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
lengthT170 °C60 °C75 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 170 to 60 °C while the cold fluid heats from 10 to 75 °C. Find the log-mean temperature difference ΔTlm.

Th: 170 → 60 °CTc: 10 → 75 °C
ΔTlm = K
2.Easy
lengthT175 °C130 °C145 °C20 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 175 to 130 °C while the cold fluid heats from 20 to 145 °C. Find the log-mean temperature difference ΔTlm.

Th: 175 → 130 °CTc: 20 → 145 °C
ΔTlm = K
3.Medium
lengthT165 °C60 °C110 °C10 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 220 kW. The hot fluid cools from 165 to 60 °C and the cold fluid heats from 10 to 110 °C. The overall heat transfer coefficient is 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 220 kWU = 500 W/(m²·K)Th: 165 → 60 °CTc: 10 → 110 °C
A = m²
4.Medium
lengthT115 °C45 °C60 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 160 kW. The hot fluid cools from 115 to 45 °C and the cold fluid heats from 15 to 60 °C. The LMTD correction factor for this arrangement is F = 0.88, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 160 kWF = 0.88U = 300 W/(m²·K)Th: 115 → 45 °CTc: 15 → 60 °C
A = m²
5.Hard
lengthT150 °C90 °C?15 °CΔT₁ΔT₂counter-flow

In a counter-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 150 to 90 °C. Water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °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: 150 → 90 °Cṁc = 1.5 kg/sTc,in = 15 °CD = 20 mmU = 300 W/(m²·K)
L = m
6.Hard
lengthT140 °C10 °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 m² and U = 2500 W/(m²·K). Cooling water (1.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 10 °C. Find the water outlet temperature Tc,out.

Ts = 140 °CA = 1 m²U = 2500 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C

Answer key

  1. 1. ΔTlm = 70.11 K
  2. 2. ΔTlm = 61.57 K
  3. 3. A = 8.387 m²
  4. 4. A = 14.69 m²
  5. 5. L = 56.12 m
  6. 6. Tc,out = 52.75 °C

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