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
lengthT135 °C120 °C45 °C15 °CΔT₁ΔT₂counter-flow

In a counter-flow heat exchanger the hot fluid cools from 135 to 120 °C while the cold fluid heats from 15 to 45 °C. Find the log-mean temperature difference ΔTlm.

Th: 135 → 120 °CTc: 15 → 45 °C
ΔTlm = K
2.Easy
lengthT170 °C90 °C?15 °CΔT₁ΔT₂counter-flow

Hot oil (0.5 kg/s, cp = 2.3 kJ/(kg·K)) cools from 170 to 90 °C in a counter-flow exchanger. It heats 0.8 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 = 0.5 kg/scp,h = 2.3 kJ/(kg·K)Th: 170 → 90 °Cṁc = 0.8 kg/scp,c = 4.18 kJ/(kg·K)Tc,in = 15 °C
Tc,out = °C
3.Medium
lengthT140 °C20 °C40 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 140 °C on the outside of the tubes. Cooling water (3 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 20 to 40 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 140 °Cṁ = 3 kg/scp = 4.18 kJ/(kg·K)Tc: 20 → 40 °CU = 2000 W/(m²·K)
A = m²
4.Medium
lengthT120 °C10 °C110 °CΔT₁ΔT₂condensing steam

In a condenser, steam condenses at a constant 120 °C on the outside of the tubes. Cooling water (4 kg/s, cp = 4.18 kJ/(kg·K)) flows through the tubes and heats from 10 to 110 °C. The overall heat transfer coefficient is 2000 W/(m²·K). Find the heat transfer area A needed.

Ts = 120 °Cṁ = 4 kg/scp = 4.18 kJ/(kg·K)Tc: 10 → 110 °CU = 2000 W/(m²·K)
A = m²
5.Hard
lengthT120 °C80 °C15 °C?ΔT₁ΔT₂parallel flow

In a parallel-flow double-pipe heat exchanger, hot oil (0.3 kg/s, cp = 2.1 kJ/(kg·K)) flows in the inner tube and cools from 120 to 80 °C. Water (1 kg/s, cp = 4.18 kJ/(kg·K)) in the annulus enters at 15 °C. The inner tube has a diameter of 20 mm, and U = 150 W/(m²·K) is based on this diameter. Find the tube length L needed.

ṁh = 0.3 kg/scp,h = 2.1 kJ/(kg·K)Th: 120 → 80 °Cṁc = 1 kg/sTc,in = 15 °CD = 20 mmU = 150 W/(m²·K)
L = m
6.Hard
lengthT170 °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 170 °C and the cold stream at 30 °C. The exchanger has A = 6 m² and U = 300 W/(m²·K). Find the hot outlet temperature Th,out.

Ch = Cc = 1 kW/KTh,in = 170 °CTc,in = 30 °CA = 6 m²U = 300 W/(m²·K)
Th,out = °C

Answer key

  1. 1. ΔTlm = 97.31 K
  2. 2. Tc,out = 42.51 °C
  3. 3. A = 1.143 m²
  4. 4. A = 20.05 m²
  5. 5. L = 33.51 m
  6. 6. Th,out = 80 °C

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