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
lengthT110 °C25 °C35 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 0.5 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 110 to 25 °C and the cold fluid heats from 10 to 35 °C. Find the heat transfer rate Q̇.

A = 0.5 m²U = 300 W/(m²·K)Th: 110 → 25 °CTc: 10 → 35 °C
Q̇ = kW
2.Easy
lengthT155 °C90 °C70 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 90 °C while the cold fluid heats from 10 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 90 °CTc: 10 → 70 °C
ΔTlm = K
3.Medium
lengthT135 °C65 °C30 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 260 kW. The hot fluid cools from 135 to 65 °C and the cold fluid heats from 30 to 40 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 260 kWU = 300 W/(m²·K)Th: 135 → 65 °CTc: 30 → 40 °C
A = m²
4.Medium
lengthT180 °C105 °C65 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 550 kW. The hot fluid cools from 180 to 105 °C and the cold fluid heats from 20 to 65 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 550 kWF = 0.85U = 1000 W/(m²·K)Th: 180 → 105 °CTc: 20 → 65 °C
A = m²
5.Hard
lengthT180 °C85 °C108.4 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 180 to 85 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 180 → 85 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT90 °C60 °C37.94 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 90 to 60 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 90 → 60 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 5.592 kW
  2. 2. ΔTlm = 82.47 K
  3. 3. A = 15.55 m²
  4. 4. A = 6.52 m²
  5. 5. A = 3.472 m²
  6. 6. A = 1.639 m²

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