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
lengthT135 °C110 °C10 °C20 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 135 to 110 °C while the cold fluid heats from 10 to 20 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 110 °CTc: 10 → 20 °C
ΔTlm = K
2.Easy
lengthT100 °C80 °C20 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 100 to 80 °C while the cold fluid heats from 20 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 80 °CTc: 20 → 30 °C
ΔTlm = K
3.Medium
lengthT140 °C35 °C85 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 150 kW. The hot fluid cools from 140 to 35 °C and the cold fluid heats from 15 to 85 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 150 kWU = 800 W/(m²·K)Th: 140 → 35 °CTc: 15 → 85 °C
A = m²
4.Medium
lengthT100 °C60 °C20 °C55 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 380 kW. Its heat transfer area is 12 m². The hot fluid cools from 100 to 60 °C and the cold fluid heats from 20 to 55 °C. Find the overall heat transfer coefficient U.

Q̇ = 380 kWA = 12 m²Th: 100 → 60 °CTc: 20 → 55 °C
U = W/(m²·K)
5.Hard
lengthT125 °C55 °C58.52 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 125 to 55 °C in a counter-flow exchanger. It heats 2 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: 125 → 55 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT100 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 100 °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 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 6 m²U = 2000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 106.5 K
  2. 2. ΔTlm = 63.83 K
  3. 3. A = 5.419 m²
  4. 4. U = 1171 W/(m²·K)
  5. 5. A = 13.12 m²
  6. 6. Tc,out = 95.18 °C

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