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 = 0.17100 mm25 °C9 °Cq″ = ?

A wall of gypsum board is 100 mm thick and has an area of 10 m². Its faces are held at 25 °C and 9 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 10 m²T1 = 25 °CT2 = 9 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.17150 mm22 °C8 °CQ̇ = ?

A wall of gypsum board is 150 mm thick and has an area of 15 m². Its faces are held at 22 °C and 8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 150 mmA = 15 m²T1 = 22 °CT2 = 8 °C
Q̇ = W
3.Medium
Glass, k = 0.96200 mmExpanded polystyrene, k = 0.03525 mm23 °C-5 °CQ̇ = ?

A wall is made of 200 mm of glass and 25 mm of expanded polystyrene, 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 = 200 mm, k1 = 0.96 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 10 m²T1 = 23 °CT3 = -5 °C
Q̇ = W
4.Medium
Expanded polystyrene, k = 0.035250 mmBrick, k = 0.7225 mm16 °C-1 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 25 mm of brick, with an area of 15 m². The outer faces are at 16 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 0.72 W/(m·K)A = 15 m²T1 = 16 °CT3 = -1 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.03550 mmMineral wool, k = 0.04150 mmroom 20 °Coutside 5 °CQ̇ = ?

A wall of 50 mm expanded polystyrene and 150 mm mineral wool separates a room at 20 °C from outside air at 5 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 6 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 6 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = 5 °C
Q̇ = W
6.Hard
Wood, k = 0.17200 mmMineral wool, k = 0.04100 mmroom 22 °Coutside -15 °CQ̇ = ?

A wall of 200 mm wood and 100 mm mineral wool separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 15 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -15 °C
Q̇ = W

Answer key

  1. 1. q″ = 27.2 W/m²
  2. 2. Q̇ = 238 W
  3. 3. Q̇ = 303.5 W
  4. 4. Ti = −0.9178 °C
  5. 5. Q̇ = 16.8 W
  6. 6. Q̇ = 144.5 W

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