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 °C70 °C25 °C60 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 110 to 70 °C while the cold fluid heats from 25 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 70 °CTc: 25 → 60 °C
ΔTlm = K
2.Easy
lengthT85 °C70 °C45 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 85 to 70 °C while the cold fluid heats from 25 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 85 → 70 °CTc: 25 → 45 °C
ΔTlm = K
3.Medium
lengthT90 °C45 °C80 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 290 kW. The hot fluid cools from 90 to 45 °C and the cold fluid heats from 30 to 80 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 290 kWF = 0.92U = 500 W/(m²·K)Th: 90 → 45 °CTc: 30 → 80 °C
A = m²
4.Medium
lengthT170 °C120 °C110 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 310 kW. The hot fluid cools from 170 to 120 °C and the cold fluid heats from 25 to 110 °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 = 310 kWF = 0.95U = 1000 W/(m²·K)Th: 170 → 120 °CTc: 25 → 110 °C
A = m²
5.Hard
lengthT100 °C65 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.2 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 100 to 65 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 50 mm, and U = 500 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.2 kg/scp,h = 2.1 kJ/(kg·K)Th: 100 → 65 °Cṁc = 0.3 kg/sTc,in = 15 °CD = 50 mmU = 500 W/(m²·K)
L = m
6.Hard
lengthT100 °C15 °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 1.5 m² and U = 1500 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 15 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 1.5 m²U = 1500 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 35.05 K
  2. 2. ΔTlm = 42.45 K
  3. 3. A = 51.12 m²
  4. 4. A = 4.284 m²
  5. 5. L = 3.073 m
  6. 6. Tc,out = 71.03 °C

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