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
lengthT150 °C45 °C130 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 45 °C while the cold fluid heats from 15 to 130 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 45 °CTc: 15 → 130 °C
ΔTlm = K
2.Easy
lengthT140 °C40 °C25 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 12 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 140 to 40 °C and the cold fluid heats from 10 to 25 °C. Find the heat transfer rate Q̇.

A = 12 m²U = 1500 W/(m²·K)Th: 140 → 40 °CTc: 10 → 25 °C
Q̇ = kW
3.Medium
lengthT130 °C90 °C65 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 130 kW. The hot fluid cools from 130 to 90 °C and the cold fluid heats from 10 to 65 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 130 kWF = 0.88U = 300 W/(m²·K)Th: 130 → 90 °CTc: 10 → 65 °C
A = m²
4.Medium
lengthT95 °C75 °C45 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 380 kW. The hot fluid cools from 95 to 75 °C and the cold fluid heats from 20 to 45 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 380 kWU = 800 W/(m²·K)Th: 95 → 75 °CTc: 20 → 45 °C
A = m²
5.Hard
lengthT115 °C45 °C50.17 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 45 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 45 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT130 °C80 °C?20 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 130 to 80 °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 50 mm, and U = 400 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.5 kJ/(kg·K)Th: 130 → 80 °Cṁc = 1 kg/sTc,in = 20 °CD = 50 mmU = 400 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 24.66 K
  2. 2. Q̇ = 1139 kW
  3. 3. A = 6.816 m²
  4. 4. A = 9.054 m²
  5. 5. A = 5.42 m²
  6. 6. L = 4.974 m

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