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

In a heat exchanger 0.8 kg/s of water (cp = 4.18 kJ/(kg·K)) is heated from 40 to 75 °C. Find the heat transfer rate Q̇.

ṁ = 0.8 kg/scp = 4.18 kJ/(kg·K)T: 40 → 75 °C
Q̇ = kW
2.Easy
lengthT105 °C85 °C25 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 5 m² and an overall heat transfer coefficient of 300 W/(m²·K). The hot fluid cools from 105 to 85 °C and the cold fluid heats from 15 to 25 °C. Find the heat transfer rate Q̇.

A = 5 m²U = 300 W/(m²·K)Th: 105 → 85 °CTc: 15 → 25 °C
Q̇ = kW
3.Medium
lengthT140 °C55 °C105 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 80 kW. The hot fluid cools from 140 to 55 °C and the cold fluid heats from 30 to 105 °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 = 80 kWF = 0.88U = 200 W/(m²·K)Th: 140 → 55 °CTc: 30 → 105 °C
A = m²
4.Medium
lengthT175 °C80 °C35 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 790 kW. The hot fluid cools from 175 to 80 °C and the cold fluid heats from 10 to 35 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 790 kWF = 0.85U = 1000 W/(m²·K)Th: 175 → 80 °CTc: 10 → 35 °C
A = m²
5.Hard
lengthT160 °C90 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 160 to 90 °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 = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.8 kg/scp,h = 2.3 kJ/(kg·K)Th: 160 → 90 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 32 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT115 °C55 °C45.14 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 55 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 55 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 117 kW
  2. 2. Q̇ = 112.3 kW
  3. 3. A = 15.29 m²
  4. 4. A = 9.203 m²
  5. 5. L = 52.48 m
  6. 6. A = 4.706 m²

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