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
lengthT120 °C65 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 120 to 65 °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 = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 120 → 65 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
2.Easy
lengthT160 °C90 °C10 °C70 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 160 to 90 °C while the cold fluid heats from 10 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 90 °CTc: 10 → 70 °C
ΔTlm = K
3.Medium
lengthT165 °C120 °C105 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 120 kW. The hot fluid cools from 165 to 120 °C and the cold fluid heats from 25 to 105 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 120 kWU = 800 W/(m²·K)Th: 165 → 120 °CTc: 25 → 105 °C
A = m²
4.Medium
lengthT165 °C60 °C140 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 40 kW. The hot fluid cools from 165 to 60 °C and the cold fluid heats from 10 to 140 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 40 kWU = 200 W/(m²·K)Th: 165 → 60 °CTc: 10 → 140 °C
A = m²
5.Hard
lengthT100 °C65 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 100 to 65 °C. Water (1.5 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 = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 65 °Cṁc = 1.5 kg/sTc,in = 10 °CD = 32 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT120 °C80 °C38.92 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 120 to 80 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 120 → 80 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 300 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 52.7 °C
  2. 2. ΔTlm = 64.52 K
  3. 3. A = 1.969 m²
  4. 4. A = 5.545 m²
  5. 5. L = 23.45 m
  6. 6. A = 6.874 m²

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