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
Brick, k = 0.72150 mm15 °C2 °CQ̇ = ?

A wall of brick is 150 mm thick and has an area of 15 m². Its faces are held at 15 °C and 2 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.72 W/(m·K)L = 150 mmA = 15 m²T1 = 15 °CT2 = 2 °C
Q̇ = W
2.Easy
Expanded polystyrene, k = 0.03550 mm22 °C1 °Cq″ = ?

A wall of expanded polystyrene is 50 mm thick and has an area of 8 m². Its faces are held at 22 °C and 1 °C. Find the heat flux q″ through the wall.

k = 0.035 W/(m·K)L = 50 mmA = 8 m²T1 = 22 °CT2 = 1 °C
q″ = W/m²
3.Medium
Concrete, k = 1.4200 mmBrick, k = 0.72150 mm22 °C3 °CQ̇ = ?

A wall is made of 200 mm of concrete and 150 mm of brick, with an area of 12 m². The outer faces are at 22 °C and 3 °C. Find the heat flow Q̇ through the wall.

L1 = 200 mm, k1 = 1.4 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 12 m²T1 = 22 °CT3 = 3 °C
Q̇ = W
4.Medium
Mineral wool, k = 0.04100 mmGlass, k = 0.9650 mm22 °C-12 °CTi​ = ?Q̇

A wall is made of 100 mm of mineral wool and 50 mm of glass, with an area of 15 m². The outer faces are at 22 °C and -12 °C. Find the temperature Ti at the interface between the two layers.

L1 = 100 mm, k1 = 0.04 W/(m·K)L2 = 50 mm, k2 = 0.96 W/(m·K)A = 15 m²T1 = 22 °CT3 = -12 °C
Ti = °C
5.Hard
Brick, k = 0.72250 mmConcrete, k = 1.4150 mmroom 22 °Coutside 5 °CTs​ = ?Q̇

A wall of 250 mm brick and 150 mm concrete separates a room at 22 °C from outside air at 5 °C. The convection coefficients are 10 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 = 0.72 W/(m·K)L2 = 150 mm, k2 = 1.4 W/(m·K)A = 6 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 22 °CTout = 5 °C
Ts = °C
6.Hard
Expanded polystyrene, k = 0.035150 mmGypsum board, k = 0.17100 mmroom 20 °Coutside -15 °CTs​ = ?Q̇

A wall of 150 mm expanded polystyrene and 100 mm gypsum board separates a room at 20 °C from outside air at -15 °C. The convection coefficients are 7.7 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 150 mm, k1 = 0.035 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 15 m²hi = 7.7 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -15 °C
Ts = °C

Answer key

  1. 1. Q̇ = 936 W
  2. 2. q″ = 14.7 W/m²
  3. 3. Q̇ = 649.2 W
  4. 4. Ti = −11.31 °C
  5. 5. Ts = 19.14 °C
  6. 6. Ts = 19.1 °C

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