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
lengthT115 °C45 °C45 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 10 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 115 to 45 °C and the cold fluid heats from 20 to 45 °C. Find the heat transfer rate Q̇.

A = 10 m²U = 1500 W/(m²·K)Th: 115 → 45 °CTc: 20 → 45 °C
Q̇ = kW
2.Easy
lengthT150 °C90 °C120 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 150 to 90 °C while the cold fluid heats from 30 to 120 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 90 °CTc: 30 → 120 °C
ΔTlm = K
3.Medium
lengthT125 °C70 °C25 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 460 kW. The hot fluid cools from 125 to 70 °C and the cold fluid heats from 25 to 40 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 460 kWU = 500 W/(m²·K)Th: 125 → 70 °CTc: 25 → 40 °C
A = m²
4.Medium
lengthT90 °C45 °C45 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 240 kW. The hot fluid cools from 90 to 45 °C and the cold fluid heats from 25 to 45 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 240 kWF = 0.95U = 200 W/(m²·K)Th: 90 → 45 °CTc: 25 → 45 °C
A = m²
5.Hard
lengthT165 °C??20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1.5 kW/K. The hot stream enters at 165 °C and the cold stream at 20 °C. The exchanger has A = 2 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 165 °CTc,in = 20 °CA = 2 m²U = 500 W/(m²·K)
Th,out = °C
6.Hard
lengthT135 °C80 °C50.26 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 135 to 80 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 135 → 80 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 655.6 kW
  2. 2. ΔTlm = 43.28 K
  3. 3. A = 15.82 m²
  4. 4. A = 40.97 m²
  5. 5. Th,out = 107 °C
  6. 6. A = 8.827 m²

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