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 = 0.04250 mm24 °C1 °Cq″ = ?

A wall of mineral wool is 250 mm thick and has an area of 10 m². Its faces are held at 24 °C and 1 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 250 mmA = 10 m²T1 = 24 °CT2 = 1 °C
q″ = W/m²
2.Easy
Expanded polystyrene, k = 0.03510 mm24 °C0 °CQ̇ = ?

A wall of expanded polystyrene is 10 mm thick and has an area of 20 m². Its faces are held at 24 °C and 0 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 10 mmA = 20 m²T1 = 24 °CT2 = 0 °C
Q̇ = W
3.Medium
Wood, k = 0.17100 mmMineral wool, k = 0.04150 mm15 °C3 °CQ̇ = ?

A wall is made of 100 mm of wood and 150 mm of mineral wool, with an area of 6 m². The outer faces are at 15 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 6 m²T1 = 15 °CT3 = 3 °C
Q̇ = W
4.Medium
Concrete, k = 1.4150 mmWood, k = 0.1750 mm23 °C10 °CTi​ = ?Q̇

A wall is made of 150 mm of concrete and 50 mm of wood, with an area of 6 m². The outer faces are at 23 °C and 10 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 23 °CT3 = 10 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17150 mmConcrete, k = 1.4150 mmroom 20 °Coutside -8 °CTs​ = ?Q̇

A wall of 150 mm gypsum board and 150 mm concrete separates a room at 20 °C from outside air at -8 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -8 °C
Ts = °C
6.Hard
Brick, k = 0.72250 mmExpanded polystyrene, k = 0.03525 mmroom 22 °Coutside -15 °CTs​ = ?Q̇

A wall of 250 mm brick and 25 mm expanded polystyrene separates a room at 22 °C from outside air at -15 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 8 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 8 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = -15 °C
Ts = °C

Answer key

  1. 1. q″ = 3.68 W/m²
  2. 2. Q̇ = 1680 W
  3. 3. Q̇ = 16.6 W
  4. 4. Ti = 19.53 °C
  5. 5. Ts = 17.51 °C
  6. 6. Ts = 18.9 °C

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