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 = 0.72200 mm25 °C-4 °Cq″ = ?

A wall of brick is 200 mm thick and has an area of 6 m². Its faces are held at 25 °C and -4 °C. Find the heat flux q″ through the wall.

k = 0.72 W/(m·K)L = 200 mmA = 6 m²T1 = 25 °CT2 = -4 °C
q″ = W/m²
2.Easy
Concrete, k = 1.4250 mm20 °C-9 °CQ̇ = ?

A wall of concrete is 250 mm thick and has an area of 4 m². Its faces are held at 20 °C and -9 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 250 mmA = 4 m²T1 = 20 °CT2 = -9 °C
Q̇ = W
3.Medium
Wood, k = 0.17150 mmExpanded polystyrene, k = 0.035150 mm22 °C8 °CTi​ = ?Q̇

A wall is made of 150 mm of wood and 150 mm of expanded polystyrene, with an area of 6 m². The outer faces are at 22 °C and 8 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 150 mm, k2 = 0.035 W/(m·K)A = 6 m²T1 = 22 °CT3 = 8 °C
Ti = °C
4.Medium
Wood, k = 0.1750 mmMineral wool, k = 0.0450 mm16 °C6 °CTi​ = ?Q̇

A wall is made of 50 mm of wood and 50 mm of mineral wool, with an area of 12 m². The outer faces are at 16 °C and 6 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.17 W/(m·K)L2 = 50 mm, k2 = 0.04 W/(m·K)A = 12 m²T1 = 16 °CT3 = 6 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17100 mmBrick, k = 0.7275 mmroom 20 °Coutside -15 °CTs​ = ?Q̇

A wall of 100 mm gypsum board and 75 mm brick separates a room at 20 °C from outside air at -15 °C. The convection coefficients are 6 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 15 m². Find the temperature Ts of the inside surface of the wall.

L1 = 100 mm, k1 = 0.17 W/(m·K)L2 = 75 mm, k2 = 0.72 W/(m·K)A = 15 m²hi = 6 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -15 °C
Ts = °C
6.Hard
Expanded polystyrene, k = 0.035200 mmGypsum board, k = 0.1750 mmroom 20 °Coutside -13 °CQ̇ = ?

A wall of 200 mm expanded polystyrene and 50 mm gypsum board separates a room at 20 °C from outside air at -13 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 10 m². Find the heat loss Q̇ through the wall.

L1 = 200 mm, k1 = 0.035 W/(m·K)L2 = 50 mm, k2 = 0.17 W/(m·K)A = 10 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 20 °CTout = -13 °C
Q̇ = W

Answer key

  1. 1. q″ = 104.4 W/m²
  2. 2. Q̇ = 649.6 W
  3. 3. Ti = 19.61 °C
  4. 4. Ti = 14.1 °C
  5. 5. Ts = 13.46 °C
  6. 6. Q̇ = 53.73 W

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