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
lengthT165 °C75 °C150 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 165 to 75 °C while the cold fluid heats from 20 to 150 °C. Find the log-mean temperature difference ΔTlm.

Th: 165 → 75 °CTc: 20 → 150 °C
ΔTlm = K
2.Easy

In a heat exchanger 1 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is cooled from 70 to 55 °C. Find the heat transfer rate Q̇.

ṁ = 1 kg/scp = 2.1 kJ/(kg·K)T: 70 → 55 °C
Q̇ = kW
3.Medium
lengthT165 °C140 °C20 °C125 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 80 kW. The hot fluid cools from 165 to 140 °C and the cold fluid heats from 20 to 125 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 80 kWU = 800 W/(m²·K)Th: 165 → 140 °CTc: 20 → 125 °C
A = m²
4.Medium
lengthT105 °C80 °C30 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 320 kW. The hot fluid cools from 105 to 80 °C and the cold fluid heats from 30 to 50 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 320 kWU = 500 W/(m²·K)Th: 105 → 80 °CTc: 30 → 50 °C
A = m²
5.Hard
lengthT130 °C30 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 1 m² and U = 1000 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 1 m²U = 1000 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
6.Hard
lengthT175 °C120 °C29.21 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 175 to 120 °C in a counter-flow exchanger. It heats 1.5 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 = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 175 → 120 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 30.79 K
  2. 2. Q̇ = 31.5 kW
  3. 3. A = 1.745 m²
  4. 4. A = 13.03 m²
  5. 5. Tc,out = 68.03 °C
  6. 6. A = 0.9509 m²

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