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 °C45 °C40 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 8 m² and an overall heat transfer coefficient of 500 W/(m²·K). The hot fluid cools from 105 to 45 °C and the cold fluid heats from 15 to 40 °C. Find the heat transfer rate Q̇.

A = 8 m²U = 500 W/(m²·K)Th: 105 → 45 °CTc: 15 → 40 °C
Q̇ = kW
2.Easy
lengthT105 °C90 °C30 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 90 °C while the cold fluid heats from 20 to 30 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 90 °CTc: 20 → 30 °C
ΔTlm = K
3.Medium
lengthT85 °C60 °C75 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 20 kW. The hot fluid cools from 85 to 60 °C and the cold fluid heats from 30 to 75 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 20 kWU = 800 W/(m²·K)Th: 85 → 60 °CTc: 30 → 75 °C
A = m²
4.Medium
lengthT110 °C20 °C65 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 65 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 65 °CU = 3500 W/(m²·K)
A = m²
5.Hard
lengthT165 °C30 °C77.82 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 165 to 30 °C in a counter-flow exchanger. It heats 1.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 10 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 165 → 30 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT170 °C80 °C137.7 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 170 to 80 °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 = 1000 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 170 → 80 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 1000 W/(m²·K)
A = m²

Answer key

  1. 1. Q̇ = 181.1 kW
  2. 2. ΔTlm = 72.47 K
  3. 3. A = 1.373 m²
  4. 4. A = 0.4139 m²
  5. 5. A = 11.65 m²
  6. 6. A = 5.551 m²

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