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.

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1.Easy
lengthT170 °C50 °C105 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2.5 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 170 to 50 °C and the cold fluid heats from 30 to 105 °C. Find the heat transfer rate Q̇.

A = 2.5 m²U = 800 W/(m²·K)Th: 170 → 50 °CTc: 30 → 105 °C
Q̇ = kW
2.Easy
lengthT95 °C30 °C10 °C25 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 95 to 30 °C while the cold fluid heats from 10 to 25 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 30 °CTc: 10 → 25 °C
ΔTlm = K
3.Medium
lengthT155 °C45 °C25 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 490 kW. The hot fluid cools from 155 to 45 °C and the cold fluid heats from 10 to 25 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 490 kWU = 300 W/(m²·K)Th: 155 → 45 °CTc: 10 → 25 °C
A = m²
4.Medium
lengthT95 °C60 °C65 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 50 kW. The hot fluid cools from 95 to 60 °C and the cold fluid heats from 25 to 65 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 50 kWF = 0.88U = 500 W/(m²·K)Th: 95 → 60 °CTc: 25 → 65 °C
A = m²
5.Hard
lengthT155 °C??10 °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 155 °C and the cold stream at 10 °C. The exchanger has A = 2 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 155 °CTc,in = 10 °CA = 2 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT90 °C??10 °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 90 °C and the cold stream at 10 °C. The exchanger has A = 2 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 90 °CTc,in = 10 °CA = 2 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 76.36 kW
  2. 2. ΔTlm = 28.24 K
  3. 3. A = 22.56 m²
  4. 4. A = 3.503 m²
  5. 5. Th,out = 113.6 °C
  6. 6. Th,out = 67.14 °C

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