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
lengthT140 °C95 °C115 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 140 to 95 °C while the cold fluid heats from 30 to 115 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 95 °CTc: 30 → 115 °C
ΔTlm = K
2.Easy
lengthT135 °C50 °C100 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 50 °C while the cold fluid heats from 20 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 50 °CTc: 20 → 100 °C
ΔTlm = K
3.Medium
lengthT105 °C55 °C30 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 750 kW. The hot fluid cools from 105 to 55 °C and the cold fluid heats from 20 to 30 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 750 kWF = 0.9U = 300 W/(m²·K)Th: 105 → 55 °CTc: 20 → 30 °C
A = m²
4.Medium
lengthT125 °C55 °C50 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 360 kW. The hot fluid cools from 125 to 55 °C and the cold fluid heats from 25 to 50 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 360 kWU = 300 W/(m²·K)Th: 125 → 55 °CTc: 25 → 50 °C
A = m²
5.Hard
lengthT90 °C55 °C20 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 90 to 55 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 25 mm, and U = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.8 kg/scp,h = 2.5 kJ/(kg·K)Th: 90 → 55 °Cṁc = 1.5 kg/sTc,in = 20 °CD = 25 mmU = 300 W/(m²·K)
L = m
6.Hard
lengthT140 °C105 °C51.87 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 140 to 105 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 140 → 105 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 41.86 K
  2. 2. ΔTlm = 32.44 K
  3. 3. A = 52.93 m²
  4. 4. A = 24.43 m²
  5. 5. L = 69.33 m
  6. 6. A = 4.78 m²

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