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
lengthT160 °C115 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 160 to 115 °C in a counter-flow exchanger. It heats 3 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 160 → 115 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
2.Easy
lengthT160 °C80 °C130 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 160 to 80 °C while the cold fluid heats from 20 to 130 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 80 °CTc: 20 → 130 °C
ΔTlm = K
3.Medium
lengthT120 °C40 °C20 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 410 kW. The hot fluid cools from 120 to 40 °C and the cold fluid heats from 20 to 30 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 410 kWU = 300 W/(m²·K)Th: 120 → 40 °CTc: 20 → 30 °C
A = m²
4.Medium
lengthT90 °C50 °C45 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 420 kW. The hot fluid cools from 90 to 50 °C and the cold fluid heats from 10 to 45 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 420 kWU = 1500 W/(m²·K)Th: 90 → 50 °CTc: 10 → 45 °C
A = m²
5.Hard
lengthT140 °C105 °C102 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 140 to 105 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 140 → 105 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT160 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 0.5 kW/K. The hot stream enters at 160 °C and the cold stream at 15 °C. The exchanger has A = 0.5 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 160 °CTc,in = 15 °CA = 0.5 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Tc,out = 36.51 °C
  2. 2. ΔTlm = 43.28 K
  3. 3. A = 34.97 m²
  4. 4. A = 6.596 m²
  5. 5. A = 1.903 m²
  6. 6. Th,out = 111.7 °C

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