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
lengthT175 °C155 °C20 °C65 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 175 to 155 °C while the cold fluid heats from 20 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 155 °CTc: 20 → 65 °C
ΔTlm = K
2.Easy
lengthT105 °C45 °C50 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 45 °C while the cold fluid heats from 30 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 45 °CTc: 30 → 50 °C
ΔTlm = K
3.Medium
lengthT155 °C130 °C20 °C85 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 360 kW. The hot fluid cools from 155 to 130 °C and the cold fluid heats from 20 to 85 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 360 kWU = 200 W/(m²·K)Th: 155 → 130 °CTc: 20 → 85 °C
A = m²
4.Medium
lengthT145 °C110 °C30 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 610 kW. The hot fluid cools from 145 to 110 °C and the cold fluid heats from 15 to 30 °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 = 610 kWF = 0.8U = 300 W/(m²·K)Th: 145 → 110 °CTc: 15 → 30 °C
A = m²
5.Hard
lengthT85 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 85 °C and the cold stream at 15 °C. The exchanger has A = 2 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 85 °CTc,in = 15 °CA = 2 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT145 °C30 °C38.89 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 145 to 30 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 145 → 30 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 119.6 K
  2. 2. ΔTlm = 30.79 K
  3. 3. A = 21.97 m²
  4. 4. A = 24.28 m²
  5. 5. Th,out = 41.92 °C
  6. 6. A = 5.85 m²

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