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

In a heat exchanger 1.2 kg/s of water (cp = 4.18 kJ/(kg·K)) is cooled from 70 to 35 °C. Find the heat transfer rate Q̇.

ṁ = 1.2 kg/scp = 4.18 kJ/(kg·K)T: 70 → 35 °C
Q̇ = kW
2.Easy

In a heat exchanger 0.5 kg/s of glycol mix (cp = 3.6 kJ/(kg·K)) is heated from 30 to 90 °C. Find the heat transfer rate Q̇.

ṁ = 0.5 kg/scp = 3.6 kJ/(kg·K)T: 30 → 90 °C
Q̇ = kW
3.Medium
lengthT130 °C25 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 130 °C on the outside of the tubes. Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 25 to 55 °C. The overall heat transfer coefficient is 3500 W/(m²·K). Find the heat transfer area A needed.

Ts = 130 °Cṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc: 25 → 55 °CU = 3500 W/(m²·K)
A = m²
4.Medium
lengthT125 °C70 °C65 °C15 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 350 kW. The hot fluid cools from 125 to 70 °C and the cold fluid heats from 15 to 65 °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 = 350 kWF = 0.85U = 800 W/(m²·K)Th: 125 → 70 °CTc: 15 → 65 °C
A = m²
5.Hard
lengthT100 °C25 °C?ΔT₁ΔT₂condensing steam

Steam condenses at a constant 100 °C on the outside of the tubes of a condenser with a heat transfer area of 5 m² and U = 2000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 25 °C. Find the water outlet temperature Tc,out.

Ts = 100 °CA = 5 m²U = 2000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
6.Hard
lengthT110 °C??30 °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 110 °C and the cold stream at 30 °C. The exchanger has A = 3 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 110 °CTc,in = 30 °CA = 3 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Q̇ = 175.6 kW
  2. 2. Q̇ = 108 kW
  3. 3. A = 0.4018 m²
  4. 4. A = 8.957 m²
  5. 5. Tc,out = 66.21 °C
  6. 6. Th,out = 72.11 °C

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