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
lengthT85 °C70 °C20 °C45 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 85 to 70 °C while the cold fluid heats from 20 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 70 °CTc: 20 → 45 °C
ΔTlm = K
2.Easy
lengthT130 °C40 °C35 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 40 °C while the cold fluid heats from 10 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 40 °CTc: 10 → 35 °C
ΔTlm = K
3.Medium
lengthT155 °C120 °C20 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 260 kW. Its heat transfer area is 8 m². The hot fluid cools from 155 to 120 °C and the cold fluid heats from 20 to 55 °C. Find the overall heat transfer coefficient U.

Q̇ = 260 kWA = 8 m²Th: 155 → 120 °CTc: 20 → 55 °C
U = W/(m²·K)
4.Medium
lengthT85 °C25 °C55 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 360 kW. The hot fluid cools from 85 to 25 °C and the cold fluid heats from 10 to 55 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 360 kWU = 800 W/(m²·K)Th: 85 → 25 °CTc: 10 → 55 °C
A = m²
5.Hard
lengthT145 °C115 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 145 to 115 °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 = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 145 → 115 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 40 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT130 °C70 °C91.77 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 130 to 70 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °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: 130 → 70 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 41.86 K
  2. 2. ΔTlm = 56.39 K
  3. 3. U = 339.3 W/(m²·K)
  4. 4. A = 20.79 m²
  5. 5. L = 14.92 m
  6. 6. A = 4.561 m²

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