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
Concrete, k = 1.4200 mm18 °C3 °CQ̇ = ?

A wall of concrete is 200 mm thick and has an area of 10 m². Its faces are held at 18 °C and 3 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 200 mmA = 10 m²T1 = 18 °CT2 = 3 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.03510 mm16 °C9 °Cq″ = ?

A wall of expanded polystyrene is 10 mm thick and has an area of 20 m². Its faces are held at 16 °C and 9 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 10 mmA = 20 m²T1 = 16 °CT2 = 9 °C
q″ = W/m²
3.Medium
Gypsum board, k = 0.1750 mmExpanded polystyrene, k = 0.03550 mm23 °C8 °CTi​ = ?Q̇

A wall is made of 50 mm of gypsum board and 50 mm of expanded polystyrene, with an area of 20 m². The outer faces are at 23 °C and 8 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 20 m²T1 = 23 °CT3 = 8 °C
Ti = °C
4.Medium
Glass, k = 0.96150 mmExpanded polystyrene, k = 0.03550 mm17 °C10 °CTi​ = ?Q̇

A wall is made of 150 mm of glass and 50 mm of expanded polystyrene, with an area of 20 m². The outer faces are at 17 °C and 10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.035 W/(m·K)A = 20 m²T1 = 17 °CT3 = 10 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17150 mmMineral wool, k = 0.0450 mmroom 22 °Coutside -1 °CTs​ = ?Q̇

A wall of 150 mm gypsum board and 50 mm mineral wool separates a room at 22 °C from outside air at -1 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 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 = 6 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -1 °C
Ts = °C
6.Hard
Concrete, k = 1.4200 mmBrick, k = 0.7275 mmroom 20 °Coutside 0 °CTs​ = ?Q̇

A wall of 200 mm concrete and 75 mm brick separates a room at 20 °C from outside air at 0 °C. The convection coefficients are 10 W/(m²·K) inside and 30 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 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 0 °C
Ts = °C

Answer key

  1. 1. Q̇ = 1050 W
  2. 2. q″ = 24.5 W/m²
  3. 3. Ti = 20.44 °C
  4. 4. Ti = 16.31 °C
  5. 5. Ts = 20.36 °C
  6. 6. Ts = 14.74 °C

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