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
lengthT145 °C45 °C80 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 45 °C while the cold fluid heats from 10 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 45 °CTc: 10 → 80 °C
ΔTlm = K
2.Easy
lengthT110 °C75 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 110 to 75 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 110 → 75 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
3.Medium
lengthT110 °C40 °C90 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 240 kW. The hot fluid cools from 110 to 40 °C and the cold fluid heats from 25 to 90 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 240 kWU = 500 W/(m²·K)Th: 110 → 40 °CTc: 25 → 90 °C
A = m²
4.Medium
lengthT140 °C10 °C80 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 80 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 80 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT85 °C60 °C31.28 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 85 to 60 °C in a counter-flow exchanger. It heats 3 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 = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 85 → 60 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT155 °C95 °C10 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 155 to 95 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 32 mm, and U = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 95 °Cṁc = 1 kg/sTc,in = 10 °CD = 32 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 48.46 K
  2. 2. Tc,out = 34.4 °C
  3. 3. A = 27.62 m²
  4. 4. A = 1.077 m²
  5. 5. A = 1.202 m²
  6. 6. L = 7.69 m

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