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
lengthT125 °C85 °C25 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 125 to 85 °C while the cold fluid heats from 25 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 85 °CTc: 25 → 40 °C
ΔTlm = K
2.Easy
lengthT135 °C100 °C30 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 135 to 100 °C while the cold fluid heats from 30 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 100 °CTc: 30 → 40 °C
ΔTlm = K
3.Medium
lengthT140 °C10 °C105 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 105 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 105 °CU = 1000 W/(m²·K)
A = m²
4.Medium
lengthT105 °C55 °C15 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 190 kW. Its heat transfer area is 12 m². The hot fluid cools from 105 to 55 °C and the cold fluid heats from 15 to 45 °C. Find the overall heat transfer coefficient U.

Q̇ = 190 kWA = 12 m²Th: 105 → 55 °CTc: 15 → 45 °C
U = W/(m²·K)
5.Hard
lengthT120 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 120 °C on the outside of the tubes of a condenser with a heat transfer area of 2.5 m² and U = 3000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 2.5 m²U = 3000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
6.Hard
lengthT100 °C10 °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 2 m² and U = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 10 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 2 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 68.88 K
  2. 2. ΔTlm = 80.41 K
  3. 3. A = 5.485 m²
  4. 4. U = 434.9 W/(m²·K)
  5. 5. Tc,out = 62.26 °C
  6. 6. Tc,out = 56.09 °C

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