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
lengthT160 °C130 °C10 °C90 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 160 to 130 °C while the cold fluid heats from 10 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 130 °CTc: 10 → 90 °C
ΔTlm = K
2.Easy
lengthT175 °C90 °C165 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 90 °C while the cold fluid heats from 30 to 165 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 90 °CTc: 30 → 165 °C
ΔTlm = K
3.Medium
lengthT130 °C10 °C100 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 100 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 100 °CU = 3000 W/(m²·K)
A = m²
4.Medium
lengthT105 °C55 °C25 °C10 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 110 kW. The hot fluid cools from 105 to 55 °C and the cold fluid heats from 10 to 25 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 110 kWF = 0.88U = 1000 W/(m²·K)Th: 105 → 55 °CTc: 10 → 25 °C
A = m²
5.Hard
lengthT115 °C50 °C87.75 °C10 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.5 kJ/(kg·K)) cools from 115 to 50 °C in a counter-flow exchanger. It heats 1 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 = 2 kg/scp,h = 2.5 kJ/(kg·K)Th: 115 → 50 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 10 °CU = 1500 W/(m²·K)
A = m²
6.Hard
lengthT130 °C20 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 6 m² and U = 3000 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 = 130 °CA = 6 m²U = 3000 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 = 83.22 K
  2. 2. ΔTlm = 27.91 K
  3. 3. A = 5.795 m²
  4. 4. A = 2.055 m²
  5. 5. A = 6.523 m²
  6. 6. Tc,out = 123.8 °C

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