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 = 0.03520 mm17 °C-8 °Cq″ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 8 m². Its faces are held at 17 °C and -8 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 8 m²T1 = 17 °CT2 = -8 °C
q″ = W/m²
2.Easy
Concrete, k = 1.4200 mm24 °C-1 °CQ̇ = ?

A wall of concrete is 200 mm thick and has an area of 10 m². Its faces are held at 24 °C and -1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 200 mmA = 10 m²T1 = 24 °CT2 = -1 °C
Q̇ = W
3.Medium
Glass, k = 0.96150 mmWood, k = 0.1750 mm20 °C-6 °CQ̇ = ?

A wall is made of 150 mm of glass and 50 mm of wood, with an area of 8 m². The outer faces are at 20 °C and -6 °C. Find the heat flow Q̇ through the wall.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 20 °CT3 = -6 °C
Q̇ = W
4.Medium
Gypsum board, k = 0.17250 mmWood, k = 0.17100 mm24 °C-7 °CQ̇ = ?

A wall is made of 250 mm of gypsum board and 100 mm of wood, with an area of 8 m². The outer faces are at 24 °C and -7 °C. Find the heat flow Q̇ through the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 24 °CT3 = -7 °C
Q̇ = W
5.Hard
Wood, k = 0.17150 mmExpanded polystyrene, k = 0.035100 mmroom 22 °Coutside -7 °CTs​ = ?Q̇

A wall of 150 mm wood and 100 mm expanded polystyrene separates a room at 22 °C from outside air at -7 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 4 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 100 mm, k2 = 0.035 W/(m·K)A = 4 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -7 °C
Ts = °C
6.Hard
Mineral wool, k = 0.04150 mmExpanded polystyrene, k = 0.03525 mmroom 20 °Coutside -13 °CQ̇

A wall of 150 mm mineral wool and 25 mm expanded polystyrene separates a room at 20 °C from outside air at -13 °C. The convection coefficients are 8 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 150 mm, k1 = 0.04 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 8 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -13 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 43.75 W/m²
  2. 2. Q̇ = 1750 W
  3. 3. Q̇ = 461.8 W
  4. 4. Q̇ = 120.5 W
  5. 5. Ts = 21.25 °C
  6. 6. U = 0.2156 W/(m²·K)

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