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
lengthT175 °C95 °C75 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2.5 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 175 to 95 °C and the cold fluid heats from 30 to 75 °C. Find the heat transfer rate Q̇.

A = 2.5 m²U = 500 W/(m²·K)Th: 175 → 95 °CTc: 30 → 75 °C
Q̇ = kW
2.Easy
lengthT160 °C25 °C75 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 25 °C while the cold fluid heats from 10 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 25 °CTc: 10 → 75 °C
ΔTlm = K
3.Medium
lengthT140 °C95 °C30 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 60 kW. The hot fluid cools from 140 to 95 °C and the cold fluid heats from 30 to 55 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 60 kWU = 200 W/(m²·K)Th: 140 → 95 °CTc: 30 → 55 °C
A = m²
4.Medium
lengthT95 °C35 °C25 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 210 kW. Its heat transfer area is 25 m². The hot fluid cools from 95 to 35 °C and the cold fluid heats from 10 to 25 °C. Find the overall heat transfer coefficient U.

Q̇ = 210 kWA = 25 m²Th: 95 → 35 °CTc: 10 → 25 °C
U = W/(m²·K)
5.Hard
lengthT180 °C80 °C69.87 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 180 to 80 °C in a counter-flow exchanger. It heats 3 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 = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 180 → 80 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT110 °C80 °C?25 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 110 to 80 °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 = 200 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 80 °Cṁc = 1 kg/sTc,in = 25 °CD = 20 mmU = 200 W/(m²·K)
L = m

Answer key

  1. 1. Q̇ = 101.6 kW
  2. 2. ΔTlm = 40.36 K
  3. 3. A = 4.335 m²
  4. 4. U = 192.2 W/(m²·K)
  5. 5. A = 21.89 m²
  6. 6. L = 98.12 m

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