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
lengthT150 °C90 °C90 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 90 °C while the cold fluid heats from 15 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 90 °CTc: 15 → 90 °C
ΔTlm = K
2.Easy
lengthT85 °C45 °C75 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 45 °C while the cold fluid heats from 20 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 45 °CTc: 20 → 75 °C
ΔTlm = K
3.Medium
lengthT135 °C95 °C110 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 260 kW. The hot fluid cools from 135 to 95 °C and the cold fluid heats from 10 to 110 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 260 kWU = 500 W/(m²·K)Th: 135 → 95 °CTc: 10 → 110 °C
A = m²
4.Medium
lengthT105 °C65 °C10 °C20 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 250 kW. The hot fluid cools from 105 to 65 °C and the cold fluid heats from 10 to 20 °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: 105 → 65 °CTc: 10 → 20 °C
A = m²
5.Hard
lengthT100 °C50 °C10 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 100 to 50 °C. Water (0.8 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 20 mm, and U = 200 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 50 °Cṁc = 0.8 kg/sTc,in = 10 °CD = 20 mmU = 200 W/(m²·K)
L = m
6.Hard
lengthT110 °C40 °C66.89 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 110 to 40 °C in a counter-flow exchanger. It heats 1.5 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 = 2.1 kJ/(kg·K)Th: 110 → 40 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 67.22 K
  2. 2. ΔTlm = 16.37 K
  3. 3. A = 10.61 m²
  4. 4. A = 18.68 m²
  5. 5. L = 50.49 m
  6. 6. A = 6.514 m²

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