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
lengthT80 °C45 °C70 °C25 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 8 m² and an overall heat transfer coefficient of 800 W/(m²·K). The hot fluid cools from 80 to 45 °C and the cold fluid heats from 25 to 70 °C. Find the heat transfer rate Q̇.

A = 8 m²U = 800 W/(m²·K)Th: 80 → 45 °CTc: 25 → 70 °C
Q̇ = kW
2.Easy
lengthT95 °C45 °C70 °C10 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 95 to 45 °C while the cold fluid heats from 10 to 70 °C. Find the log-mean temperature difference ΔTlm.

Th: 95 → 45 °CTc: 10 → 70 °C
ΔTlm = K
3.Medium
lengthT170 °C140 °C80 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 340 kW. The hot fluid cools from 170 to 140 °C and the cold fluid heats from 25 to 80 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 340 kWF = 0.9U = 1000 W/(m²·K)Th: 170 → 140 °CTc: 25 → 80 °C
A = m²
4.Medium
lengthT180 °C150 °C25 °C60 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 490 kW. Its heat transfer area is 25 m². The hot fluid cools from 180 to 150 °C and the cold fluid heats from 25 to 60 °C. Find the overall heat transfer coefficient U.

Q̇ = 490 kWA = 25 m²Th: 180 → 150 °CTc: 25 → 60 °C
U = W/(m²·K)
5.Hard
lengthT170 °C145 °C65.24 °C15 °CΔT₁ΔT₂counter-flow

Hot oil (2 kg/s, cp = 2.1 kJ/(kg·K)) cools from 170 to 145 °C in a counter-flow exchanger. It heats 0.5 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. With U = 500 W/(m²·K), find the heat transfer area A needed.

ṁh = 2 kg/scp,h = 2.1 kJ/(kg·K)Th: 170 → 145 °Cṁc = 0.5 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °CU = 500 W/(m²·K)
A = m²
6.Hard
lengthT120 °C10 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 120 °C on the outside of the tubes of a condenser with a heat transfer area of 8 m² and U = 1500 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 = 120 °CA = 8 m²U = 1500 W/(m²·K)ṁ = 1.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 10 °C
Tc,out = °C

Answer key

  1. 1. Q̇ = 92.33 kW
  2. 2. ΔTlm = 29.72 K
  3. 3. A = 3.704 m²
  4. 4. U = 163.9 W/(m²·K)
  5. 5. A = 1.796 m²
  6. 6. Tc,out = 103.8 °C

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