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
Wood, k = 0.17250 mm18 °C-10 °Cq″ = ?

A wall of wood is 250 mm thick and has an area of 15 m². Its faces are held at 18 °C and -10 °C. Find the heat flux q″ through the wall.

k = 0.17 W/(m·K)L = 250 mmA = 15 m²T1 = 18 °CT2 = -10 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.035250 mm16 °C1 °CQ̇ = ?

A wall of expanded polystyrene is 250 mm thick and has an area of 4 m². Its faces are held at 16 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 250 mmA = 4 m²T1 = 16 °CT2 = 1 °C
Q̇ = W
3.Medium
Glass, k = 0.96250 mmGypsum board, k = 0.17100 mm22 °C-12 °CQ̇ = ?

A wall is made of 250 mm of glass and 100 mm of gypsum board, with an area of 20 m². The outer faces are at 22 °C and -12 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 20 m²T1 = 22 °CT3 = -12 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.04200 mmBrick, k = 0.7250 mm18 °C-3 °CTi​ = ?Q̇

A wall is made of 200 mm of mineral wool and 50 mm of brick, with an area of 15 m². The outer faces are at 18 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 200 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.72 W/(m·K)A = 15 m²T1 = 18 °CT3 = -3 °C
Ti = °C
5.Hard
Brick, k = 0.7250 mmMineral wool, k = 0.04100 mmroom 21 °Coutside -12 °CQ̇

A wall of 50 mm brick and 100 mm mineral wool separates a room at 21 °C from outside air at -12 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 0.04 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 21 °CTout = -12 °C
U = W/(m²·K)
6.Hard
Glass, k = 0.9650 mmBrick, k = 0.72100 mmroom 21 °Coutside -7 °CQ̇ = ?

A wall of 50 mm glass and 100 mm brick separates a room at 21 °C from outside air at -7 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 15 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.72 W/(m·K)A = 15 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -7 °C
Q̇ = W

Answer key

  1. 1. q″ = 19.04 W/m²
  2. 2. Q̇ = 8.4 W
  3. 3. Q̇ = 801.3 W
  4. 4. Ti = −2.712 °C
  5. 5. U = 0.3589 W/(m²·K)
  6. 6. Q̇ = 1180 W

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