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
lengthT150 °C80 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 150 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 20 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 150 → 80 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
2.Easy
lengthT150 °C130 °C25 °C125 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 150 to 130 °C while the cold fluid heats from 25 to 125 °C. Find the log-mean temperature difference ΔTlm.

Th: 150 → 130 °CTc: 25 → 125 °C
ΔTlm = K
3.Medium
lengthT100 °C25 °C85 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 85 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 85 °CU = 2000 W/(m²·K)
A = m²
4.Medium
lengthT90 °C45 °C65 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 260 kW. The hot fluid cools from 90 to 45 °C and the cold fluid heats from 10 to 65 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 260 kWU = 200 W/(m²·K)Th: 90 → 45 °CTc: 10 → 65 °C
A = m²
5.Hard
lengthT130 °C70 °C86.03 °C20 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.3 kJ/(kg·K)) cools from 130 to 70 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 20 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.3 kJ/(kg·K)Th: 130 → 70 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °CU = 800 W/(m²·K)
A = m²
6.Hard
lengthT90 °C45 °C37.61 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 90 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 15 °C. With U = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 90 → 45 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 58.52 °C
  2. 2. ΔTlm = 37.28 K
  3. 3. A = 3.364 m²
  4. 4. A = 43.74 m²
  5. 5. A = 7.353 m²
  6. 6. A = 2.353 m²

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