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
lengthT140 °C80 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 140 to 80 °C in a counter-flow exchanger. It heats 3 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 = 2.1 kJ/(kg·K)Th: 140 → 80 °Cṁc = 3 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
2.Easy
lengthT120 °C70 °C85 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 70 °C while the cold fluid heats from 25 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 70 °CTc: 25 → 85 °C
ΔTlm = K
3.Medium
lengthT100 °C80 °C90 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 210 kW. The hot fluid cools from 100 to 80 °C and the cold fluid heats from 25 to 90 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 210 kWU = 300 W/(m²·K)Th: 100 → 80 °CTc: 25 → 90 °C
A = m²
4.Medium
lengthT165 °C100 °C105 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 420 kW. Its heat transfer area is 3 m². The hot fluid cools from 165 to 100 °C and the cold fluid heats from 25 to 105 °C. Find the overall heat transfer coefficient U.

Q̇ = 420 kWA = 3 m²Th: 165 → 100 °CTc: 25 → 105 °C
U = W/(m²·K)
5.Hard
lengthT105 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 105 °C on the outside of the tubes of a condenser with a heat transfer area of 1 m² and U = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 105 °CA = 1 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT105 °C80 °C22.48 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.5 kJ/(kg·K)) cools from 105 to 80 °C in a counter-flow exchanger. It heats 2 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.5 kJ/(kg·K)Th: 105 → 80 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 25.02 °C
  2. 2. ΔTlm = 39.79 K
  3. 3. A = 26.52 m²
  4. 4. U = 2083 W/(m²·K)
  5. 5. Tc,out = 49.12 °C
  6. 6. A = 1.064 m²

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