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 2.5 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is heated from 15 to 35 °C. Find the heat transfer rate Q̇.

ṁ = 2.5 kg/scp = 2.1 kJ/(kg·K)T: 15 → 35 °C
Q̇ = kW
2.Easy
lengthT90 °C30 °C55 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 6 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 90 to 30 °C and the cold fluid heats from 10 to 55 °C. Find the heat transfer rate Q̇.

A = 6 m²U = 300 W/(m²·K)Th: 90 → 30 °CTc: 10 → 55 °C
Q̇ = kW
3.Medium
lengthT155 °C115 °C100 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 80 kW. Its heat transfer area is 2.5 m². The hot fluid cools from 155 to 115 °C and the cold fluid heats from 15 to 100 °C. Find the overall heat transfer coefficient U.

Q̇ = 80 kWA = 2.5 m²Th: 155 → 115 °CTc: 15 → 100 °C
U = W/(m²·K)
4.Medium
lengthT80 °C55 °C30 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 200 kW. The hot fluid cools from 80 to 55 °C and the cold fluid heats from 30 to 40 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 200 kWU = 500 W/(m²·K)Th: 80 → 55 °CTc: 30 → 40 °C
A = m²
5.Hard
lengthT105 °C65 °C?25 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 105 to 65 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °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 = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 105 → 65 °Cṁc = 1 kg/sTc,in = 25 °CD = 32 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT115 °C65 °C58.49 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 65 °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 = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 65 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 105 kW
  2. 2. Q̇ = 48.25 kW
  3. 3. U = 425.1 W/(m²·K)
  4. 4. A = 13.76 m²
  5. 5. L = 125.9 m
  6. 6. A = 14.65 m²

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