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
lengthT140 °C120 °C85 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 4 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 140 to 120 °C and the cold fluid heats from 20 to 85 °C. Find the heat transfer rate Q̇.

A = 4 m²U = 800 W/(m²·K)Th: 140 → 120 °CTc: 20 → 85 °C
Q̇ = kW
2.Easy

In a heat exchanger 0.2 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 30 to 50 °C. Find the heat transfer rate Q̇.

ṁ = 0.2 kg/scp = 4.18 kJ/(kg·K)T: 30 → 50 °C
Q̇ = kW
3.Medium
lengthT160 °C140 °C140 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 340 kW. The hot fluid cools from 160 to 140 °C and the cold fluid heats from 10 to 140 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 340 kWU = 300 W/(m²·K)Th: 160 → 140 °CTc: 10 → 140 °C
A = m²
4.Medium
lengthT130 °C110 °C20 °C80 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 420 kW. Its heat transfer area is 3 m². The hot fluid cools from 130 to 110 °C and the cold fluid heats from 20 to 80 °C. Find the overall heat transfer coefficient U.

Q̇ = 420 kWA = 3 m²Th: 130 → 110 °CTc: 20 → 80 °C
U = W/(m²·K)
5.Hard
lengthT115 °C75 °C26 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 115 to 75 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 115 → 75 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT130 °C95 °C45.93 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 130 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 25 °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: 130 → 95 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 240.9 kW
  2. 2. Q̇ = 16.72 kW
  3. 3. A = 19.29 m²
  4. 4. U = 2274 W/(m²·K)
  5. 5. A = 2.085 m²
  6. 6. A = 8.543 m²

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