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
lengthT110 °C45 °C90 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 8 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 110 to 45 °C and the cold fluid heats from 20 to 90 °C. Find the heat transfer rate Q̇.

A = 8 m²U = 1500 W/(m²·K)Th: 110 → 45 °CTc: 20 → 90 °C
Q̇ = kW
2.Easy
lengthT175 °C35 °C20 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 35 °C while the cold fluid heats from 10 to 20 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 35 °CTc: 10 → 20 °C
ΔTlm = K
3.Medium
lengthT135 °C80 °C90 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 670 kW. The hot fluid cools from 135 to 80 °C and the cold fluid heats from 25 to 90 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 670 kWF = 0.88U = 200 W/(m²·K)Th: 135 → 80 °CTc: 25 → 90 °C
A = m²
4.Medium
lengthT130 °C110 °C85 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 390 kW. The hot fluid cools from 130 to 110 °C and the cold fluid heats from 20 to 85 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWF = 0.85U = 500 W/(m²·K)Th: 130 → 110 °CTc: 20 → 85 °C
A = m²
5.Hard
lengthT145 °C55 °C91.03 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 145 to 55 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °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: 145 → 55 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT95 °C65 °C?15 °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 95 to 65 °C. Water (0.2 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 50 mm, and U = 300 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: 95 → 65 °Cṁc = 0.2 kg/sTc,in = 15 °CD = 50 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. Q̇ = 268.9 kW
  2. 2. ΔTlm = 71.25 K
  3. 3. A = 76.39 m²
  4. 4. A = 14.13 m²
  5. 5. A = 50.71 m²
  6. 6. L = 16.59 m

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