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 °C100 °C100 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 130 to 100 °C while the cold fluid heats from 20 to 100 °C. Find the log-mean temperature difference ΔTlm.

Th: 130 → 100 °CTc: 20 → 100 °C
ΔTlm = K
2.Easy
lengthT90 °C40 °C35 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 90 to 40 °C while the cold fluid heats from 15 to 35 °C. Find the log-mean temperature difference ΔTlm.

Th: 90 → 40 °CTc: 15 → 35 °C
ΔTlm = K
3.Medium
lengthT155 °C40 °C35 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 500 kW. The hot fluid cools from 155 to 40 °C and the cold fluid heats from 20 to 35 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 500 kWF = 0.95U = 1000 W/(m²·K)Th: 155 → 40 °CTc: 20 → 35 °C
A = m²
4.Medium
lengthT125 °C50 °C25 °C15 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 380 kW. The hot fluid cools from 125 to 50 °C and the cold fluid heats from 15 to 25 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 380 kWU = 500 W/(m²·K)Th: 125 → 50 °CTc: 15 → 25 °C
A = m²
5.Hard
lengthT115 °C80 °C?20 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 115 to 80 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 25 mm, and U = 250 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 80 °Cṁc = 0.5 kg/sTc,in = 20 °CD = 25 mmU = 250 W/(m²·K)
L = m
6.Hard
lengthT100 °C30 °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 8 m² and U = 1000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 8 m²U = 1000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 50.98 K
  2. 2. ΔTlm = 38.05 K
  3. 3. A = 9.43 m²
  4. 4. A = 12.27 m²
  5. 5. L = 15.7 m
  6. 6. Tc,out = 63.01 °C

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