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 mm16 °C-4 °CQ̇ = ?

A wall of gypsum board is 100 mm thick and has an area of 20 m². Its faces are held at 16 °C and -4 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 100 mmA = 20 m²T1 = 16 °CT2 = -4 °C
Q̇ = W
2.Easy
Wood, k = 0.17200 mm18 °C-13 °Cq″ = ?

A wall of wood is 200 mm thick and has an area of 10 m². Its faces are held at 18 °C and -13 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 200 mmA = 10 m²T1 = 18 °CT2 = -13 °C
q″ = W/m²
3.Medium
Concrete, k = 1.4250 mmExpanded polystyrene, k = 0.035100 mm25 °C-3 °CTi​ = ?Q̇

A wall is made of 250 mm of concrete and 100 mm of expanded polystyrene, with an area of 12 m². The outer faces are at 25 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 12 m²T1 = 25 °CT3 = -3 °C
Ti = °C
4.Medium
Mineral wool, k = 0.04250 mmGlass, k = 0.9625 mm22 °C10 °CQ̇ = ?

A wall is made of 250 mm of mineral wool and 25 mm of glass, with an area of 20 m². The outer faces are at 22 °C and 10 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 20 m²T1 = 22 °CT3 = 10 °C
Q̇ = W
5.Hard
Mineral wool, k = 0.04200 mmGlass, k = 0.9625 mmroom 22 °Coutside -4 °CQ̇ = ?

A wall of 200 mm mineral wool and 25 mm glass separates a room at 22 °C from outside air at -4 °C. The convection coefficients are 7.7 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 8 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.96 W/(m·K)A = 8 m²hi = 7.7 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = -4 °C
Q̇ = W
6.Hard
Brick, k = 0.72100 mmMineral wool, k = 0.0425 mmroom 20 °Coutside -8 °CQ̇ = ?

A wall of 100 mm brick and 25 mm mineral wool separates a room at 20 °C from outside air at -8 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -8 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 680 W
  2. 2. q″ = 26.35 W/m²
  3. 3. Ti = 23.35 °C
  4. 4. Q̇ = 38.24 W
  5. 5. Q̇ = 40.03 W
  6. 6. Q̇ = 120.8 W

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