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
lengthT155 °C50 °C55 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 50 °C while the cold fluid heats from 30 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 50 °CTc: 30 → 55 °C
ΔTlm = K
2.Easy
lengthT150 °C55 °C130 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 0.5 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 150 to 55 °C and the cold fluid heats from 25 to 130 °C. Find the heat transfer rate Q̇.

A = 0.5 m²U = 1000 W/(m²·K)Th: 150 → 55 °CTc: 25 → 130 °C
Q̇ = kW
3.Medium
lengthT170 °C110 °C40 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 790 kW. The hot fluid cools from 170 to 110 °C and the cold fluid heats from 15 to 40 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 790 kWF = 0.88U = 800 W/(m²·K)Th: 170 → 110 °CTc: 15 → 40 °C
A = m²
4.Medium
lengthT160 °C135 °C20 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 150 kW. Its heat transfer area is 10 m². The hot fluid cools from 160 to 135 °C and the cold fluid heats from 20 to 55 °C. Find the overall heat transfer coefficient U.

Q̇ = 150 kWA = 10 m²Th: 160 → 135 °CTc: 20 → 55 °C
U = W/(m²·K)
5.Hard
lengthT100 °C60 °C?10 °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 100 to 60 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 25 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: 100 → 60 °Cṁc = 0.3 kg/sTc,in = 10 °CD = 25 mmU = 500 W/(m²·K)
L = m
6.Hard
lengthT95 °C50 °C29.13 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 95 to 50 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 95 → 50 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 49.71 K
  2. 2. Q̇ = 12.33 kW
  3. 3. A = 10.06 m²
  4. 4. U = 139.9 W/(m²·K)
  5. 5. L = 13.25 m
  6. 6. A = 6.133 m²

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