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 = 0.04100 mm18 °C-2 °Cq″ = ?

A wall of mineral wool is 100 mm thick and has an area of 4 m². Its faces are held at 18 °C and -2 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 100 mmA = 4 m²T1 = 18 °CT2 = -2 °C
q″ = W/m²
2.Easy
Brick, k = 0.7210 mm18 °C3 °Cq″ = ?

A wall of brick is 10 mm thick and has an area of 8 m². Its faces are held at 18 °C and 3 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 10 mmA = 8 m²T1 = 18 °CT2 = 3 °C
q″ = W/m²
3.Medium
Expanded polystyrene, k = 0.035100 mmWood, k = 0.1750 mm25 °C-7 °CTi​ = ?Q̇

A wall is made of 100 mm of expanded polystyrene and 50 mm of wood, with an area of 8 m². The outer faces are at 25 °C and -7 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 8 m²T1 = 25 °CT3 = -7 °C
Ti = °C
4.Medium
Expanded polystyrene, k = 0.035250 mmConcrete, k = 1.475 mm25 °C-6 °CTi​ = ?Q̇

A wall is made of 250 mm of expanded polystyrene and 75 mm of concrete, with an area of 12 m². The outer faces are at 25 °C and -6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 12 m²T1 = 25 °CT3 = -6 °C
Ti = °C
5.Hard
Expanded polystyrene, k = 0.035250 mmMineral wool, k = 0.04150 mmroom 21 °Coutside -4 °CTs​ = ?Q̇

A wall of 250 mm expanded polystyrene and 150 mm mineral wool separates a room at 21 °C from outside air at -4 °C. The convection coefficients are 7.7 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.04 W/(m·K)A = 10 m²hi = 7.7 W/(m²·K)ho = 30 W/(m²·K)Troom = 21 °CTout = -4 °C
Ts = °C
6.Hard
Expanded polystyrene, k = 0.035250 mmConcrete, k = 1.425 mmroom 20 °Coutside 4 °CTs​ = ?Q̇

A wall of 250 mm expanded polystyrene and 25 mm concrete separates a room at 20 °C from outside air at 4 °C. The convection coefficients are 6 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 6 m². Find the temperature Ts of the inside surface of the wall.

L1 = 250 mm, k1 = 0.035 W/(m·K)L2 = 25 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 6 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = 4 °C
Ts = °C

Answer key

  1. 1. q″ = 8 W/m²
  2. 2. q″ = 1080 W/m²
  3. 3. Ti = −4.013 °C
  4. 4. Ti = −5.769 °C
  5. 5. Ts = 20.71 °C
  6. 6. Ts = 19.64 °C

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