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 = 0.035200 mm17 °C-6 °CQ̇ = ?

A wall of expanded polystyrene is 200 mm thick and has an area of 20 m². Its faces are held at 17 °C and -6 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.035 W/(m·K)L = 200 mmA = 20 m²T1 = 17 °CT2 = -6 °C
Q̇ = W
2.Easy
Mineral wool, k = 0.0420 mm25 °C-1 °Cq″ = ?

A wall of mineral wool is 20 mm thick and has an area of 10 m². Its faces are held at 25 °C and -1 °C. Find the heat flux q″ through the wall.

k = 0.04 W/(m·K)L = 20 mmA = 10 m²T1 = 25 °CT2 = -1 °C
q″ = W/m²
3.Medium
Brick, k = 0.7250 mmConcrete, k = 1.475 mm15 °C5 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 75 mm of concrete, with an area of 12 m². The outer faces are at 15 °C and 5 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 75 mm, k2 = 1.4 W/(m·K)A = 12 m²T1 = 15 °CT3 = 5 °C
Ti = °C
4.Medium
Concrete, k = 1.4150 mmExpanded polystyrene, k = 0.03525 mm22 °C2 °CTi​ = ?Q̇

A wall is made of 150 mm of concrete and 25 mm of expanded polystyrene, with an area of 6 m². The outer faces are at 22 °C and 2 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 1.4 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 6 m²T1 = 22 °CT3 = 2 °C
Ti = °C
5.Hard
Concrete, k = 1.450 mmGypsum board, k = 0.17100 mmroom 20 °Coutside -13 °CQ̇ = ?

A wall of 50 mm concrete and 100 mm gypsum board separates a room at 20 °C from outside air at -13 °C. The convection coefficients are 8 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 50 mm, k1 = 1.4 W/(m·K)L2 = 100 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 8 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = -13 °C
Q̇ = W
6.Hard
Gypsum board, k = 0.17150 mmWood, k = 0.17150 mmroom 21 °Coutside -3 °CTs​ = ?Q̇

A wall of 150 mm gypsum board and 150 mm wood separates a room at 21 °C from outside air at -3 °C. The convection coefficients are 10 W/(m²·K) inside and 25 W/(m²·K) outside, and the wall area is 10 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 = 0.17 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 21 °CTout = -3 °C
Ts = °C

Answer key

  1. 1. Q̇ = 80.5 W
  2. 2. q″ = 52 W/m²
  3. 3. Ti = 9.355 °C
  4. 4. Ti = 19.39 °C
  5. 5. Q̇ = 418.3 W
  6. 6. Ts = 19.74 °C

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