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
lengthT155 °C120 °C60 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 155 to 120 °C while the cold fluid heats from 15 to 60 °C. Find the log-mean temperature difference ΔTlm.

Th: 155 → 120 °CTc: 15 → 60 °C
ΔTlm = K
2.Easy
lengthT170 °C105 °C?25 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.5 kJ/(kg·K)) cools from 170 to 105 °C in a counter-flow exchanger. It heats 2 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 = 1.5 kg/scp,h = 2.5 kJ/(kg·K)Th: 170 → 105 °Cṁc = 2 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 25 °C
Tc,out = °C
3.Medium
lengthT105 °C50 °C55 °C20 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 760 kW. The hot fluid cools from 105 to 50 °C and the cold fluid heats from 20 to 55 °C. The LMTD correction factor for this arrangement is F = 0.9, and U = 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 760 kWF = 0.9U = 300 W/(m²·K)Th: 105 → 50 °CTc: 20 → 55 °C
A = m²
4.Medium
lengthT165 °C55 °C45 °C20 °CΔT₁ΔT₂counter-flow

A counter-flow heat exchanger transfers 140 kW. The hot fluid cools from 165 to 55 °C and the cold fluid heats from 20 to 45 °C. The overall heat transfer coefficient is 300 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 140 kWU = 300 W/(m²·K)Th: 165 → 55 °CTc: 20 → 45 °C
A = m²
5.Hard
lengthT120 °C20 °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 6 m² and U = 2000 W/(m²·K). Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 20 °C. Find the water outlet temperature Tc,out.

Ts = 120 °CA = 6 m²U = 2000 W/(m²·K)ṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc,in = 20 °C
Tc,out = °C
6.Hard
lengthT155 °C??25 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger both streams have the same heat capacity rate, ṁ·cp = 2 kW/K. The hot stream enters at 155 °C and the cold stream at 25 °C. The exchanger has A = 2 m² and U = 500 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 2 kW/KTh,in = 155 °CTc,in = 25 °CA = 2 m²U = 500 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 99.92 K
  2. 2. Tc,out = 54.16 °C
  3. 3. A = 71.89 m²
  4. 4. A = 6.765 m²
  5. 5. Tc,out = 81.59 °C
  6. 6. Th,out = 111.7 °C

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