Heat conduction worksheet with answers

Free printable Heat conduction 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
Glass, k = 0.96100 mm20 °C6 °Cq″ = ?

A wall of glass is 100 mm thick and has an area of 8 m². Its faces are held at 20 °C and 6 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 100 mmA = 8 m²T1 = 20 °CT2 = 6 °C
q″ = W/m²
2.Easy
Glass, k = 0.96200 mm18 °C-6 °Cq″ = ?

A wall of glass is 200 mm thick and has an area of 12 m². Its faces are held at 18 °C and -6 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 200 mmA = 12 m²T1 = 18 °CT2 = -6 °C
q″ = W/m²
3.Medium
Mineral wool, k = 0.04200 mmGlass, k = 0.9675 mm24 °C-3 °CTi​ = ?Q̇

A wall is made of 200 mm of mineral wool and 75 mm of glass, with an area of 6 m². The outer faces are at 24 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 0.96 W/(m·K)A = 6 m²T1 = 24 °CT3 = -3 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035200 mmConcrete, k = 1.4150 mm25 °C2 °CTi​ = ?Q̇

A wall is made of 200 mm of expanded polystyrene and 150 mm of concrete, with an area of 10 m². The outer faces are at 25 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 10 m²T1 = 25 °CT3 = 2 °C
Ti = °C
5.Hard
Brick, k = 0.72200 mmGlass, k = 0.9625 mmroom 22 °Coutside -12 °CTs​ = ?Q̇

A wall of 200 mm brick and 25 mm glass separates a room at 22 °C from outside air at -12 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 200 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -12 °C
Ts = °C
6.Hard
Mineral wool, k = 0.04100 mmConcrete, k = 1.475 mmroom 20 °Coutside 4 °CQ̇

A wall of 100 mm mineral wool and 75 mm concrete separates a room at 20 °C from outside air at 4 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 15 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = 4 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 134.4 W/m²
  2. 2. q″ = 115.2 W/m²
  3. 3. Ti = −2.585 °C
  4. 4. Ti = 2.423 °C
  5. 5. Ts = 14.34 °C
  6. 6. U = 0.3713 W/(m²·K)

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