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
lengthT160 °C85 °C130 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 20 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 160 to 85 °C and the cold fluid heats from 30 to 130 °C. Find the heat transfer rate Q̇.

A = 20 m²U = 300 W/(m²·K)Th: 160 → 85 °CTc: 30 → 130 °C
Q̇ = kW
2.Easy

In a heat exchanger 0.3 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is cooled from 120 to 30 °C. Find the heat transfer rate Q̇.

ṁ = 0.3 kg/scp = 3.6 kJ/(kg·K)T: 120 → 30 °C
Q̇ = kW
3.Medium
lengthT135 °C100 °C30 °C75 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 300 kW. Its heat transfer area is 6 m². The hot fluid cools from 135 to 100 °C and the cold fluid heats from 30 to 75 °C. Find the overall heat transfer coefficient U.

Q̇ = 300 kWA = 6 m²Th: 135 → 100 °CTc: 30 → 75 °C
U = W/(m²·K)
4.Medium
lengthT140 °C100 °C90 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 350 kW. The hot fluid cools from 140 to 100 °C and the cold fluid heats from 25 to 90 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 350 kWF = 0.95U = 800 W/(m²·K)Th: 140 → 100 °CTc: 25 → 90 °C
A = m²
5.Hard
lengthT130 °C25 °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 6 m² and U = 2000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 6 m²U = 2000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT150 °C70 °C38.4 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 150 to 70 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 150 → 70 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 247.5 kW
  2. 2. Q̇ = 97.2 kW
  3. 3. U = 896.9 W/(m²·K)
  4. 4. A = 7.469 m²
  5. 5. Tc,out = 114.5 °C
  6. 6. A = 0.7637 m²

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