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
lengthT95 °C65 °C75 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 4 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 95 to 65 °C and the cold fluid heats from 30 to 75 °C. Find the heat transfer rate Q̇.

A = 4 m²U = 200 W/(m²·K)Th: 95 → 65 °CTc: 30 → 75 °C
Q̇ = kW
2.Easy
lengthT100 °C65 °C80 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 100 to 65 °C while the cold fluid heats from 30 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 65 °CTc: 30 → 80 °C
ΔTlm = K
3.Medium
lengthT180 °C150 °C30 °C130 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 260 kW. The hot fluid cools from 180 to 150 °C and the cold fluid heats from 30 to 130 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 260 kWU = 200 W/(m²·K)Th: 180 → 150 °CTc: 30 → 130 °C
A = m²
4.Medium
lengthT155 °C45 °C95 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 180 kW. The hot fluid cools from 155 to 45 °C and the cold fluid heats from 20 to 95 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 180 kWU = 300 W/(m²·K)Th: 155 → 45 °CTc: 20 → 95 °C
A = m²
5.Hard
lengthT85 °C??30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 85 °C and the cold stream at 30 °C. The exchanger has A = 4 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 85 °CTc,in = 30 °CA = 4 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT120 °C60 °C81.03 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 120 to 60 °C in a counter-flow exchanger. It heats 0.5 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 = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 120 → 60 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 21.44 kW
  2. 2. ΔTlm = 26.8 K
  3. 3. A = 20.15 m²
  4. 4. A = 15.01 m²
  5. 5. Th,out = 55 °C
  6. 6. A = 6.585 m²

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