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
lengthT180 °C105 °C125 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 105 °C while the cold fluid heats from 10 to 125 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 105 °CTc: 10 → 125 °C
ΔTlm = K
2.Easy
lengthT135 °C105 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 135 to 105 °C in a counter-flow exchanger. It heats 0.8 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 135 → 105 °Cṁc = 0.8 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
3.Medium
lengthT85 °C65 °C30 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 100 kW. The hot fluid cools from 85 to 65 °C and the cold fluid heats from 30 to 60 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 100 kWU = 500 W/(m²·K)Th: 85 → 65 °CTc: 30 → 60 °C
A = m²
4.Medium
lengthT85 °C65 °C20 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 90 kW. The hot fluid cools from 85 to 65 °C and the cold fluid heats from 20 to 30 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 90 kWU = 800 W/(m²·K)Th: 85 → 65 °CTc: 20 → 30 °C
A = m²
5.Hard
lengthT130 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 2 m² and U = 2000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 2 m²U = 2000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT175 °C80 °C67.88 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 175 to 80 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 175 → 80 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 73.19 K
  2. 2. Tc,out = 58.64 °C
  3. 3. A = 9.592 m²
  4. 4. A = 2.321 m²
  5. 5. Tc,out = 71.88 °C
  6. 6. A = 2.112 m²

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