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 °C60 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 130 to 60 °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. 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: 130 → 60 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
2.Easy
lengthT90 °C60 °C20 °C30 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 90 to 60 °C while the cold fluid heats from 20 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 60 °CTc: 20 → 30 °C
ΔTlm = K
3.Medium
lengthT180 °C100 °C30 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 260 kW. The hot fluid cools from 180 to 100 °C and the cold fluid heats from 20 to 30 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 260 kWF = 0.9U = 200 W/(m²·K)Th: 180 → 100 °CTc: 20 → 30 °C
A = m²
4.Medium
lengthT170 °C120 °C145 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 400 kW. Its heat transfer area is 3 m². The hot fluid cools from 170 to 120 °C and the cold fluid heats from 25 to 145 °C. Find the overall heat transfer coefficient U.

Q̇ = 400 kWA = 3 m²Th: 170 → 120 °CTc: 25 → 145 °C
U = W/(m²·K)
5.Hard
lengthT100 °C65 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.5 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 15 °C. The inner tube has a diameter of 32 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.5 kJ/(kg·K)Th: 100 → 65 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 32 mmU = 500 W/(m²·K)
L = m
6.Hard
lengthT100 °C60 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 100 to 60 °C. Water (0.3 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 = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 100 → 60 °Cṁc = 0.3 kg/sTc,in = 10 °CD = 32 mmU = 150 W/(m²·K)
L = m

Answer key

  1. 1. Tc,out = 66.36 °C
  2. 2. ΔTlm = 47.21 K
  3. 3. A = 12.97 m²
  4. 4. U = 2543 W/(m²·K)
  5. 5. L = 8.137 m
  6. 6. L = 28.13 m

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