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
lengthT105 °C55 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1 kg/s, cp = 2.3 kJ/(kg·K)) cools from 105 to 55 °C in a counter-flow exchanger. It heats 0.8 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 25 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1 kg/scp,h = 2.3 kJ/(kg·K)Th: 105 → 55 °Cṁc = 0.8 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
2.Easy
lengthT130 °C95 °C55 °C30 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger has a heat transfer area of 1 m² and an overall heat transfer coefficient of 1500 W/(m²·K). The hot fluid cools from 130 to 95 °C and the cold fluid heats from 30 to 55 °C. Find the heat transfer rate Q̇.

A = 1 m²U = 1500 W/(m²·K)Th: 130 → 95 °CTc: 30 → 55 °C
Q̇ = kW
3.Medium
lengthT135 °C45 °C45 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 390 kW. The hot fluid cools from 135 to 45 °C and the cold fluid heats from 20 to 45 °C. The LMTD correction factor for this arrangement is F = 0.85, and U = 800 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 390 kWF = 0.85U = 800 W/(m²·K)Th: 135 → 45 °CTc: 20 → 45 °C
A = m²
4.Medium
lengthT130 °C90 °C30 °C75 °CΔT₁ΔT₂parallel flow

A parallel-flow heat exchanger transfers 220 kW. The hot fluid cools from 130 to 90 °C and the cold fluid heats from 30 to 75 °C. The overall heat transfer coefficient is 1000 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 220 kWU = 1000 W/(m²·K)Th: 130 → 90 °CTc: 30 → 75 °C
A = m²
5.Hard
lengthT130 °C30 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 130 °C on the outside of the tubes of a condenser with a heat transfer area of 1 m² and U = 3000 W/(m²·K). Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 1 m²U = 3000 W/(m²·K)ṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
6.Hard
lengthT100 °C??25 °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 100 °C and the cold stream at 25 °C. The exchanger has A = 4 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 100 °CTc,in = 25 °CA = 4 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Tc,out = 59.39 °C
  2. 2. Q̇ = 104.8 kW
  3. 3. A = 11.3 m²
  4. 4. A = 4.91 m²
  5. 5. Tc,out = 106.2 °C
  6. 6. Th,out = 40 °C

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