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
lengthT130 °C55 °C110 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 55 °C while the cold fluid heats from 10 to 110 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 55 °CTc: 10 → 110 °C
ΔTlm = K
2.Easy
lengthT115 °C95 °C30 °C60 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 115 to 95 °C while the cold fluid heats from 30 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 115 → 95 °CTc: 30 → 60 °C
ΔTlm = K
3.Medium
lengthT100 °C30 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °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 30 to 55 °C. The overall heat transfer coefficient is 2500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 30 → 55 °CU = 2500 W/(m²·K)
A = m²
4.Medium
lengthT140 °C20 °C40 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (4 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 40 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 40 °CU = 3000 W/(m²·K)
A = m²
5.Hard
lengthT120 °C30 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 120 °C on the outside of the tubes of a condenser with a heat transfer area of 2 m² and U = 3000 W/(m²·K). Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 2 m²U = 3000 W/(m²·K)ṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
6.Hard
lengthT170 °C70 °C65.02 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 170 to 70 °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 = 1500 W/(m²·K), find the heat transfer area A needed.

ṁh = 1.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 170 → 70 °Cṁc = 1.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1500 W/(m²·K)
A = m²

Answer key

  1. 1. ΔTlm = 30.83 K
  2. 2. ΔTlm = 56.35 K
  3. 3. A = 0.3694 m²
  4. 4. A = 1.016 m²
  5. 5. Tc,out = 76.09 °C
  6. 6. A = 2.861 m²

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