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 glycol mix (cp = 3.6 kJ/(kg·K)) is heated from 20 to 80 °C. Find the heat transfer rate Q̇.

ṁ = 0.8 kg/scp = 3.6 kJ/(kg·K)T: 20 → 80 °C
Q̇ = kW
2.Easy
lengthT155 °C105 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 155 to 105 °C in a counter-flow exchanger. It heats 3 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 = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 155 → 105 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
3.Medium
lengthT130 °C90 °C25 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 410 kW. The hot fluid cools from 130 to 90 °C and the cold fluid heats from 25 to 55 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 200 W/(m²·K)Th: 130 → 90 °CTc: 25 → 55 °C
A = m²
4.Medium
lengthT150 °C125 °C25 °C120 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 410 kW. The hot fluid cools from 150 to 125 °C and the cold fluid heats from 25 to 120 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 500 W/(m²·K)Th: 150 → 125 °CTc: 25 → 120 °C
A = m²
5.Hard
lengthT135 °C55 °C?25 °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 135 to 55 °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 20 mm, and U = 400 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: 135 → 55 °Cṁc = 1 kg/sTc,in = 25 °CD = 20 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT120 °C55 °C65.77 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 120 to 55 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 120 → 55 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 172.8 kW
  2. 2. Tc,out = 38.76 °C
  3. 3. A = 32.17 m²
  4. 4. A = 22 m²
  5. 5. L = 61.24 m
  6. 6. A = 13.2 m²

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