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
lengthT180 °C100 °C65 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 180 to 100 °C while the cold fluid heats from 15 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 180 → 100 °CTc: 15 → 65 °C
ΔTlm = K
2.Easy
lengthT175 °C105 °C30 °C45 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 175 to 105 °C while the cold fluid heats from 30 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 105 °CTc: 30 → 45 °C
ΔTlm = K
3.Medium
lengthT175 °C150 °C20 °C145 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 240 kW. The hot fluid cools from 175 to 150 °C and the cold fluid heats from 20 to 145 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 240 kWU = 200 W/(m²·K)Th: 175 → 150 °CTc: 20 → 145 °C
A = m²
4.Medium
lengthT180 °C130 °C95 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 220 kW. The hot fluid cools from 180 to 130 °C and the cold fluid heats from 15 to 95 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 220 kWU = 300 W/(m²·K)Th: 180 → 130 °CTc: 15 → 95 °C
A = m²
5.Hard
lengthT180 °C??20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 0.5 kW/K. The hot stream enters at 180 °C and the cold stream at 20 °C. The exchanger has A = 1 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 180 °CTc,in = 20 °CA = 1 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT95 °C45 °C31.88 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 95 to 45 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 95 → 45 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 99.25 K
  2. 2. ΔTlm = 96.33 K
  3. 3. A = 27.47 m²
  4. 4. A = 7.389 m²
  5. 5. Th,out = 100 °C
  6. 6. A = 1.533 m²

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