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
Expanded polystyrene, k = 0.035150 mm20 °C0 °Cq″ = ?

A wall of expanded polystyrene is 150 mm thick and has an area of 20 m². Its faces are held at 20 °C and 0 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 150 mmA = 20 m²T1 = 20 °CT2 = 0 °C
q″ = W/m²
2.Easy
Glass, k = 0.9620 mm17 °C-5 °Cq″ = ?

A wall of glass is 20 mm thick and has an area of 6 m². Its faces are held at 17 °C and -5 °C. Find the heat flux q″ through the wall.

k = 0.96 W/(m·K)L = 20 mmA = 6 m²T1 = 17 °CT2 = -5 °C
q″ = W/m²
3.Medium
Brick, k = 0.7250 mmExpanded polystyrene, k = 0.035100 mm16 °C10 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 100 mm of expanded polystyrene, with an area of 6 m². The outer faces are at 16 °C and 10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 6 m²T1 = 16 °CT3 = 10 °C
Ti = °C
4.Medium
Glass, k = 0.96150 mmGypsum board, k = 0.1775 mm25 °C-4 °CTi​ = ?Q̇

A wall is made of 150 mm of glass and 75 mm of gypsum board, with an area of 10 m². The outer faces are at 25 °C and -4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 10 m²T1 = 25 °CT3 = -4 °C
Ti = °C
5.Hard
Wood, k = 0.17250 mmGlass, k = 0.9625 mmroom 21 °Coutside -14 °CTs​ = ?Q̇

A wall of 250 mm wood and 25 mm glass separates a room at 21 °C from outside air at -14 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -14 °C
Ts = °C
6.Hard
Concrete, k = 1.4100 mmGypsum board, k = 0.1775 mmroom 20 °Coutside -8 °CTs​ = ?Q̇

A wall of 100 mm concrete and 75 mm gypsum board separates a room at 20 °C from outside air at -8 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -8 °C
Ts = °C

Answer key

  1. 1. q″ = 4.667 W/m²
  2. 2. q″ = 1056 W/m²
  3. 3. Ti = 15.86 °C
  4. 4. Ti = 17.42 °C
  5. 5. Ts = 18.27 °C
  6. 6. Ts = 15.67 °C

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