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
lengthT180 °C100 °C75 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 100 °C while the cold fluid heats from 30 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 100 °CTc: 30 → 75 °C
ΔTlm = K
2.Easy
lengthT130 °C35 °C35 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 35 °C while the cold fluid heats from 15 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 35 °CTc: 15 → 35 °C
ΔTlm = K
3.Medium
lengthT155 °C65 °C95 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 90 kW. Its heat transfer area is 20 m². The hot fluid cools from 155 to 65 °C and the cold fluid heats from 10 to 95 °C. Find the overall heat transfer coefficient U.

Q̇ = 90 kWA = 20 m²Th: 155 → 65 °CTc: 10 → 95 °C
U = W/(m²·K)
4.Medium
lengthT120 °C90 °C35 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 110 kW. Its heat transfer area is 2 m². The hot fluid cools from 120 to 90 °C and the cold fluid heats from 10 to 35 °C. Find the overall heat transfer coefficient U.

Q̇ = 110 kWA = 2 m²Th: 120 → 90 °CTc: 10 → 35 °C
U = W/(m²·K)
5.Hard
lengthT105 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 105 °C on the outside of the tubes of a condenser with a heat transfer area of 2.5 m² and U = 2500 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 2.5 m²U = 2500 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT140 °C55 °C?25 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 140 to 55 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 25 mm, and U = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.1 kJ/(kg·K)Th: 140 → 55 °Cṁc = 0.3 kg/sTc,in = 25 °CD = 25 mmU = 150 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 86.32 K
  2. 2. ΔTlm = 48.13 K
  3. 3. U = 78.31 W/(m²·K)
  4. 4. U = 666.9 W/(m²·K)
  5. 5. Tc,out = 85.94 °C
  6. 6. L = 56.78 m

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