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 0.3 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is cooled from 110 to 55 °C. Find the heat transfer rate Q̇.

ṁ = 0.3 kg/scp = 3.6 kJ/(kg·K)T: 110 → 55 °C
Q̇ = kW
2.Easy
lengthT110 °C45 °C80 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 45 °C while the cold fluid heats from 25 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 45 °CTc: 25 → 80 °C
ΔTlm = K
3.Medium
lengthT90 °C45 °C10 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 330 kW. The hot fluid cools from 90 to 45 °C and the cold fluid heats from 10 to 40 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 330 kWU = 800 W/(m²·K)Th: 90 → 45 °CTc: 10 → 40 °C
A = m²
4.Medium
lengthT135 °C120 °C20 °C100 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 480 kW. Its heat transfer area is 3 m². The hot fluid cools from 135 to 120 °C and the cold fluid heats from 20 to 100 °C. Find the overall heat transfer coefficient U.

Q̇ = 480 kWA = 3 m²Th: 135 → 120 °CTc: 20 → 100 °C
U = W/(m²·K)
5.Hard
lengthT155 °C??30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 3 kW/K. The hot stream enters at 155 °C and the cold stream at 30 °C. The exchanger has A = 2 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 3 kW/KTh,in = 155 °CTc,in = 30 °CA = 2 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT145 °C40 °C41.4 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 145 to 40 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 145 → 40 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 59.4 kW
  2. 2. ΔTlm = 24.66 K
  3. 3. A = 15.25 m²
  4. 4. U = 2946 W/(m²·K)
  5. 5. Th,out = 111.5 °C
  6. 6. A = 7.367 m²

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