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

In a heat exchanger 1.2 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is heated from 35 to 65 °C. Find the heat transfer rate Q̇.

ṁ = 1.2 kg/scp = 2.44 kJ/(kg·K)T: 35 → 65 °C
Q̇ = kW
2.Easy
lengthT85 °C40 °C60 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 40 °C while the cold fluid heats from 20 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 40 °CTc: 20 → 60 °C
ΔTlm = K
3.Medium
lengthT100 °C50 °C50 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 760 kW. The hot fluid cools from 100 to 50 °C and the cold fluid heats from 10 to 50 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 760 kWF = 0.85U = 200 W/(m²·K)Th: 100 → 50 °CTc: 10 → 50 °C
A = m²
4.Medium
lengthT100 °C70 °C20 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 480 kW. The hot fluid cools from 100 to 70 °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 = 480 kWU = 800 W/(m²·K)Th: 100 → 70 °CTc: 20 → 45 °C
A = m²
5.Hard
lengthT85 °C50 °C58.89 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 85 to 50 °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 = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 85 → 50 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT145 °C85 °C48.01 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 145 to 85 °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 = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 145 → 85 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 87.84 kW
  2. 2. ΔTlm = 22.41 K
  3. 3. A = 99.76 m²
  4. 4. A = 12.69 m²
  5. 5. A = 26.34 m²
  6. 6. A = 1.667 m²

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