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
lengthT155 °C120 °C40 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 120 °C while the cold fluid heats from 15 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 120 °CTc: 15 → 40 °C
ΔTlm = K
2.Easy
lengthT95 °C55 °C40 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 55 °C while the cold fluid heats from 30 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 55 °CTc: 30 → 40 °C
ΔTlm = K
3.Medium
lengthT100 °C35 °C80 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 210 kW. The hot fluid cools from 100 to 35 °C and the cold fluid heats from 20 to 80 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 210 kWF = 0.95U = 1000 W/(m²·K)Th: 100 → 35 °CTc: 20 → 80 °C
A = m²
4.Medium
lengthT105 °C60 °C25 °C45 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 160 kW. The hot fluid cools from 105 to 60 °C and the cold fluid heats from 25 to 45 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 160 kWU = 800 W/(m²·K)Th: 105 → 60 °CTc: 25 → 45 °C
A = m²
5.Hard
lengthT110 °C??20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 4 kW/K. The hot stream enters at 110 °C and the cold stream at 20 °C. The exchanger has A = 1.5 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 4 kW/KTh,in = 110 °CTc,in = 20 °CA = 1.5 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT140 °C120 °C32.51 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 140 to 120 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 200 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 140 → 120 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 200 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 109.9 K
  2. 2. ΔTlm = 38.05 K
  3. 3. A = 12.72 m²
  4. 4. A = 5.151 m²
  5. 5. Th,out = 89.23 °C
  6. 6. A = 1.066 m²

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