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
lengthT90 °C55 °C25 °C50 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 55 °C while the cold fluid heats from 25 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 55 °CTc: 25 → 50 °C
ΔTlm = K
2.Easy
lengthT175 °C80 °C75 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 2.5 m² and an overall heat transfer coefficient of 200 W/(m²·K). The hot fluid cools from 175 to 80 °C and the cold fluid heats from 25 to 75 °C. Find the heat transfer rate Q̇.

A = 2.5 m²U = 200 W/(m²·K)Th: 175 → 80 °CTc: 25 → 75 °C
Q̇ = kW
3.Medium
lengthT130 °C115 °C15 °C35 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 30 kW. Its heat transfer area is 6 m². The hot fluid cools from 130 to 115 °C and the cold fluid heats from 15 to 35 °C. Find the overall heat transfer coefficient U.

Q̇ = 30 kWA = 6 m²Th: 130 → 115 °CTc: 15 → 35 °C
U = W/(m²·K)
4.Medium
lengthT105 °C25 °C60 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 105 °C on the outside of the tubes. Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 60 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 105 °Cṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 60 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT165 °C??20 °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 165 °C and the cold stream at 20 °C. The exchanger has A = 2 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 165 °CTc,in = 20 °CA = 2 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT150 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 150 °C and the cold stream at 10 °C. The exchanger has A = 5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 150 °CTc,in = 10 °CA = 5 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 23.39 K
  2. 2. Q̇ = 37.64 kW
  3. 3. U = 51.84 W/(m²·K)
  4. 4. A = 2.405 m²
  5. 5. Th,out = 100.6 °C
  6. 6. Th,out = 50 °C

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