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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
lengthT130 °C50 °C110 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 50 °C while the cold fluid heats from 20 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 50 °CTc: 20 → 110 °C
ΔTlm = K
2.Easy
lengthT90 °C70 °C25 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 70 °C while the cold fluid heats from 25 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 70 °CTc: 25 → 40 °C
ΔTlm = K
3.Medium
lengthT95 °C25 °C30 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 220 kW. The hot fluid cools from 95 to 25 °C and the cold fluid heats from 10 to 30 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 220 kWU = 300 W/(m²·K)Th: 95 → 25 °CTc: 10 → 30 °C
A = m²
4.Medium
lengthT130 °C50 °C10 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 230 kW. The hot fluid cools from 130 to 50 °C and the cold fluid heats from 10 to 45 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWU = 500 W/(m²·K)Th: 130 → 50 °CTc: 10 → 45 °C
A = m²
5.Hard
lengthT85 °C65 °C25.5 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 85 to 65 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 85 → 65 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT155 °C65 °C18.97 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 155 to 65 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 155 → 65 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 24.66 K
  2. 2. ΔTlm = 45.27 K
  3. 3. A = 21.51 m²
  4. 4. A = 12.71 m²
  5. 5. A = 1.661 m²
  6. 6. A = 1.257 m²

Full step-by-step solutions: practise this topic on examproblems.com.