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 °C135 °C10 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 155 to 135 °C while the cold fluid heats from 10 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 135 °CTc: 10 → 40 °C
ΔTlm = K
2.Easy

In a heat exchanger 1.5 kg/s of light oil (cp = 2.1 kJ/(kg·K)) is heated from 20 to 70 °C. Find the heat transfer rate Q̇.

ṁ = 1.5 kg/scp = 2.1 kJ/(kg·K)T: 20 → 70 °C
Q̇ = kW
3.Medium
lengthT125 °C50 °C65 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 330 kW. Its heat transfer area is 15 m². The hot fluid cools from 125 to 50 °C and the cold fluid heats from 15 to 65 °C. Find the overall heat transfer coefficient U.

Q̇ = 330 kWA = 15 m²Th: 125 → 50 °CTc: 15 → 65 °C
U = W/(m²·K)
4.Medium
lengthT105 °C10 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 105 °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 55 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 105 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 55 °CU = 2500 W/(m²·K)
A = m²
5.Hard
lengthT110 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 110 °C and the cold stream at 15 °C. The exchanger has A = 3 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 110 °CTc,in = 15 °CA = 3 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT115 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 115 °C and the cold stream at 10 °C. The exchanger has A = 6 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 115 °CTc,in = 10 °CA = 6 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 118.2 K
  2. 2. Q̇ = 157.5 kW
  3. 3. U = 474.3 W/(m²·K)
  4. 4. A = 1.073 m²
  5. 5. Th,out = 69.29 °C
  6. 6. Th,out = 75.63 °C

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