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
lengthT105 °C65 °C85 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 65 °C while the cold fluid heats from 25 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 65 °CTc: 25 → 85 °C
ΔTlm = K
2.Easy
lengthT115 °C70 °C100 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 115 to 70 °C and the cold fluid heats from 25 to 100 °C. Find the heat transfer rate Q̇.

A = 2 m²U = 500 W/(m²·K)Th: 115 → 70 °CTc: 25 → 100 °C
Q̇ = kW
3.Medium
lengthT175 °C60 °C150 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 550 kW. The hot fluid cools from 175 to 60 °C and the cold fluid heats from 15 to 150 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 550 kWF = 0.92U = 200 W/(m²·K)Th: 175 → 60 °CTc: 15 → 150 °C
A = m²
4.Medium
lengthT170 °C70 °C15 °C25 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 390 kW. The hot fluid cools from 170 to 70 °C and the cold fluid heats from 15 to 25 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 500 W/(m²·K)Th: 170 → 70 °CTc: 15 → 25 °C
A = m²
5.Hard
lengthT105 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 105 °C on the outside of the tubes of a condenser with a heat transfer area of 1.5 m² and U = 1000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 1.5 m²U = 1000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
6.Hard
lengthT145 °C125 °C64.02 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 145 to 125 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 145 → 125 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 28.85 K
  2. 2. Q̇ = 27.31 kW
  3. 3. A = 87.85 m²
  4. 4. A = 8.77 m²
  5. 5. Tc,out = 42.14 °C
  6. 6. A = 1.99 m²

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