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
lengthT90 °C35 °C20 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 35 °C while the cold fluid heats from 20 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 35 °CTc: 20 → 30 °C
ΔTlm = K
2.Easy
lengthT90 °C75 °C75 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2.5 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 90 to 75 °C and the cold fluid heats from 25 to 75 °C. Find the heat transfer rate Q̇.

A = 2.5 m²U = 200 W/(m²·K)Th: 90 → 75 °CTc: 25 → 75 °C
Q̇ = kW
3.Medium
lengthT130 °C95 °C120 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. The hot fluid cools from 130 to 95 °C and the cold fluid heats from 20 to 120 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 300 kWU = 800 W/(m²·K)Th: 130 → 95 °CTc: 20 → 120 °C
A = m²
4.Medium
lengthT125 °C60 °C30 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 180 kW. The hot fluid cools from 125 to 60 °C and the cold fluid heats from 30 to 40 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 180 kWU = 800 W/(m²·K)Th: 125 → 60 °CTc: 30 → 40 °C
A = m²
5.Hard
lengthT110 °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 110 °C and the cold stream at 10 °C. The exchanger has A = 5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 110 °CTc,in = 10 °CA = 5 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT125 °C40 °C103.5 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 125 to 40 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 125 → 40 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 24.63 K
  2. 2. Q̇ = 14.54 kW
  3. 3. A = 11.62 m²
  4. 4. A = 4.674 m²
  5. 5. Th,out = 47.5 °C
  6. 6. A = 25.56 m²

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