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
lengthT130 °C105 °C20 °C70 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 130 to 105 °C while the cold fluid heats from 20 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 105 °CTc: 20 → 70 °C
ΔTlm = K
2.Easy
lengthT140 °C125 °C15 °C115 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 140 to 125 °C while the cold fluid heats from 15 to 115 °C. Find the log-mean temperature difference ΔTlm.

Th: 140 → 125 °CTc: 15 → 115 °C
ΔTlm = K
3.Medium
lengthT165 °C95 °C70 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 190 kW. The hot fluid cools from 165 to 95 °C and the cold fluid heats from 30 to 70 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 190 kWF = 0.9U = 1000 W/(m²·K)Th: 165 → 95 °CTc: 30 → 70 °C
A = m²
4.Medium
lengthT115 °C85 °C25 °C65 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 310 kW. The hot fluid cools from 115 to 85 °C and the cold fluid heats from 25 to 65 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 310 kWU = 1000 W/(m²·K)Th: 115 → 85 °CTc: 25 → 65 °C
A = m²
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 6 m² and U = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 6 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
6.Hard
lengthT105 °C20 °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 = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 4 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 65.49 K
  2. 2. ΔTlm = 45.53 K
  3. 3. A = 2.67 m²
  4. 4. A = 6.661 m²
  5. 5. Tc,out = 107.8 °C
  6. 6. Tc,out = 84.77 °C

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