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
lengthT175 °C45 °C105 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 45 °C while the cold fluid heats from 10 to 105 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 45 °CTc: 10 → 105 °C
ΔTlm = K
2.Easy
lengthT85 °C50 °C35 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1.5 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 85 to 50 °C and the cold fluid heats from 10 to 35 °C. Find the heat transfer rate Q̇.

A = 1.5 m²U = 800 W/(m²·K)Th: 85 → 50 °CTc: 10 → 35 °C
Q̇ = kW
3.Medium
lengthT125 °C105 °C20 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 340 kW. Its heat transfer area is 25 m². The hot fluid cools from 125 to 105 °C and the cold fluid heats from 20 to 60 °C. Find the overall heat transfer coefficient U.

Q̇ = 340 kWA = 25 m²Th: 125 → 105 °CTc: 20 → 60 °C
U = W/(m²·K)
4.Medium
lengthT125 °C100 °C25 °C95 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 160 kW. Its heat transfer area is 2 m². The hot fluid cools from 125 to 100 °C and the cold fluid heats from 25 to 95 °C. Find the overall heat transfer coefficient U.

Q̇ = 160 kWA = 2 m²Th: 125 → 100 °CTc: 25 → 95 °C
U = W/(m²·K)
5.Hard
lengthT80 °C55 °C23.37 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 80 to 55 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 80 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT95 °C60 °C10 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 95 to 60 °C. Water (0.8 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 50 mm, and U = 200 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 95 → 60 °Cṁc = 0.8 kg/sTc,in = 10 °CD = 50 mmU = 200 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 50.49 K
  2. 2. Q̇ = 53.78 kW
  3. 3. U = 192.1 W/(m²·K)
  4. 4. U = 2523 W/(m²·K)
  5. 5. A = 1.372 m²
  6. 6. L = 11.34 m

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