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
lengthT80 °C25 °C60 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 80 to 25 °C while the cold fluid heats from 10 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 25 °CTc: 10 → 60 °C
ΔTlm = K
2.Easy

In a heat exchanger 0.8 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is cooled from 65 to 50 °C. Find the heat transfer rate Q̇.

ṁ = 0.8 kg/scp = 2.1 kJ/(kg·K)T: 65 → 50 °C
Q̇ = kW
3.Medium
lengthT105 °C35 °C50 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 350 kW. The hot fluid cools from 105 to 35 °C and the cold fluid heats from 15 to 50 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 350 kWU = 300 W/(m²·K)Th: 105 → 35 °CTc: 15 → 50 °C
A = m²
4.Medium
lengthT135 °C100 °C50 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 350 kW. The hot fluid cools from 135 to 100 °C and the cold fluid heats from 30 to 50 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 350 kWU = 300 W/(m²·K)Th: 135 → 100 °CTc: 30 → 50 °C
A = m²
5.Hard
lengthT135 °C95 °C50.1 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 135 to 95 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 135 → 95 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT95 °C??30 °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 95 °C and the cold stream at 30 °C. The exchanger has A = 2 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 95 °CTc,in = 30 °CA = 2 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 17.38 K
  2. 2. Q̇ = 25.2 kW
  3. 3. A = 33.72 m²
  4. 4. A = 15.1 m²
  5. 5. A = 5.637 m²
  6. 6. Th,out = 80 °C

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