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 = 0.03550 mm19 °C6 °Cq″ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 4 m². Its faces are held at 19 °C and 6 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 4 m²T1 = 19 °CT2 = 6 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.1710 mm23 °C-9 °CQ̇ = ?

A wall of gypsum board is 10 mm thick and has an area of 12 m². Its faces are held at 23 °C and -9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 12 m²T1 = 23 °CT2 = -9 °C
Q̇ = W
3.Medium
Wood, k = 0.17100 mmMineral wool, k = 0.04150 mm23 °C5 °CQ̇ = ?

A wall is made of 100 mm of wood and 150 mm of mineral wool, with an area of 10 m². The outer faces are at 23 °C and 5 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 10 m²T1 = 23 °CT3 = 5 °C
Q̇ = W
4.Medium
Glass, k = 0.96100 mmBrick, k = 0.7250 mm22 °C8 °CQ̇ = ?

A wall is made of 100 mm of glass and 50 mm of brick, with an area of 20 m². The outer faces are at 22 °C and 8 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 20 m²T1 = 22 °CT3 = 8 °C
Q̇ = W
5.Hard
Brick, k = 0.72250 mmMineral wool, k = 0.0450 mmroom 21 °Coutside -13 °CQ̇

A wall of 250 mm brick and 50 mm mineral wool separates a room at 21 °C from outside air at -13 °C. The convection coefficients are 8 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 8 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -13 °C
U = W/(m²·K)
6.Hard
Brick, k = 0.7250 mmMineral wool, k = 0.0425 mmroom 21 °Coutside -12 °CTs​ = ?Q̇

A wall of 50 mm brick and 25 mm mineral wool separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 12 m². Find the temperature Ts of the inside surface of the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 12 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -12 °C
Ts = °C

Answer key

  1. 1. q″ = 9.1 W/m²
  2. 2. Q̇ = 6528 W
  3. 3. Q̇ = 41.49 W
  4. 4. Q̇ = 1613 W
  5. 5. U = 0.5696 W/(m²·K)
  6. 6. Ts = 16 °C

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