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 °C45 °C70 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 45 °C while the cold fluid heats from 15 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 45 °CTc: 15 → 70 °C
ΔTlm = K
2.Easy
lengthT140 °C110 °C20 °C70 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 140 to 110 °C while the cold fluid heats from 20 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 110 °CTc: 20 → 70 °C
ΔTlm = K
3.Medium
lengthT160 °C70 °C85 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. The hot fluid cools from 160 to 70 °C and the cold fluid heats from 30 to 85 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 1500 W/(m²·K)Th: 160 → 70 °CTc: 30 → 85 °C
A = m²
4.Medium
lengthT100 °C65 °C20 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 320 kW. Its heat transfer area is 15 m². The hot fluid cools from 100 to 65 °C and the cold fluid heats from 20 to 40 °C. Find the overall heat transfer coefficient U.

Q̇ = 320 kWA = 15 m²Th: 100 → 65 °CTc: 20 → 40 °C
U = W/(m²·K)
5.Hard
lengthT170 °C95 °C22.56 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 170 to 95 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 170 → 95 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT135 °C75 °C25 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 135 to 75 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 20 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.3 kJ/(kg·K)Th: 135 → 75 °Cṁc = 0.5 kg/sTc,in = 25 °CD = 20 mmU = 500 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 24.66 K
  2. 2. ΔTlm = 72.82 K
  3. 3. A = 4.43 m²
  4. 4. U = 451.2 W/(m²·K)
  5. 5. A = 2.779 m²
  6. 6. L = 21.35 m

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