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
lengthT140 °C115 °C15 °C65 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 140 to 115 °C while the cold fluid heats from 15 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 115 °CTc: 15 → 65 °C
ΔTlm = K
2.Easy

In a heat exchanger 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) is cooled from 120 to 75 °C. Find the heat transfer rate Q̇.

ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)T: 120 → 75 °C
Q̇ = kW
3.Medium
lengthT145 °C115 °C125 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 30 kW. The hot fluid cools from 145 to 115 °C and the cold fluid heats from 15 to 125 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 30 kWU = 300 W/(m²·K)Th: 145 → 115 °CTc: 15 → 125 °C
A = m²
4.Medium
lengthT115 °C45 °C105 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 490 kW. The hot fluid cools from 115 to 45 °C and the cold fluid heats from 25 to 105 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 490 kWU = 200 W/(m²·K)Th: 115 → 45 °CTc: 25 → 105 °C
A = m²
5.Hard
lengthT150 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 3 kW/K. The hot stream enters at 150 °C and the cold stream at 10 °C. The exchanger has A = 3 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 3 kW/KTh,in = 150 °CTc,in = 10 °CA = 3 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT165 °C140 °C54.9 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 165 to 140 °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 = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 165 → 140 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 81.85 K
  2. 2. Q̇ = 282.1 kW
  3. 3. A = 2.012 m²
  4. 4. A = 169.8 m²
  5. 5. Th,out = 87.78 °C
  6. 6. A = 2.777 m²

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