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
lengthT175 °C145 °C155 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 145 °C while the cold fluid heats from 25 to 155 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 145 °CTc: 25 → 155 °C
ΔTlm = K
2.Easy
lengthT155 °C120 °C80 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 120 °C while the cold fluid heats from 10 to 80 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 120 °CTc: 10 → 80 °C
ΔTlm = K
3.Medium
lengthT100 °C10 °C60 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °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 10 to 60 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 60 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT120 °C70 °C75 °C30 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 670 kW. The hot fluid cools from 120 to 70 °C and the cold fluid heats from 30 to 75 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 670 kWF = 0.85U = 500 W/(m²·K)Th: 120 → 70 °CTc: 30 → 75 °C
A = m²
5.Hard
lengthT140 °C20 °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 1.5 m² and U = 1500 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 1.5 m²U = 1500 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT140 °C105 °C20 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.8 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 140 to 105 °C. Water (0.3 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 20 °C. The inner tube has a diameter of 20 mm, and U = 300 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.8 kg/scp,h = 2.1 kJ/(kg·K)Th: 140 → 105 °Cṁc = 0.3 kg/sTc,in = 20 °CD = 20 mmU = 300 W/(m²·K)
L = m

Answer key

  1. 1. ΔTlm = 55.81 K
  2. 2. ΔTlm = 91.39 K
  3. 3. A = 4.842 m²
  4. 4. A = 37.14 m²
  5. 5. Tc,out = 69.95 °C
  6. 6. L = 43.69 m

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