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 °C125 °C10 °C85 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 160 to 125 °C while the cold fluid heats from 10 to 85 °C. Find the log-mean temperature difference ΔTlm.

Th: 160 → 125 °CTc: 10 → 85 °C
ΔTlm = K
2.Easy
lengthT105 °C45 °C65 °C25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 105 to 45 °C while the cold fluid heats from 25 to 65 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 45 °CTc: 25 → 65 °C
ΔTlm = K
3.Medium
lengthT155 °C110 °C90 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 190 kW. The hot fluid cools from 155 to 110 °C and the cold fluid heats from 20 to 90 °C. The LMTD correction factor for this arrangement is F = 0.95, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 190 kWF = 0.95U = 300 W/(m²·K)Th: 155 → 110 °CTc: 20 → 90 °C
A = m²
4.Medium
lengthT100 °C15 °C50 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 100 °C on the outside of the tubes. Cooling water (2 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 15 to 50 °C. The overall heat transfer coefficient is 1500 W/(m²·K). Find the heat transfer area A needed.

Ts = 100 °Cṁ = 2 kg/scp = 4.18 kJ/(kg·K)Tc: 15 → 50 °CU = 1500 W/(m²·K)
A = m²
5.Hard
lengthT90 °C60 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) flows in the inner tube and cools from 90 to 60 °C. Water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 25 mm, and U = 200 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 90 → 60 °Cṁc = 0.5 kg/sTc,in = 10 °CD = 25 mmU = 200 W/(m²·K)
L = m
6.Hard
lengthT130 °C??10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 0.5 kW/K. The hot stream enters at 130 °C and the cold stream at 10 °C. The exchanger has A = 1 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 130 °CTc,in = 10 °CA = 1 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 83.22 K
  2. 2. ΔTlm = 28.85 K
  3. 3. A = 8.678 m²
  4. 4. A = 2.957 m²
  5. 5. L = 38.89 m
  6. 6. Th,out = 85 °C

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