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
lengthT85 °C25 °C45 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 85 to 25 °C and the cold fluid heats from 10 to 45 °C. Find the heat transfer rate Q̇.

A = 1 m²U = 1000 W/(m²·K)Th: 85 → 25 °CTc: 10 → 45 °C
Q̇ = kW
2.Easy
lengthT145 °C120 °C25 °C105 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 145 to 120 °C while the cold fluid heats from 25 to 105 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 120 °CTc: 25 → 105 °C
ΔTlm = K
3.Medium
lengthT125 °C55 °C100 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 210 kW. The hot fluid cools from 125 to 55 °C and the cold fluid heats from 25 to 100 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 210 kWU = 800 W/(m²·K)Th: 125 → 55 °CTc: 25 → 100 °C
A = m²
4.Medium
lengthT85 °C55 °C70 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 50 kW. Its heat transfer area is 12 m². The hot fluid cools from 85 to 55 °C and the cold fluid heats from 30 to 70 °C. Find the overall heat transfer coefficient U.

Q̇ = 50 kWA = 12 m²Th: 85 → 55 °CTc: 30 → 70 °C
U = W/(m²·K)
5.Hard
lengthT105 °C55 °C29.17 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 105 to 55 °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 = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 105 → 55 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT100 °C55 °C43.46 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 100 to 55 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 100 → 55 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 25.49 kW
  2. 2. ΔTlm = 50.49 K
  3. 3. A = 9.572 m²
  4. 4. U = 212.8 W/(m²·K)
  5. 5. A = 4.355 m²
  6. 6. A = 1.819 m²

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