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 °C65 °C15 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 65 °C while the cold fluid heats from 15 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 65 °CTc: 15 → 30 °C
ΔTlm = K
2.Easy
lengthT90 °C60 °C40 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 60 °C while the cold fluid heats from 25 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 60 °CTc: 25 → 40 °C
ΔTlm = K
3.Medium
lengthT150 °C45 °C120 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 330 kW. The hot fluid cools from 150 to 45 °C and the cold fluid heats from 20 to 120 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 330 kWU = 500 W/(m²·K)Th: 150 → 45 °CTc: 20 → 120 °C
A = m²
4.Medium
lengthT95 °C70 °C20 °C35 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 420 kW. The hot fluid cools from 95 to 70 °C and the cold fluid heats from 20 to 35 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 420 kWU = 300 W/(m²·K)Th: 95 → 70 °CTc: 20 → 35 °C
A = m²
5.Hard
lengthT140 °C95 °C41.91 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 to 95 °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 = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 140 → 95 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT95 °C50 °C?20 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 95 to 50 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 50 mm, and U = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 95 → 50 °Cṁc = 0.5 kg/sTc,in = 20 °CD = 50 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 52.48 K
  2. 2. ΔTlm = 42.06 K
  3. 3. A = 24.07 m²
  4. 4. A = 26.67 m²
  5. 5. A = 9.509 m²
  6. 6. L = 27.98 m

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