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 °C35 °C80 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 0.5 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 130 to 35 °C and the cold fluid heats from 15 to 80 °C. Find the heat transfer rate Q̇.

A = 0.5 m²U = 800 W/(m²·K)Th: 130 → 35 °CTc: 15 → 80 °C
Q̇ = kW
2.Easy

In a heat exchanger 3 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is heated from 35 to 60 °C. Find the heat transfer rate Q̇.

ṁ = 3 kg/scp = 3.6 kJ/(kg·K)T: 35 → 60 °C
Q̇ = kW
3.Medium
lengthT150 °C60 °C50 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 240 kW. The hot fluid cools from 150 to 60 °C and the cold fluid heats from 10 to 50 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 240 kWU = 500 W/(m²·K)Th: 150 → 60 °CTc: 10 → 50 °C
A = m²
4.Medium
lengthT145 °C110 °C115 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 50 kW. The hot fluid cools from 145 to 110 °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 = 50 kWU = 500 W/(m²·K)Th: 145 → 110 °CTc: 15 → 115 °C
A = m²
5.Hard
lengthT170 °C75 °C31.93 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 170 to 75 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 170 → 75 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT180 °C??30 °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 180 °C and the cold stream at 30 °C. The exchanger has A = 6 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 180 °CTc,in = 30 °CA = 6 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 13.1 kW
  2. 2. Q̇ = 270 kW
  3. 3. A = 6.654 m²
  4. 4. A = 1.773 m²
  5. 5. A = 1.105 m²
  6. 6. Th,out = 67.5 °C

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