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 °C70 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 130 to 70 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 130 → 70 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
2.Easy
lengthT120 °C35 °C35 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 35 °C while the cold fluid heats from 20 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 35 °CTc: 20 → 35 °C
ΔTlm = K
3.Medium
lengthT140 °C125 °C125 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 290 kW. The hot fluid cools from 140 to 125 °C and the cold fluid heats from 15 to 125 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 290 kWU = 200 W/(m²·K)Th: 140 → 125 °CTc: 15 → 125 °C
A = m²
4.Medium
lengthT115 °C85 °C100 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 390 kW. The hot fluid cools from 115 to 85 °C and the cold fluid heats from 15 to 100 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWU = 1000 W/(m²·K)Th: 115 → 85 °CTc: 15 → 100 °C
A = m²
5.Hard
lengthT160 °C130 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 160 to 130 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 25 mm, and U = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 160 → 130 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 25 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT135 °C90 °C63.01 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 135 to 90 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 135 → 90 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 42.94 °C
  2. 2. ΔTlm = 40.36 K
  3. 3. A = 30.41 m²
  4. 4. A = 10.92 m²
  5. 5. L = 12.62 m
  6. 6. A = 15.73 m²

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