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
Brick, k = 0.72200 mm16 °C2 °CQ̇ = ?

A wall of brick is 200 mm thick and has an area of 15 m². Its faces are held at 16 °C and 2 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 200 mmA = 15 m²T1 = 16 °CT2 = 2 °C
Q̇ = W
2.Easy
Concrete, k = 1.4150 mm25 °C3 °CQ̇ = ?

A wall of concrete is 150 mm thick and has an area of 12 m². Its faces are held at 25 °C and 3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 150 mmA = 12 m²T1 = 25 °CT2 = 3 °C
Q̇ = W
3.Medium
Expanded polystyrene, k = 0.03550 mmConcrete, k = 1.425 mm16 °C-12 °CTi​ = ?Q̇

A wall is made of 50 mm of expanded polystyrene and 25 mm of concrete, with an area of 10 m². The outer faces are at 16 °C and -12 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 10 m²T1 = 16 °CT3 = -12 °C
Ti = °C
4.Medium
Wood, k = 0.17100 mmConcrete, k = 1.4100 mm22 °C3 °CQ̇ = ?

A wall is made of 100 mm of wood and 100 mm of concrete, with an area of 12 m². The outer faces are at 22 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 12 m²T1 = 22 °CT3 = 3 °C
Q̇ = W
5.Hard
Gypsum board, k = 0.17150 mmMineral wool, k = 0.0450 mmroom 21 °Coutside -7 °CTs​ = ?Q̇

A wall of 150 mm gypsum board and 50 mm mineral wool separates a room at 21 °C from outside air at -7 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -7 °C
Ts = °C
6.Hard
Glass, k = 0.96100 mmWood, k = 0.1775 mmroom 22 °Coutside 1 °CQ̇

A wall of 100 mm glass and 75 mm wood separates a room at 22 °C from outside air at 1 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 10 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = 1 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 756 W
  2. 2. Q̇ = 2464 W
  3. 3. Ti = −11.65 °C
  4. 4. Q̇ = 345.6 W
  5. 5. Ts = 19.77 °C
  6. 6. U = 1.438 W/(m²·K)

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