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
lengthT110 °C95 °C25 °C35 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 110 to 95 °C while the cold fluid heats from 25 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 95 °CTc: 25 → 35 °C
ΔTlm = K
2.Easy
lengthT125 °C85 °C?20 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 125 to 85 °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 = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 125 → 85 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
3.Medium
lengthT140 °C20 °C90 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 90 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 90 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT80 °C55 °C20 °C30 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 50 kW. The hot fluid cools from 80 to 55 °C and the cold fluid heats from 20 to 30 °C. The overall heat transfer coefficient is 200 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 50 kWU = 200 W/(m²·K)Th: 80 → 55 °CTc: 20 → 30 °C
A = m²
5.Hard
lengthT95 °C65 °C25 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 95 to 65 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 25 °C. The inner tube has a diameter of 25 mm, and U = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.5 kJ/(kg·K)Th: 95 → 65 °Cṁc = 1.5 kg/sTc,in = 25 °CD = 25 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT175 °C110 °C44.44 °C25 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 175 to 110 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 0.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 175 → 110 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °CU = 500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 71.78 K
  2. 2. Tc,out = 64.02 °C
  3. 3. A = 2.091 m²
  4. 4. A = 6.253 m²
  5. 5. L = 37.16 m
  6. 6. A = 1.531 m²

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