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 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) is cooled from 75 to 40 °C. Find the heat transfer rate Q̇.

ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)T: 75 → 40 °C
Q̇ = kW
2.Easy
lengthT90 °C65 °C30 °C55 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 65 °C while the cold fluid heats from 30 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 65 °CTc: 30 → 55 °C
ΔTlm = K
3.Medium
lengthT140 °C30 °C25 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 390 kW. Its heat transfer area is 4 m². The hot fluid cools from 140 to 30 °C and the cold fluid heats from 15 to 25 °C. Find the overall heat transfer coefficient U.

Q̇ = 390 kWA = 4 m²Th: 140 → 30 °CTc: 15 → 25 °C
U = W/(m²·K)
4.Medium
lengthT90 °C40 °C45 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 110 kW. The hot fluid cools from 90 to 40 °C and the cold fluid heats from 20 to 45 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 110 kWU = 300 W/(m²·K)Th: 90 → 40 °CTc: 20 → 45 °C
A = m²
5.Hard
lengthT80 °C??15 °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 80 °C and the cold stream at 15 °C. The exchanger has A = 6 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 80 °CTc,in = 15 °CA = 6 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT120 °C90 °C47.94 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 90 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 90 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 73.15 kW
  2. 2. ΔTlm = 27.91 K
  3. 3. U = 1986 W/(m²·K)
  4. 4. A = 11.89 m²
  5. 5. Th,out = 44.55 °C
  6. 6. A = 2.278 m²

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