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
Concrete, k = 1.4200 mm25 °C-11 °Cq″ = ?

A wall of concrete is 200 mm thick and has an area of 10 m². Its faces are held at 25 °C and -11 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 200 mmA = 10 m²T1 = 25 °CT2 = -11 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03520 mm18 °C5 °CQ̇ = ?

A wall of expanded polystyrene is 20 mm thick and has an area of 4 m². Its faces are held at 18 °C and 5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 20 mmA = 4 m²T1 = 18 °CT2 = 5 °C
Q̇ = W
3.Medium
Glass, k = 0.9650 mmWood, k = 0.17100 mm22 °C0 °CTi​ = ?Q̇

A wall is made of 50 mm of glass and 100 mm of wood, with an area of 8 m². The outer faces are at 22 °C and 0 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.96 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 22 °CT3 = 0 °C
Ti = °C
4.Medium
Concrete, k = 1.4100 mmMineral wool, k = 0.0450 mm19 °C-13 °CTi​ = ?Q̇

A wall is made of 100 mm of concrete and 50 mm of mineral wool, with an area of 10 m². The outer faces are at 19 °C and -13 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 10 m²T1 = 19 °CT3 = -13 °C
Ti = °C
5.Hard
Glass, k = 0.96250 mmConcrete, k = 1.450 mmroom 22 °Coutside -7 °CTs​ = ?Q̇

A wall of 250 mm glass and 50 mm concrete separates a room at 22 °C from outside air at -7 °C. The convection coefficients are 10 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 20 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 50 mm, k2 = 1.4 W/(m·K)A = 20 m²hi = 10 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -7 °C
Ts = °C
6.Hard
Gypsum board, k = 0.17250 mmExpanded polystyrene, k = 0.035150 mmroom 20 °Coutside 2 °CQ̇

A wall of 250 mm gypsum board and 150 mm expanded polystyrene separates a room at 20 °C from outside air at 2 °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 overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = 2 °C
U = W/(m²·K)

Answer key

  1. 1. q″ = 252 W/m²
  2. 2. Q̇ = 91 W
  3. 3. Ti = 20.21 °C
  4. 4. Ti = 17.27 °C
  5. 5. Ts = 15.5 °C
  6. 6. U = 0.1698 W/(m²·K)

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