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
lengthT180 °C75 °C15 °C65 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 180 to 75 °C while the cold fluid heats from 15 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 75 °CTc: 15 → 65 °C
ΔTlm = K
2.Easy
lengthT125 °C85 °C60 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 3 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 125 to 85 °C and the cold fluid heats from 25 to 60 °C. Find the heat transfer rate Q̇.

A = 3 m²U = 500 W/(m²·K)Th: 125 → 85 °CTc: 25 → 60 °C
Q̇ = kW
3.Medium
lengthT105 °C55 °C70 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 240 kW. The hot fluid cools from 105 to 55 °C and the cold fluid heats from 25 to 70 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 240 kWU = 1000 W/(m²·K)Th: 105 → 55 °CTc: 25 → 70 °C
A = m²
4.Medium
lengthT110 °C75 °C30 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 130 kW. The hot fluid cools from 110 to 75 °C and the cold fluid heats from 30 to 55 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 130 kWU = 800 W/(m²·K)Th: 110 → 75 °CTc: 30 → 55 °C
A = m²
5.Hard
lengthT125 °C85 °C52.01 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 125 to 85 °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 = 2.3 kJ/(kg·K)Th: 125 → 85 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT130 °C??30 °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 130 °C and the cold stream at 30 °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 = 130 °CTc,in = 30 °CA = 2 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 55.29 K
  2. 2. Q̇ = 93.7 kW
  3. 3. A = 7.399 m²
  4. 4. A = 3.755 m²
  5. 5. A = 7.236 m²
  6. 6. Th,out = 101.4 °C

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