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
lengthT115 °C25 °C10 °C20 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 115 to 25 °C while the cold fluid heats from 10 to 20 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 25 °CTc: 10 → 20 °C
ΔTlm = K
2.Easy
lengthT150 °C105 °C90 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 150 to 105 °C and the cold fluid heats from 20 to 90 °C. Find the heat transfer rate Q̇.

A = 2 m²U = 1500 W/(m²·K)Th: 150 → 105 °CTc: 20 → 90 °C
Q̇ = kW
3.Medium
lengthT150 °C95 °C100 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 420 kW. The hot fluid cools from 150 to 95 °C and the cold fluid heats from 20 to 100 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 420 kWU = 500 W/(m²·K)Th: 150 → 95 °CTc: 20 → 100 °C
A = m²
4.Medium
lengthT155 °C125 °C30 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 370 kW. Its heat transfer area is 12 m². The hot fluid cools from 155 to 125 °C and the cold fluid heats from 30 to 60 °C. Find the overall heat transfer coefficient U.

Q̇ = 370 kWA = 12 m²Th: 155 → 125 °CTc: 30 → 60 °C
U = W/(m²·K)
5.Hard
lengthT120 °C90 °C47.94 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 90 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 90 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT150 °C60 °C15 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 150 to 60 °C. Water (0.8 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 50 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.5 kJ/(kg·K)Th: 150 → 60 °Cṁc = 0.8 kg/sTc,in = 15 °CD = 50 mmU = 500 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 32.85 K
  2. 2. Q̇ = 215.3 kW
  3. 3. A = 13.62 m²
  4. 4. U = 336 W/(m²·K)
  5. 5. A = 1.519 m²
  6. 6. L = 13.21 m

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