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 °C60 °C55 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 60 °C while the cold fluid heats from 25 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 60 °CTc: 25 → 55 °C
ΔTlm = K
2.Easy
lengthT110 °C70 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 110 to 70 °C in a counter-flow exchanger. It heats 0.8 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 70 °Cṁc = 0.8 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
3.Medium
lengthT100 °C60 °C65 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 120 kW. The hot fluid cools from 100 to 60 °C and the cold fluid heats from 20 to 65 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 120 kWU = 1500 W/(m²·K)Th: 100 → 60 °CTc: 20 → 65 °C
A = m²
4.Medium
lengthT150 °C90 °C60 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. The hot fluid cools from 150 to 90 °C and the cold fluid heats from 15 to 60 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 800 W/(m²·K)Th: 150 → 90 °CTc: 15 → 60 °C
A = m²
5.Hard
lengthT175 °C140 °C35.93 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 175 to 140 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 175 → 140 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT100 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 100 °C on the outside of the tubes of a condenser with a heat transfer area of 8 m² and U = 1500 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 8 m²U = 1500 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 37.44 K
  2. 2. Tc,out = 69.81 °C
  3. 3. A = 2.137 m²
  4. 4. A = 4.558 m²
  5. 5. A = 0.995 m²
  6. 6. Tc,out = 95.75 °C

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