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
lengthT135 °C95 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 135 to 95 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 135 → 95 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
2.Easy
lengthT80 °C55 °C50 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 80 to 55 °C while the cold fluid heats from 15 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 80 → 55 °CTc: 15 → 50 °C
ΔTlm = K
3.Medium
lengthT130 °C30 °C50 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 430 kW. The hot fluid cools from 130 to 30 °C and the cold fluid heats from 15 to 50 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 430 kWU = 200 W/(m²·K)Th: 130 → 30 °CTc: 15 → 50 °C
A = m²
4.Medium
lengthT110 °C90 °C55 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 130 kW. The hot fluid cools from 110 to 90 °C and the cold fluid heats from 20 to 55 °C. The LMTD correction factor for this arrangement is F = 0.8, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 130 kWF = 0.8U = 300 W/(m²·K)Th: 110 → 90 °CTc: 20 → 55 °C
A = m²
5.Hard
lengthT155 °C50 °C104.1 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 50 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 50 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT85 °C45 °C48.92 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 85 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 25 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 85 → 45 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 21.7 °C
  2. 2. ΔTlm = 34.76 K
  3. 3. A = 55.37 m²
  4. 4. A = 8.709 m²
  5. 5. A = 18.16 m²
  6. 6. A = 2.293 m²

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