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
lengthT95 °C65 °C60 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 65 °C while the cold fluid heats from 10 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 65 °CTc: 10 → 60 °C
ΔTlm = K
2.Easy
lengthT135 °C80 °C25 °C55 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 135 to 80 °C while the cold fluid heats from 25 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 80 °CTc: 25 → 55 °C
ΔTlm = K
3.Medium
lengthT120 °C85 °C45 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 240 kW. The hot fluid cools from 120 to 85 °C and the cold fluid heats from 30 to 45 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 240 kWF = 0.9U = 200 W/(m²·K)Th: 120 → 85 °CTc: 30 → 45 °C
A = m²
4.Medium
lengthT175 °C60 °C135 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 250 kW. The hot fluid cools from 175 to 60 °C and the cold fluid heats from 25 to 135 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 250 kWU = 1500 W/(m²·K)Th: 175 → 60 °CTc: 25 → 135 °C
A = m²
5.Hard
lengthT130 °C95 °C?20 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 130 to 95 °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 = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 130 → 95 °Cṁc = 1.5 kg/sTc,in = 20 °CD = 25 mmU = 400 W/(m²·K)
L = m
6.Hard
lengthT140 °C85 °C?15 °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 85 °C. Water (0.8 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 32 mm, and U = 250 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 → 85 °Cṁc = 0.8 kg/sTc,in = 15 °CD = 32 mmU = 250 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 44.25 K
  2. 2. ΔTlm = 57.37 K
  3. 3. A = 20.68 m²
  4. 4. A = 4.451 m²
  5. 5. L = 27.17 m
  6. 6. L = 9.995 m

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