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
lengthT155 °C130 °C110 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 130 °C while the cold fluid heats from 15 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 130 °CTc: 15 → 110 °C
ΔTlm = K
2.Easy
lengthT115 °C40 °C35 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 115 to 40 °C while the cold fluid heats from 20 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 40 °CTc: 20 → 35 °C
ΔTlm = K
3.Medium
lengthT135 °C120 °C30 °C50 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 200 kW. The hot fluid cools from 135 to 120 °C and the cold fluid heats from 30 to 50 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 200 kWU = 800 W/(m²·K)Th: 135 → 120 °CTc: 30 → 50 °C
A = m²
4.Medium
lengthT165 °C130 °C90 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 140 kW. The hot fluid cools from 165 to 130 °C and the cold fluid heats from 10 to 90 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWF = 0.88U = 500 W/(m²·K)Th: 165 → 130 °CTc: 10 → 90 °C
A = m²
5.Hard
lengthT105 °C15 °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 4 m² and U = 2000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 4 m²U = 2000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
6.Hard
lengthT110 °C30 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 1 m² and U = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 1 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 74.61 K
  2. 2. ΔTlm = 43.28 K
  3. 3. A = 2.896 m²
  4. 4. A = 3.323 m²
  5. 5. Tc,out = 79.87 °C
  6. 6. Tc,out = 54.12 °C

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