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
lengthT160 °C75 °C75 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 75 °C while the cold fluid heats from 25 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 75 °CTc: 25 → 75 °C
ΔTlm = K
2.Easy
lengthT125 °C40 °C50 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 40 °C while the cold fluid heats from 25 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 40 °CTc: 25 → 50 °C
ΔTlm = K
3.Medium
lengthT95 °C45 °C60 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 50 kW. The hot fluid cools from 95 to 45 °C and the cold fluid heats from 20 to 60 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 50 kWU = 800 W/(m²·K)Th: 95 → 45 °CTc: 20 → 60 °C
A = m²
4.Medium
lengthT90 °C70 °C40 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 170 kW. The hot fluid cools from 90 to 70 °C and the cold fluid heats from 30 to 40 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 170 kWU = 1000 W/(m²·K)Th: 90 → 70 °CTc: 30 → 40 °C
A = m²
5.Hard
lengthT140 °C75 °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 140 to 75 °C. Water (1.5 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 = 250 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: 140 → 75 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 40 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT115 °C90 °C29.94 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 115 to 90 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 115 → 90 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 65.96 K
  2. 2. ΔTlm = 37.28 K
  3. 3. A = 2.103 m²
  4. 4. A = 3.793 m²
  5. 5. L = 18.61 m
  6. 6. A = 5.05 m²

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