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
lengthT110 °C55 °C20 °C40 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 110 to 55 °C while the cold fluid heats from 20 to 40 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 55 °CTc: 20 → 40 °C
ΔTlm = K
2.Easy
lengthT120 °C65 °C45 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 65 °C while the cold fluid heats from 10 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 65 °CTc: 10 → 45 °C
ΔTlm = K
3.Medium
lengthT170 °C155 °C10 °C120 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 230 kW. The hot fluid cools from 170 to 155 °C and the cold fluid heats from 10 to 120 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWU = 200 W/(m²·K)Th: 170 → 155 °CTc: 10 → 120 °C
A = m²
4.Medium
lengthT120 °C85 °C40 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 140 kW. The hot fluid cools from 120 to 85 °C and the cold fluid heats from 25 to 40 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWU = 1500 W/(m²·K)Th: 120 → 85 °CTc: 25 → 40 °C
A = m²
5.Hard
lengthT130 °C90 °C38.92 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 130 to 90 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 130 → 90 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1000 W/(m²·K)
A = m²
6.Hard
lengthT110 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 110 °C on the outside of the tubes of a condenser with a heat transfer area of 3 m² and U = 1500 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 110 °CA = 3 m²U = 1500 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 41.86 K
  2. 2. ΔTlm = 64.48 K
  3. 3. A = 13.98 m²
  4. 4. A = 1.343 m²
  5. 5. A = 1.812 m²
  6. 6. Tc,out = 98.97 °C

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