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
Mineral wool, k = 0.0450 mm24 °C-12 °Cq″ = ?

A wall of mineral wool is 50 mm thick and has an area of 12 m². Its faces are held at 24 °C and -12 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 50 mmA = 12 m²T1 = 24 °CT2 = -12 °C
q″ = W/m²
2.Easy
Gypsum board, k = 0.17200 mm18 °C8 °CQ̇ = ?

A wall of gypsum board is 200 mm thick and has an area of 4 m². Its faces are held at 18 °C and 8 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 4 m²T1 = 18 °CT2 = 8 °C
Q̇ = W
3.Medium
Gypsum board, k = 0.17200 mmExpanded polystyrene, k = 0.03525 mm23 °C6 °CTi​ = ?Q̇

A wall is made of 200 mm of gypsum board and 25 mm of expanded polystyrene, with an area of 15 m². The outer faces are at 23 °C and 6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 15 m²T1 = 23 °CT3 = 6 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17150 mmGlass, k = 0.96150 mm23 °C-9 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 150 mm of glass, with an area of 4 m². The outer faces are at 23 °C and -9 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 4 m²T1 = 23 °CT3 = -9 °C
Ti = °C
5.Hard
Mineral wool, k = 0.04250 mmGlass, k = 0.96150 mmroom 22 °Coutside -13 °CQ̇ = ?

A wall of 250 mm mineral wool and 150 mm glass separates a room at 22 °C from outside air at -13 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 20 m². Find the heat loss Q̇ through the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 20 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -13 °C
Q̇ = W
6.Hard
Glass, k = 0.96100 mmWood, k = 0.17150 mmroom 20 °Coutside 1 °CQ̇ = ?

A wall of 100 mm glass and 150 mm wood separates a room at 20 °C from outside air at 1 °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 heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 1 °C
Q̇ = W

Answer key

  1. 1. q″ = 28.8 W/m²
  2. 2. Q̇ = 34 W
  3. 3. Ti = 12.42 °C
  4. 4. Ti = −4.186 °C
  5. 5. Q̇ = 106.6 W
  6. 6. Q̇ = 101.8 W

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