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

In a heat exchanger 0.8 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 25 to 40 °C. Find the heat transfer rate Q̇.

ṁ = 0.8 kg/scp = 4.18 kJ/(kg·K)T: 25 → 40 °C
Q̇ = kW
2.Easy
lengthT125 °C85 °C95 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 15 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 125 to 85 °C and the cold fluid heats from 30 to 95 °C. Find the heat transfer rate Q̇.

A = 15 m²U = 1000 W/(m²·K)Th: 125 → 85 °CTc: 30 → 95 °C
Q̇ = kW
3.Medium
lengthT170 °C90 °C25 °C35 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 370 kW. The hot fluid cools from 170 to 90 °C and the cold fluid heats from 25 to 35 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 800 W/(m²·K)Th: 170 → 90 °CTc: 25 → 35 °C
A = m²
4.Medium
lengthT140 °C65 °C85 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 50 kW. The hot fluid cools from 140 to 65 °C and the cold fluid heats from 15 to 85 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 50 kWU = 1500 W/(m²·K)Th: 140 → 65 °CTc: 15 → 85 °C
A = m²
5.Hard
lengthT125 °C60 °C15 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 125 to 60 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °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 = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 125 → 60 °Cṁc = 0.3 kg/sTc,in = 15 °CD = 20 mmU = 300 W/(m²·K)
L = m
6.Hard
lengthT165 °C45 °C81.03 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 165 to 45 °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 = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 165 → 45 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 50.16 kW
  2. 2. Q̇ = 618.7 kW
  3. 3. A = 4.982 m²
  4. 4. A = 0.6354 m²
  5. 5. L = 48.66 m
  6. 6. A = 6.579 m²

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