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
lengthT110 °C80 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 110 to 80 °C in a counter-flow exchanger. It heats 3 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 = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 110 → 80 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
2.Easy
lengthT115 °C60 °C30 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 115 to 60 °C while the cold fluid heats from 30 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 60 °CTc: 30 → 40 °C
ΔTlm = K
3.Medium
lengthT80 °C55 °C65 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 410 kW. The hot fluid cools from 80 to 55 °C and the cold fluid heats from 15 to 65 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 500 W/(m²·K)Th: 80 → 55 °CTc: 15 → 65 °C
A = m²
4.Medium
lengthT155 °C125 °C85 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 90 kW. The hot fluid cools from 155 to 125 °C and the cold fluid heats from 25 to 85 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 90 kWU = 1500 W/(m²·K)Th: 155 → 125 °CTc: 25 → 85 °C
A = m²
5.Hard
lengthT105 °C70 °C10 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 105 to 70 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 25 mm, and U = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.8 kg/scp,h = 2.3 kJ/(kg·K)Th: 105 → 70 °Cṁc = 1.5 kg/sTc,in = 10 °CD = 25 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT85 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 85 °C and the cold stream at 25 °C. The exchanger has A = 4 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 85 °CTc,in = 25 °CA = 4 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Tc,out = 33.25 °C
  2. 2. ΔTlm = 44.92 K
  3. 3. A = 32.17 m²
  4. 4. A = 0.7133 m²
  5. 5. L = 46.9 m
  6. 6. Th,out = 50.71 °C

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