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
lengthT95 °C70 °C55 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 70 °C while the cold fluid heats from 15 to 55 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 70 °CTc: 15 → 55 °C
ΔTlm = K
2.Easy
lengthT110 °C55 °C90 °C30 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 110 to 55 °C while the cold fluid heats from 30 to 90 °C. Find the log-mean temperature difference ΔTlm.

Th: 110 → 55 °CTc: 30 → 90 °C
ΔTlm = K
3.Medium
lengthT120 °C20 °C80 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °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 20 to 80 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 5 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 80 °CU = 1000 W/(m²·K)
A = m²
4.Medium
lengthT175 °C70 °C155 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 30 kW. The hot fluid cools from 175 to 70 °C and the cold fluid heats from 30 to 155 °C. The overall heat transfer coefficient is 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 30 kWU = 800 W/(m²·K)Th: 175 → 70 °CTc: 30 → 155 °C
A = m²
5.Hard
lengthT130 °C50 °C?10 °CΔT₁ΔT₂counter-flow

In a counter-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.5 kJ/(kg·K)) flows in the inner tube and cools from 130 to 50 °C. Water (0.2 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 10 °C. The inner tube has a diameter of 20 mm, and U = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.5 kJ/(kg·K)Th: 130 → 50 °Cṁc = 0.2 kg/sTc,in = 10 °CD = 20 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT155 °C??15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 1 kW/K. The hot stream enters at 155 °C and the cold stream at 15 °C. The exchanger has A = 2 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 155 °CTc,in = 15 °CA = 2 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 47.1 K
  2. 2. ΔTlm = 22.41 K
  3. 3. A = 19.15 m²
  4. 4. A = 1.3 m²
  5. 5. L = 144.7 m
  6. 6. Th,out = 85 °C

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