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

In a heat exchanger 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 35 to 80 °C. Find the heat transfer rate Q̇.

ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)T: 35 → 80 °C
Q̇ = kW
2.Easy
lengthT85 °C55 °C50 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1.5 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 85 to 55 °C and the cold fluid heats from 15 to 50 °C. Find the heat transfer rate Q̇.

A = 1.5 m²U = 300 W/(m²·K)Th: 85 → 55 °CTc: 15 → 50 °C
Q̇ = kW
3.Medium
lengthT120 °C25 °C105 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 105 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 105 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT90 °C55 °C80 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 250 kW. The hot fluid cools from 90 to 55 °C and the cold fluid heats from 10 to 80 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 250 kWU = 500 W/(m²·K)Th: 90 → 55 °CTc: 10 → 80 °C
A = m²
5.Hard
lengthT135 °C95 °C23.35 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 135 to 95 °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 = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 135 → 95 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT105 °C50 °C50.35 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 105 to 50 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 105 → 50 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 282.1 kW
  2. 2. Q̇ = 16.85 kW
  3. 3. A = 11.02 m²
  4. 4. A = 21.49 m²
  5. 5. A = 2.28 m²
  6. 6. A = 26.95 m²

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