while the cold fluid heats from 30 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 110 °CTc: 30 → 55 °C
ΔTlm = K
2.Easy
lengthT115 °C65 °C75 °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 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 65 °CTc: 10 → 75 °C
ΔTlm = K
3.Medium
lengthT145 °C130 °C110 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. The hot fluid cools from 145 to 130 °C and the cold fluid heats from 20 to 110 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 800 W/(m²·K)Th: 145 → 130 °CTc: 20 → 110 °C
A = m²
4.Medium
lengthT130 °C25 °C70 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 390 kW. The hot fluid cools from 130 to 25 °C and the cold fluid heats from 10 to 70 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 800 W/(m²·K)Th: 130 → 25 °CTc: 10 → 70 °C
A = m²
5.Hard
lengthT160 °C120 °C35.1 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 160 to 120 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 160 → 120 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT160 °C120 °C115.7 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 160 to 120 °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 = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 160 → 120 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 74.89 K
  2. 2. ΔTlm = 47.1 K
  3. 3. A = 7.062 m²
  4. 4. A = 15.02 m²
  5. 5. A = 2.93 m²
  6. 6. A = 1.949 m²

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