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
lengthT115 °C85 °C55 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 85 °C while the cold fluid heats from 15 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 85 °CTc: 15 → 55 °C
ΔTlm = K
2.Easy
lengthT110 °C90 °C60 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 90 °C while the cold fluid heats from 15 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 90 °CTc: 15 → 60 °C
ΔTlm = K
3.Medium
lengthT160 °C80 °C35 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 470 kW. The hot fluid cools from 160 to 80 °C and the cold fluid heats from 20 to 35 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 470 kWU = 300 W/(m²·K)Th: 160 → 80 °CTc: 20 → 35 °C
A = m²
4.Medium
lengthT180 °C125 °C15 °C25 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 120 kW. The hot fluid cools from 180 to 125 °C and the cold fluid heats from 15 to 25 °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: 180 → 125 °CTc: 15 → 25 °C
A = m²
5.Hard
lengthT130 °C50 °C15 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 130 to 50 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 40 mm, and U = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 130 → 50 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 40 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT105 °C10 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 105 °C on the outside of the tubes of a condenser with a heat transfer area of 1.5 m² and U = 2500 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 10 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 1.5 m²U = 2500 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 64.87 K
  2. 2. ΔTlm = 61.66 K
  3. 3. A = 17.69 m²
  4. 4. A = 0.6163 m²
  5. 5. L = 161.4 m
  6. 6. Tc,out = 89.21 °C

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