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
lengthT125 °C70 °C85 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 125 to 70 °C while the cold fluid heats from 25 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 125 → 70 °CTc: 25 → 85 °C
ΔTlm = K
2.Easy
lengthT95 °C55 °C65 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 12 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 95 to 55 °C and the cold fluid heats from 20 to 65 °C. Find the heat transfer rate Q̇.

A = 12 m²U = 1500 W/(m²·K)Th: 95 → 55 °CTc: 20 → 65 °C
Q̇ = kW
3.Medium
lengthT140 °C115 °C25 °C110 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 30 kW. Its heat transfer area is 2.5 m². The hot fluid cools from 140 to 115 °C and the cold fluid heats from 25 to 110 °C. Find the overall heat transfer coefficient U.

Q̇ = 30 kWA = 2.5 m²Th: 140 → 115 °CTc: 25 → 110 °C
U = W/(m²·K)
4.Medium
lengthT160 °C95 °C40 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 790 kW. The hot fluid cools from 160 to 95 °C and the cold fluid heats from 20 to 40 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 790 kWF = 0.9U = 500 W/(m²·K)Th: 160 → 95 °CTc: 20 → 40 °C
A = m²
5.Hard
lengthT175 °C110 °C18.94 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 175 to 110 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 175 → 110 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 200 W/(m²·K)
A = m²
6.Hard
lengthT80 °C??20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 80 °C and the cold stream at 20 °C. The exchanger has A = 4 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 80 °CTc,in = 20 °CA = 4 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 42.45 K
  2. 2. Q̇ = 583.8 kW
  3. 3. U = 342.1 W/(m²·K)
  4. 4. A = 18.34 m²
  5. 5. A = 2.967 m²
  6. 6. Th,out = 62.86 °C

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