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
lengthT175 °C85 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 175 to 85 °C in a counter-flow exchanger. It heats 1 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 = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 175 → 85 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
2.Easy
lengthT120 °C65 °C75 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 65 °C while the cold fluid heats from 15 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 65 °CTc: 15 → 75 °C
ΔTlm = K
3.Medium
lengthT105 °C10 °C95 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 105 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 95 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 105 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 95 °CU = 3000 W/(m²·K)
A = m²
4.Medium
lengthT180 °C55 °C125 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 150 kW. The hot fluid cools from 180 to 55 °C and the cold fluid heats from 20 to 125 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 150 kWU = 1000 W/(m²·K)Th: 180 → 55 °CTc: 20 → 125 °C
A = m²
5.Hard
lengthT160 °C120 °C69.02 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 160 to 120 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °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: 160 → 120 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT85 °C45 °C39.67 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 85 to 45 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 85 → 45 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 49.76 °C
  2. 2. ΔTlm = 47.46 K
  3. 3. A = 3.137 m²
  4. 4. A = 3.39 m²
  5. 5. A = 9.895 m²
  6. 6. A = 14.86 m²

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