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
lengthT95 °C30 °C60 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 30 °C while the cold fluid heats from 15 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 30 °CTc: 15 → 60 °C
ΔTlm = K
2.Easy
lengthT175 °C140 °C120 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 4 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 175 to 140 °C and the cold fluid heats from 20 to 120 °C. Find the heat transfer rate Q̇.

A = 4 m²U = 800 W/(m²·K)Th: 175 → 140 °CTc: 20 → 120 °C
Q̇ = kW
3.Medium
lengthT175 °C80 °C165 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 340 kW. The hot fluid cools from 175 to 80 °C and the cold fluid heats from 15 to 165 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 340 kWF = 0.88U = 800 W/(m²·K)Th: 175 → 80 °CTc: 15 → 165 °C
A = m²
4.Medium
lengthT120 °C55 °C35 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 70 kW. The hot fluid cools from 120 to 55 °C and the cold fluid heats from 10 to 35 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 70 kWU = 300 W/(m²·K)Th: 120 → 55 °CTc: 10 → 35 °C
A = m²
5.Hard
lengthT105 °C80 °C34.59 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 105 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 30 °C. With U = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 105 → 80 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT100 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 100 °C and the cold stream at 15 °C. The exchanger has A = 5 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 100 °CTc,in = 15 °CA = 5 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 23.6 K
  2. 2. Q̇ = 266.6 kW
  3. 3. A = 16.44 m²
  4. 4. A = 3.71 m²
  5. 5. A = 1.607 m²
  6. 6. Th,out = 49 °C

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