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
Gypsum board, k = 0.1710 mm25 °C1 °CQ̇ = ?

A wall of gypsum board is 10 mm thick and has an area of 8 m². Its faces are held at 25 °C and 1 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.17 W/(m·K)L = 10 mmA = 8 m²T1 = 25 °CT2 = 1 °C
Q̇ = W
2.Easy
Concrete, k = 1.4100 mm15 °C9 °Cq″ = ?

A wall of concrete is 100 mm thick and has an area of 6 m². Its faces are held at 15 °C and 9 °C. Find the heat flux q″ through the wall.

k = 1.4 W/(m·K)L = 100 mmA = 6 m²T1 = 15 °CT2 = 9 °C
q″ = W/m²
3.Medium
Glass, k = 0.96250 mmBrick, k = 0.72150 mm15 °C-3 °CTi​ = ?Q̇

A wall is made of 250 mm of glass and 150 mm of brick, with an area of 8 m². The outer faces are at 15 °C and -3 °C. Find the temperature Ti at the interface between the two layers.

L1 = 250 mm, k1 = 0.96 W/(m·K)L2 = 150 mm, k2 = 0.72 W/(m·K)A = 8 m²T1 = 15 °CT3 = -3 °C
Ti = °C
4.Medium
Brick, k = 0.7250 mmConcrete, k = 1.4100 mm23 °C-1 °CTi​ = ?Q̇

A wall is made of 50 mm of brick and 100 mm of concrete, with an area of 10 m². The outer faces are at 23 °C and -1 °C. Find the temperature Ti at the interface between the two layers.

L1 = 50 mm, k1 = 0.72 W/(m·K)L2 = 100 mm, k2 = 1.4 W/(m·K)A = 10 m²T1 = 23 °CT3 = -1 °C
Ti = °C
5.Hard
Gypsum board, k = 0.17150 mmGlass, k = 0.9650 mmroom 20 °Coutside -10 °CTs​ = ?Q̇

A wall of 150 mm gypsum board and 50 mm glass separates a room at 20 °C from outside air at -10 °C. The convection coefficients are 6 W/(m²·K) inside and 20 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 = 50 mm, k2 = 0.96 W/(m·K)A = 10 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 20 °CTout = -10 °C
Ts = °C
6.Hard
Brick, k = 0.72100 mmExpanded polystyrene, k = 0.03525 mmroom 20 °Coutside 5 °CQ̇

A wall of 100 mm brick and 25 mm expanded polystyrene separates a room at 20 °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 12 m². Find the overall heat transfer coefficient U of the wall.

L1 = 100 mm, k1 = 0.72 W/(m·K)L2 = 25 mm, k2 = 0.035 W/(m·K)A = 12 m²hi = 10 W/(m²·K)ho = 25 W/(m²·K)Troom = 20 °CTout = 5 °C
U = W/(m²·K)

Answer key

  1. 1. Q̇ = 3264 W
  2. 2. q″ = 84 W/m²
  3. 3. Ti = 5 °C
  4. 4. Ti = 11.17 °C
  5. 5. Ts = 15.66 °C
  6. 6. U = 1.007 W/(m²·K)

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