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
lengthT155 °C125 °C?30 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 155 to 125 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °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: 155 → 125 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
2.Easy
lengthT95 °C75 °C45 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 75 °C while the cold fluid heats from 15 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 75 °CTc: 15 → 45 °C
ΔTlm = K
3.Medium
lengthT110 °C25 °C65 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 110 °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 65 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 110 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 65 °CU = 2000 W/(m²·K)
A = m²
4.Medium
lengthT110 °C75 °C15 °C40 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 350 kW. Its heat transfer area is 4 m². The hot fluid cools from 110 to 75 °C and the cold fluid heats from 15 to 40 °C. Find the overall heat transfer coefficient U.

Q̇ = 350 kWA = 4 m²Th: 110 → 75 °CTc: 15 → 40 °C
U = W/(m²·K)
5.Hard
lengthT165 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 0.5 kW/K. The hot stream enters at 165 °C and the cold stream at 10 °C. The exchanger has A = 2 m² and U = 800 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 165 °CTc,in = 10 °CA = 2 m²U = 800 W/(m²·K)
Th,out = °C
6.Hard
lengthT165 °C95 °C65.17 °C30 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.1 kJ/(kg·K)) cools from 165 to 95 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 30 °C. With U = 800 W/(m²·K), find the heat transfer area A needed.

ṁh = 1 kg/scp,h = 2.1 kJ/(kg·K)Th: 165 → 95 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 30 °CU = 800 W/(m²·K)
A = m²

Answer key

  1. 1. Tc,out = 37.54 °C
  2. 2. ΔTlm = 54.85 K
  3. 3. A = 1.329 m²
  4. 4. U = 1456 W/(m²·K)
  5. 5. Th,out = 46.9 °C
  6. 6. A = 2.264 m²

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