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
lengthT120 °C85 °C90 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 120 to 85 °C while the cold fluid heats from 15 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 120 → 85 °CTc: 15 → 90 °C
ΔTlm = K
2.Easy

In a heat exchanger 1.5 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is cooled from 70 to 35 °C. Find the heat transfer rate Q̇.

ṁ = 1.5 kg/scp = 3.6 kJ/(kg·K)T: 70 → 35 °C
Q̇ = kW
3.Medium
lengthT120 °C40 °C60 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 230 kW. The hot fluid cools from 120 to 40 °C and the cold fluid heats from 25 to 60 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWU = 500 W/(m²·K)Th: 120 → 40 °CTc: 25 → 60 °C
A = m²
4.Medium
lengthT140 °C20 °C95 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 95 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 95 °CU = 2000 W/(m²·K)
A = m²
5.Hard
lengthT140 °C15 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 140 °C on the outside of the tubes of a condenser with a heat transfer area of 5 m² and U = 2000 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 5 m²U = 2000 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
6.Hard
lengthT100 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 100 °C on the outside of the tubes of a condenser with a heat transfer area of 6 m² and U = 1500 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 6 m²U = 1500 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 47.21 K
  2. 2. Q̇ = 189 kW
  3. 3. A = 14.17 m²
  4. 4. A = 10.25 m²
  5. 5. Tc,out = 114.6 °C
  6. 6. Tc,out = 80.96 °C

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