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 °C90 °C50 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 10 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 135 to 90 °C and the cold fluid heats from 10 to 50 °C. Find the heat transfer rate Q̇.

A = 10 m²U = 300 W/(m²·K)Th: 135 → 90 °CTc: 10 → 50 °C
Q̇ = kW
2.Easy
lengthT100 °C60 °C80 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 100 to 60 °C while the cold fluid heats from 15 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 60 °CTc: 15 → 80 °C
ΔTlm = K
3.Medium
lengthT140 °C105 °C75 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 230 kW. The hot fluid cools from 140 to 105 °C and the cold fluid heats from 25 to 75 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWU = 500 W/(m²·K)Th: 140 → 105 °CTc: 25 → 75 °C
A = m²
4.Medium
lengthT105 °C20 °C75 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 105 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 75 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 105 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 75 °CU = 1000 W/(m²·K)
A = m²
5.Hard
lengthT105 °C25 °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 1 m² and U = 2000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 1 m²U = 2000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT105 °C25 °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 6 m² and U = 1500 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 = 105 °CA = 6 m²U = 1500 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C

Answer key

  1. 1. Q̇ = 247.4 kW
  2. 2. ΔTlm = 30.83 K
  3. 3. A = 6.368 m²
  4. 4. A = 13.06 m²
  5. 5. Tc,out = 55.42 °C
  6. 6. Tc,out = 85.96 °C

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