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

In a heat exchanger 1.5 kg/s of ethanol (cp = 2.44 kJ/(kg·K)) is cooled from 60 to 30 °C. Find the heat transfer rate Q̇.

ṁ = 1.5 kg/scp = 2.44 kJ/(kg·K)T: 60 → 30 °C
Q̇ = kW
2.Easy
lengthT95 °C35 °C55 °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 95 to 35 °C and the cold fluid heats from 10 to 55 °C. Find the heat transfer rate Q̇.

A = 10 m²U = 300 W/(m²·K)Th: 95 → 35 °CTc: 10 → 55 °C
Q̇ = kW
3.Medium
lengthT175 °C80 °C65 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 120 kW. The hot fluid cools from 175 to 80 °C and the cold fluid heats from 30 to 65 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 120 kWU = 800 W/(m²·K)Th: 175 → 80 °CTc: 30 → 65 °C
A = m²
4.Medium
lengthT125 °C45 °C115 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 250 kW. The hot fluid cools from 125 to 45 °C and the cold fluid heats from 15 to 115 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 250 kWU = 500 W/(m²·K)Th: 125 → 45 °CTc: 15 → 115 °C
A = m²
5.Hard
lengthT120 °C??20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 4 kW/K. The hot stream enters at 120 °C and the cold stream at 20 °C. The exchanger has A = 5 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 120 °CTc,in = 20 °CA = 5 m²U = 300 W/(m²·K)
Th,out = °C
6.Hard
lengthT160 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 160 °C and the cold stream at 10 °C. The exchanger has A = 6 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 160 °CTc,in = 10 °CA = 6 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 109.8 kW
  2. 2. Q̇ = 95.74 kW
  3. 3. A = 1.971 m²
  4. 4. A = 27.47 m²
  5. 5. Th,out = 92.73 °C
  6. 6. Th,out = 60 °C

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