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
lengthT150 °C120 °C20 °C115 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 150 to 120 °C while the cold fluid heats from 20 to 115 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 120 °CTc: 20 → 115 °C
ΔTlm = K
2.Easy
lengthT90 °C55 °C65 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 55 °C while the cold fluid heats from 25 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 55 °CTc: 25 → 65 °C
ΔTlm = K
3.Medium
lengthT180 °C150 °C120 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 20 kW. The hot fluid cools from 180 to 150 °C and the cold fluid heats from 25 to 120 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 20 kWU = 300 W/(m²·K)Th: 180 → 150 °CTc: 25 → 120 °C
A = m²
4.Medium
lengthT170 °C135 °C75 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 100 kW. The hot fluid cools from 170 to 135 °C and the cold fluid heats from 25 to 75 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 100 kWU = 200 W/(m²·K)Th: 170 → 135 °CTc: 25 → 75 °C
A = m²
5.Hard
lengthT125 °C60 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 125 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 40 mm, and U = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 125 → 60 °Cṁc = 0.8 kg/sTc,in = 15 °CD = 40 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT155 °C110 °C47.94 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 155 to 110 °C in a counter-flow exchanger. It heats 3 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 = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 155 → 110 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 38.37 K
  2. 2. ΔTlm = 27.42 K
  3. 3. A = 0.7528 m²
  4. 4. A = 4.887 m²
  5. 5. L = 61.25 m
  6. 6. A = 12.11 m²

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