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
lengthT120 °C50 °C35 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 50 °C while the cold fluid heats from 25 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 50 °CTc: 25 → 35 °C
ΔTlm = K
2.Easy
lengthT160 °C50 °C135 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 50 °C while the cold fluid heats from 20 to 135 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 50 °CTc: 20 → 135 °C
ΔTlm = K
3.Medium
lengthT110 °C95 °C90 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 130 kW. Its heat transfer area is 5 m². The hot fluid cools from 110 to 95 °C and the cold fluid heats from 25 to 90 °C. Find the overall heat transfer coefficient U.

Q̇ = 130 kWA = 5 m²Th: 110 → 95 °CTc: 25 → 90 °C
U = W/(m²·K)
4.Medium
lengthT130 °C20 °C80 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 80 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 80 °CU = 3000 W/(m²·K)
A = m²
5.Hard
lengthT110 °C10 °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 8 m² and U = 1500 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 10 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 8 m²U = 1500 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
6.Hard
lengthT125 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 3 kW/K. The hot stream enters at 125 °C and the cold stream at 10 °C. The exchanger has A = 1.5 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 3 kW/KTh,in = 125 °CTc,in = 10 °CA = 1.5 m²U = 800 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 49.03 K
  2. 2. ΔTlm = 27.42 K
  3. 3. U = 651.4 W/(m²·K)
  4. 4. A = 0.5493 m²
  5. 5. Tc,out = 86.2 °C
  6. 6. Th,out = 92.14 °C

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