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
lengthT100 °C65 °C75 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 100 to 65 °C while the cold fluid heats from 10 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 65 °CTc: 10 → 75 °C
ΔTlm = K
2.Easy
lengthT95 °C30 °C45 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 30 °C while the cold fluid heats from 15 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 30 °CTc: 15 → 45 °C
ΔTlm = K
3.Medium
lengthT175 °C135 °C25 °C65 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 220 kW. The hot fluid cools from 175 to 135 °C and the cold fluid heats from 25 to 65 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 220 kWU = 1000 W/(m²·K)Th: 175 → 135 °CTc: 25 → 65 °C
A = m²
4.Medium
lengthT90 °C45 °C60 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 210 kW. The hot fluid cools from 90 to 45 °C and the cold fluid heats from 30 to 60 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 210 kWF = 0.85U = 300 W/(m²·K)Th: 90 → 45 °CTc: 30 → 60 °C
A = m²
5.Hard
lengthT160 °C100 °C?20 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 160 to 100 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °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 = 0.3 kg/scp,h = 2.5 kJ/(kg·K)Th: 160 → 100 °Cṁc = 1 kg/sTc,in = 20 °CD = 20 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT110 °C75 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 110 to 75 °C. Water (0.2 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 40 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.5 kJ/(kg·K)Th: 110 → 75 °Cṁc = 0.2 kg/sTc,in = 15 °CD = 40 mmU = 500 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 38.05 K
  2. 2. ΔTlm = 29.07 K
  3. 3. A = 2.096 m²
  4. 4. A = 38.06 m²
  5. 5. L = 17.44 m
  6. 6. L = 6.762 m

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