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
lengthT165 °C65 °C?10 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 165 to 65 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 165 → 65 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C
2.Easy
lengthT100 °C60 °C50 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 100 to 60 °C while the cold fluid heats from 25 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 100 → 60 °CTc: 25 → 50 °C
ΔTlm = K
3.Medium
lengthT110 °C60 °C10 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 40 kW. Its heat transfer area is 2.5 m². The hot fluid cools from 110 to 60 °C and the cold fluid heats from 10 to 45 °C. Find the overall heat transfer coefficient U.

Q̇ = 40 kWA = 2.5 m²Th: 110 → 60 °CTc: 10 → 45 °C
U = W/(m²·K)
4.Medium
lengthT130 °C95 °C115 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 140 kW. The hot fluid cools from 130 to 95 °C and the cold fluid heats from 30 to 115 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWU = 800 W/(m²·K)Th: 130 → 95 °CTc: 30 → 115 °C
A = m²
5.Hard
lengthT170 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 170 °C and the cold stream at 25 °C. The exchanger has A = 3 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 170 °CTc,in = 25 °CA = 3 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT105 °C75 °C38.46 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 105 to 75 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 105 → 75 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 65.02 °C
  2. 2. ΔTlm = 42.06 K
  3. 3. U = 357.1 W/(m²·K)
  4. 4. A = 5.132 m²
  5. 5. Th,out = 107.9 °C
  6. 6. A = 1.944 m²

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