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
lengthT145 °C45 °C50 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 145 to 45 °C while the cold fluid heats from 25 to 50 °C. Find the log-mean temperature difference ΔTlm.

Th: 145 → 45 °CTc: 25 → 50 °C
ΔTlm = K
2.Easy
lengthT165 °C55 °C120 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 165 to 55 °C while the cold fluid heats from 30 to 120 °C. Find the log-mean temperature difference ΔTlm.

Th: 165 → 55 °CTc: 30 → 120 °C
ΔTlm = K
3.Medium
lengthT105 °C55 °C95 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 430 kW. The hot fluid cools from 105 to 55 °C and the cold fluid heats from 30 to 95 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 430 kWU = 800 W/(m²·K)Th: 105 → 55 °CTc: 30 → 95 °C
A = m²
4.Medium
lengthT120 °C95 °C30 °C65 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 230 kW. The hot fluid cools from 120 to 95 °C and the cold fluid heats from 30 to 65 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWU = 800 W/(m²·K)Th: 120 → 95 °CTc: 30 → 65 °C
A = m²
5.Hard
lengthT155 °C95 °C120.4 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 95 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 155 → 95 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT130 °C30 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 4 m² and U = 3000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 4 m²U = 3000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 48.13 K
  2. 2. ΔTlm = 34.03 K
  3. 3. A = 32.83 m²
  4. 4. A = 5.264 m²
  5. 5. A = 7.843 m²
  6. 6. Tc,out = 124.3 °C

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