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
lengthT145 °C110 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 145 to 110 °C in a counter-flow exchanger. It heats 0.8 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 145 → 110 °Cṁc = 0.8 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
2.Easy
lengthT150 °C130 °C25 °C110 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 150 to 130 °C while the cold fluid heats from 25 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 130 °CTc: 25 → 110 °C
ΔTlm = K
3.Medium
lengthT120 °C100 °C30 °C80 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 440 kW. The hot fluid cools from 120 to 100 °C and the cold fluid heats from 30 to 80 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 440 kWU = 300 W/(m²·K)Th: 120 → 100 °CTc: 30 → 80 °C
A = m²
4.Medium
lengthT90 °C70 °C25 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 260 kW. Its heat transfer area is 20 m². The hot fluid cools from 90 to 70 °C and the cold fluid heats from 25 to 50 °C. Find the overall heat transfer coefficient U.

Q̇ = 260 kWA = 20 m²Th: 90 → 70 °CTc: 25 → 50 °C
U = W/(m²·K)
5.Hard
lengthT135 °C85 °C?25 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 135 to 85 °C. Water (0.3 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 = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.5 kJ/(kg·K)Th: 135 → 85 °Cṁc = 0.3 kg/sTc,in = 25 °CD = 20 mmU = 300 W/(m²·K)
L = m
6.Hard
lengthT100 °C60 °C26 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 100 to 60 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 60 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 68.96 °C
  2. 2. ΔTlm = 57.3 K
  3. 3. A = 31.51 m²
  4. 4. U = 340.5 W/(m²·K)
  5. 5. L = 17.92 m
  6. 6. A = 4.734 m²

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