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
lengthT95 °C65 °C75 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 20 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 95 to 65 °C and the cold fluid heats from 10 to 75 °C. Find the heat transfer rate Q̇.

A = 20 m²U = 1000 W/(m²·K)Th: 95 → 65 °CTc: 10 → 75 °C
Q̇ = kW
2.Easy
lengthT150 °C120 °C130 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 120 °C while the cold fluid heats from 20 to 130 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 120 °CTc: 20 → 130 °C
ΔTlm = K
3.Medium
lengthT90 °C75 °C70 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 170 kW. The hot fluid cools from 90 to 75 °C and the cold fluid heats from 30 to 70 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 170 kWF = 0.95U = 1000 W/(m²·K)Th: 90 → 75 °CTc: 30 → 70 °C
A = m²
4.Medium
lengthT150 °C100 °C15 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 340 kW. Its heat transfer area is 2 m². The hot fluid cools from 150 to 100 °C and the cold fluid heats from 15 to 40 °C. Find the overall heat transfer coefficient U.

Q̇ = 340 kWA = 2 m²Th: 150 → 100 °CTc: 15 → 40 °C
U = W/(m²·K)
5.Hard
lengthT130 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 130 °C and the cold stream at 10 °C. The exchanger has A = 5 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 130 °CTc,in = 10 °CA = 5 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT145 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 145 °C and the cold stream at 15 °C. The exchanger has A = 1.5 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 145 °CTc,in = 15 °CA = 1.5 m²U = 800 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 692 kW
  2. 2. ΔTlm = 49.71 K
  3. 3. A = 5.805 m²
  4. 4. U = 1838 W/(m²·K)
  5. 5. Th,out = 78.57 °C
  6. 6. Th,out = 74.09 °C

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