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 °C50 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 65 °C while the cold fluid heats from 20 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 65 °CTc: 20 → 50 °C
ΔTlm = K
2.Easy
lengthT165 °C110 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 165 to 110 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 165 → 110 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT115 °C95 °C30 °C85 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 150 kW. The hot fluid cools from 115 to 95 °C and the cold fluid heats from 30 to 85 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 150 kWU = 1000 W/(m²·K)Th: 115 → 95 °CTc: 30 → 85 °C
A = m²
4.Medium
lengthT180 °C40 °C135 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 300 kW. Its heat transfer area is 25 m². The hot fluid cools from 180 to 40 °C and the cold fluid heats from 20 to 135 °C. Find the overall heat transfer coefficient U.

Q̇ = 300 kWA = 25 m²Th: 180 → 40 °CTc: 20 → 135 °C
U = W/(m²·K)
5.Hard
lengthT115 °C50 °C?10 °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 115 to 50 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 32 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: 115 → 50 °Cṁc = 1.5 kg/sTc,in = 10 °CD = 32 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT180 °C85 °C39.47 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 180 to 85 °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 = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 180 → 85 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 42.45 K
  2. 2. Tc,out = 52.7 °C
  3. 3. A = 4.28 m²
  4. 4. U = 389.2 W/(m²·K)
  5. 5. L = 71.56 m
  6. 6. A = 1.302 m²

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