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 °C70 °C15 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 95 to 70 °C while the cold fluid heats from 15 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 70 °CTc: 15 → 30 °C
ΔTlm = K
2.Easy
lengthT80 °C45 °C65 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2.5 m² and an overall heat transfer coefficient of 1000 W/(m²·K). The hot fluid cools from 80 to 45 °C and the cold fluid heats from 25 to 65 °C. Find the heat transfer rate Q̇.

A = 2.5 m²U = 1000 W/(m²·K)Th: 80 → 45 °CTc: 25 → 65 °C
Q̇ = kW
3.Medium
lengthT115 °C95 °C80 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 460 kW. The hot fluid cools from 115 to 95 °C and the cold fluid heats from 10 to 80 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 460 kWF = 0.95U = 800 W/(m²·K)Th: 115 → 95 °CTc: 10 → 80 °C
A = m²
4.Medium
lengthT100 °C50 °C85 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 120 kW. The hot fluid cools from 100 to 50 °C and the cold fluid heats from 30 to 85 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 120 kWU = 1000 W/(m²·K)Th: 100 → 50 °CTc: 30 → 85 °C
A = m²
5.Hard
lengthT175 °C65 °C110.7 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 175 to 65 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 175 → 65 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT180 °C60 °C105.4 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 180 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 25 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 180 → 60 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 57.71 K
  2. 2. Q̇ = 43.45 kW
  3. 3. A = 10.74 m²
  4. 4. A = 6.904 m²
  5. 5. A = 10.5 m²
  6. 6. A = 32.1 m²

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