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
Gypsum board, k = 0.1720 mm24 °C10 °Cq″ = ?

A wall of gypsum board is 20 mm thick and has an area of 12 m². Its faces are held at 24 °C and 10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 20 mmA = 12 m²T1 = 24 °CT2 = 10 °C
q″ = W/m²
2.Easy
Mineral wool, k = 0.04150 mm25 °C3 °Cq″ = ?

A wall of mineral wool is 150 mm thick and has an area of 8 m². Its faces are held at 25 °C and 3 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 150 mmA = 8 m²T1 = 25 °CT2 = 3 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035100 mmWood, k = 0.1750 mm16 °C-12 °CTi​ = ?Q̇

A wall is made of 100 mm of expanded polystyrene and 50 mm of wood, 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 = 100 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 10 m²T1 = 16 °CT3 = -12 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17100 mmWood, k = 0.1725 mm18 °C5 °CQ̇ = ?

A wall is made of 100 mm of gypsum board and 25 mm of wood, with an area of 6 m². The outer faces are at 18 °C and 5 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 18 °CT3 = 5 °C
Q̇ = W
5.Hard
Wood, k = 0.17200 mmExpanded polystyrene, k = 0.035150 mmroom 21 °Coutside 3 °CQ̇

A wall of 200 mm wood and 150 mm expanded polystyrene separates a room at 21 °C from outside air at 3 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = 3 °C
U = W/(m²·K)
6.Hard
Brick, k = 0.72100 mmExpanded polystyrene, k = 0.035100 mmroom 21 °Coutside 1 °CTs​ = ?Q̇

A wall of 100 mm brick and 100 mm expanded polystyrene separates a room at 21 °C from outside air at 1 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 8 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = 1 °C
Ts = °C

Answer key

  1. 1. q″ = 119 W/m²
  2. 2. q″ = 5.867 W/m²
  3. 3. Ti = −9.387 °C
  4. 4. Q̇ = 106.1 W
  5. 5. U = 0.1764 W/(m²·K)
  6. 6. Ts = 20.21 °C

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