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

In a heat exchanger 1 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is cooled from 110 to 65 °C. Find the heat transfer rate Q̇.

ṁ = 1 kg/scp = 2.1 kJ/(kg·K)T: 110 → 65 °C
Q̇ = kW
2.Easy
lengthT105 °C45 °C95 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 6 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 105 to 45 °C and the cold fluid heats from 20 to 95 °C. Find the heat transfer rate Q̇.

A = 6 m²U = 200 W/(m²·K)Th: 105 → 45 °CTc: 20 → 95 °C
Q̇ = kW
3.Medium
lengthT85 °C65 °C35 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 370 kW. The hot fluid cools from 85 to 65 °C and the cold fluid heats from 10 to 35 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 370 kWU = 500 W/(m²·K)Th: 85 → 65 °CTc: 10 → 35 °C
A = m²
4.Medium
lengthT170 °C95 °C25 °C65 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 330 kW. The hot fluid cools from 170 to 95 °C and the cold fluid heats from 25 to 65 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 330 kWU = 300 W/(m²·K)Th: 170 → 95 °CTc: 25 → 65 °C
A = m²
5.Hard
lengthT105 °C30 °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 3 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 = 105 °CA = 3 m²U = 1000 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
6.Hard
lengthT80 °C40 °C25.05 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 80 to 40 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °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: 80 → 40 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 94.5 kW
  2. 2. Q̇ = 19.64 kW
  3. 3. A = 14.11 m²
  4. 4. A = 15.07 m²
  5. 5. Tc,out = 87.15 °C
  6. 6. A = 2.209 m²

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