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
lengthT115 °C85 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (1.5 kg/s, cp = 2.1 kJ/(kg·K)) cools from 115 to 85 °C in a counter-flow exchanger. It heats 1 kg/s of water (cp = 4.18 kJ/(kg·K)) that enters at 15 °C. No heat is lost to the surroundings. Find the water outlet temperature Tc,out.

ṁh = 1.5 kg/scp,h = 2.1 kJ/(kg·K)Th: 115 → 85 °Cṁc = 1 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
2.Easy
lengthT105 °C90 °C10 °C20 °CΔT₁ΔT₂parallel flow

In a parallel-flow heat exchanger the hot fluid cools from 105 to 90 °C while the cold fluid heats from 10 to 20 °C. Find the log-mean temperature difference ΔTlm.

Th: 105 → 90 °CTc: 10 → 20 °C
ΔTlm = K
3.Medium
lengthT105 °C10 °C55 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 105 °C on the outside of the tubes. Cooling water (0.5 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 55 °C. The overall heat transfer coefficient is 3000 W/(m²·K). Find the heat transfer area A needed.

Ts = 105 °Cṁ = 0.5 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 55 °CU = 3000 W/(m²·K)
A = m²
4.Medium
lengthT140 °C105 °C130 °C25 °CΔT₁ΔT₂counter-flow

A shell-and-tube heat exchanger (one shell pass, two tube passes) must transfer 230 kW. The hot fluid cools from 140 to 105 °C and the cold fluid heats from 25 to 130 °C. The LMTD correction factor for this arrangement is F = 0.92, and U = 500 W/(m²·K). Find the heat transfer area A needed.

Q̇ = 230 kWF = 0.92U = 500 W/(m²·K)Th: 140 → 105 °CTc: 25 → 130 °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 2.5 m² and U = 3000 W/(m²·K). Cooling water (1 kg/s, cp = 4.18 kJ/(kg·K)) enters the tubes at 30 °C. Find the water outlet temperature Tc,out.

Ts = 130 °CA = 2.5 m²U = 3000 W/(m²·K)ṁ = 1 kg/scp = 4.18 kJ/(kg·K)Tc,in = 30 °C
Tc,out = °C
6.Hard
lengthT150 °C??15 °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 150 °C and the cold stream at 15 °C. The exchanger has A = 1.5 m² and U = 200 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 0.5 kW/KTh,in = 150 °CTc,in = 15 °CA = 1.5 m²U = 200 W/(m²·K)
Th,out = °C

Answer key

  1. 1. Tc,out = 37.61 °C
  2. 2. ΔTlm = 81.86 K
  3. 3. A = 0.4472 m²
  4. 4. A = 14.85 m²
  5. 5. Tc,out = 113.4 °C
  6. 6. Th,out = 99.38 °C

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