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
lengthT150 °C55 °C120 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 55 °C while the cold fluid heats from 15 to 120 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 55 °CTc: 15 → 120 °C
ΔTlm = K
2.Easy
lengthT175 °C110 °C135 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 6 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 175 to 110 °C and the cold fluid heats from 10 to 135 °C. Find the heat transfer rate Q̇.

A = 6 m²U = 500 W/(m²·K)Th: 175 → 110 °CTc: 10 → 135 °C
Q̇ = kW
3.Medium
lengthT100 °C10 °C65 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (4 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 65 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 65 °CU = 3000 W/(m²·K)
A = m²
4.Medium
lengthT130 °C20 °C100 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °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 20 to 100 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 100 °CU = 2000 W/(m²·K)
A = m²
5.Hard
lengthT80 °C55 °C34.97 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 80 to 55 °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 = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 80 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT110 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 5 m² and U = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 5 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 34.76 K
  2. 2. Q̇ = 196.4 kW
  3. 3. A = 5.264 m²
  4. 4. A = 2.716 m²
  5. 5. A = 5.629 m²
  6. 6. Tc,out = 95.04 °C

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