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
lengthT105 °C70 °C30 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 70 °C while the cold fluid heats from 15 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 70 °CTc: 15 → 30 °C
ΔTlm = K
2.Easy
lengthT135 °C40 °C60 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 40 °C while the cold fluid heats from 15 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 40 °CTc: 15 → 60 °C
ΔTlm = K
3.Medium
lengthT115 °C60 °C70 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 160 kW. The hot fluid cools from 115 to 60 °C and the cold fluid heats from 30 to 70 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 160 kWF = 0.92U = 500 W/(m²·K)Th: 115 → 60 °CTc: 30 → 70 °C
A = m²
4.Medium
lengthT110 °C90 °C90 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 210 kW. The hot fluid cools from 110 to 90 °C and the cold fluid heats from 30 to 90 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 210 kWU = 1500 W/(m²·K)Th: 110 → 90 °CTc: 30 → 90 °C
A = m²
5.Hard
lengthT100 °C45 °C45.18 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 100 to 45 °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 = 300 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 100 → 45 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 300 W/(m²·K)
A = m²
6.Hard
lengthT165 °C??15 °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 15 °C. The exchanger has A = 6 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1.5 kW/KTh,in = 165 °CTc,in = 15 °CA = 6 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 64.48 K
  2. 2. ΔTlm = 45.51 K
  3. 3. A = 9.402 m²
  4. 4. A = 3.845 m²
  5. 5. A = 12.21 m²
  6. 6. Th,out = 83.18 °C

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